9.1: Introducing Ratios and Ratio Language
Lesson
Let's describe two quantities at the same time.
Exercise \(\PageIndex{1}\): What Kind and How Many?
Think of different ways you could sort these figures. What categories could you use? How many groups would you have?
Exercise \(\PageIndex{2}\): The Teacher's Collection
- Think of a way to sort your teacher’s collection into two or three categories. Count the items in each category, and record the information in the table.
| category name | |||
|---|---|---|---|
| category amount |
Pause here so your teacher can review your work.
-
Write at least two sentences that describe
ratios
in the collection. Remember, there are many ways to write a ratio:
- The ratio of one category to another category is ________ to ________.
- The ratio of one category to another category is ________ : ________.
- There are _______ of one category for every _______ of another category .
Exercise \(\PageIndex{3}\): The Student's Collection
- Sort your collection into three categories. You can experiment with different ways of arranging these categories. Then, count the items in each category, and record the information in the table.
| category name | |||
|---|---|---|---|
| category amount |
-
Write at least two sentences that describe
ratios
in the collection. Remember, there are many ways to write a ratio:
- The ratio of one category to another category is ________ to ________.
- The ratio of one category to another category is ________ : ________.
-
There are _______ of
one category
for every _______ of
another category
.
Pause here so your teacher can review your sentences.
- Make a visual display of your items that clearly shows one of your statements. Be prepared to share your display with the class.
Are you ready for more?
- Use two colors to shade the rectangle so there are 2 square units of one color for every 1 square unit of the other color.
- The rectangle you just colored has an area of 24 square units. Draw a different shape that does not have an area of 24 square units, but that can also be shaded with two colors in a \(2:1\) ratio. Shade your new shape using two colors.
Summary
A ratio is an association between two or more quantities. There are many ways to describe a situation in terms of ratios. For example, look at this collection:
Here are some correct ways to describe the collection:
- The ratio of squares to circles is \(6:3\).
- The ratio of circles to squares is 3 to 6.
Notice that the shapes can be arranged in equal groups, which allow us to describe the shapes using other numbers.
- There are 2 squares for every 1 circle.
- There is 1 circle for every 2 squares.
Glossary Entries
Definition: Ratio
A ratio is an association between two or more quantities.
For example, the ratio \(3:2\) could describe a recipe that uses 3 cups of flour for every 2 eggs, or a boat that moves 3 meters every 2 seconds. One way to represent the ratio \(3:2\) is with a diagram that has 3 blue squares for every 2 green squares.
Practice
Exercise \(\PageIndex{4}\)
In a fruit basket there are 9 bananas, 4 apples, and 3 plums.
- The ratio of bananas to apples is ________ : ________.
- The ratio of plums to apples is ________ to ________.
- For every ________ apples, there are ________ plums.
- For every 3 bananas there is one ________.
Exercise \(\PageIndex{5}\)
Complete the sentences to describe this picture.
- The ratio of dogs to cats is ________.
- For every ________ dogs, there are ________ cats.
Exercise \(\PageIndex{6}\)
Write two different sentences that use ratios to describe the number of eyes and legs in this picture.
Exercise \(\PageIndex{7}\)
Choose an appropriate unit of measurement for each quantity.
- area of a rectangle
- volume of a prism
- side of a square
- area of a square
- volume of a cube
- cm
- cm 3
- cm 2
(From Unit 1.6.1)
Exercise \(\PageIndex{8}\)
Find the volume and surface area of each prism.
- Prism A: 3 cm by 3 cm by 3 cm
- Prism B: 5 cm by 5 cm by 1 cm
- Compare the volumes of the prisms and then their surface areas. Does the prism with the greater volume also have the greater surface area?
(From Unit 1.5.5)
Exercise \(\PageIndex{9}\)
Which figure is a triangular prism? Select all that apply.
- A
- B
- C
- D
- E
(From Unit 1.5.2)


11.3: Causality and the Time-Domain Green's Function
Let us try converting Eq. (11.2.13) into a time-domain Green’s function by using the inverse Fourier transform: \[\begin{align} G(x,x';t-t') &= \int_{-\infty}^\infty \frac{d\omega}{2\pi} \, e^{-i\omega (t-t')} \, G(x,x'; \omega) \\ \nonumber &= \int_{-\infty}^\infty d\omega \, \frac{e^{i\omega \left[|x-x'| - (t-t')\right]}}{4\pi i\omega}\qquad (?!?) \nonumber\end{align}\] There is a problem on the last line: the integral runs over the real- \(\omega\) line, yet the integrand has a pole at \(\omega = 0\) , on the real axis, making the integral ill-defined.
To resolve this, we redefine \(G(x,x';\omega)\) as an integral over a deformed contour \(\Gamma\) : \[G(x,x';t-t') \equiv \int_\Gamma d\omega \, \frac{e^{i\omega \left[|x-x'| - (t-t')\right]}}{4\pi i\omega}.\] We will choose the deformed contour in a very specific way, which turns out to be the choice that satisfies causality. As shown in the left subplot of the figure below, it runs along the real axis, but skips above the pole at the origin.
The integral can be solved by either closing the contour in the upper half-plane, or in the lower half-plane. If we close the contour above, then the loop contour does not enclose the pole, and hence \(G(x,x';t-t') = 0\) . According to Jordan’s lemma, we must do this if the exponent in the integrand obeys \[|x-x'| - (t-t') > 0 \quad \Rightarrow \quad |x-x'| > t-t'.\] This inequality is satisfied in two cases: either (i) \(t < t'\) (in which case the inequality is satisfied for all \(x,x'\) because \(|x-x'|\) is strictly non-negative), or (ii) \(t > t'\) but the value of \(t-t'\) is smaller than \(|x-x'|\) . To understand the physical meaning of these two cases, recall that \(G(x,x';t-t')\) represents the field at position \(x\) and time \(t\) resulting from a pulse at the space-time point \((x',t')\) . Thus, case (i) corresponds to times occurring before the pulse, and case (ii) corresponds to times occurring after the pulse but too far away from the pulse location for a wave to reach in time.
For the other case, \(|x-x'| - (t-t') < 0\) , the residue theorem gives \[G(x,x';t-t') = -1/2.\] The space-time diagram below summarizes the above results:
The resulting time-domain wavefunctions can be written as \[\psi(x,t) = \int_{-\infty}^\infty dx' \int_{-\infty}^\infty dt' \left[-\frac{1}{2}\,\Theta(t-t' - |x-x'|)\right] f(x',t'),\] where \(\Theta\) denotes the unit step function. In other words, the wavefunction at each space-time point \((x,t)\) receives equal contribution from the sources \(f(x',t')\) at space-time points \((x',t')\) lying within the “past light cone”.


16.5: Summary
The topics covered in this chapter can be summarized as follows:
| Section | Summary |
|---|---|
| 16.1 Glacial Periods in Earth’s History | There have been many glaciations in Earth’s distant past, the oldest known starting around 2,400 Ma. The late Proterozoic “Snowball Earth” glaciations were thought to be sufficiently intense to affect the entire planet. The current glacial period is known as the Pleistocene Glaciation, and while it was much more intense 20,000 years ago than it is now, we are still in the middle of it. The periodicity of the Pleistocene glaciations is related to subtle changes in Earth’s orbital characteristics, which are exaggerated by a variety of positive feedback processes. |
| 16.2 How Glaciers Work | The two main types of glaciers are continental glaciers, which cover large parts of continents, and alpine glaciers, which occupy mountainous regions. Ice accumulates at higher elevations—above the equilibrium line—where the snow that falls in winter does not all melt in summer. In continental glaciers, ice flows outward from where it is thickest. In alpine glaciers, ice flows downslope. At depth in the glacier ice, flow is by internal deformation, but glaciers that have liquid water at their base can also flow by basal sliding. Crevasses form in the rigid surface ice in places where the lower plastic ice is changing shape. |
| 16.3 Glacial Erosion | Glaciers are important agents of erosion. Continental glaciers tend to erode the land surface into flat plains, while alpine glaciers create a wide variety of different forms. The key feature of alpine glacial erosion is the U-shaped valley. Arêtes are sharp ridges that form between two valleys, and horns form where a mountain is glacially eroded on at least three sides. Because tributary glaciers do not erode as deeply as main-valley glaciers, hanging valleys exist where the two meet. On a smaller scale, both types of glaciers form drumlins, roches moutonées, and glacial grooves or striae. |
| 16.4 Glacial Deposition | Glacial deposits are quite varied, as materials are transported and deposited in a variety of different ways in a glacial environment. Sediments that are moved and deposited directly by ice are known as till. Glaciofluvial sediments are deposited by glacial streams, either forming eskers or large proglacial plains known as sandurs. Glaciolacustrine and glaciomarine sediments originate within glaciers and are deposited in lakes and the ocean respectively. |
See Appendix 2 for answers to Review Questions.
- Why are the Cryogenian glaciations called Snowball Earth?
- Earth cooled dramatically from the end of the Paleocene until the Holocene. Describe some of the geological events that contributed to that cooling.
- When and where was the first glaciation of the Cenozoic?
- Describe the extent of the Laurentide Ice Sheet during the height of the last Pleistocene glacial period.
- In an alpine glacier, the ice flows down the slope of the underlying valley. Continental glaciers do not have a sloped surface to flow down. What feature of a continental glacier facilitates its flow?
- What does the equilibrium line represent in a glacier? Explain.
- Which of the following is more important to the growth of a glacier: very cold winters or relatively cool summers? Explain.
- Describe the relative rates of ice flow within the following parts of a glacier: (a) the bottom versus the top and (b) the edges versus the middle. Explain.
- What condition is necessary for basal sliding to take place?
- Why do glaciers carve U-shaped valleys, and how does a hanging valley form?
- A horn is typically surrounded by cirques. What is the minimum number of cirques you would expect to find around a horn?
- A drumlin and a roche moutonée are both streamlined glacial erosion features. How do they differ in shape?
- Four examples of glacial sediments are shown here. Describe the important characteristics (e.g., sorting, layering, grain-size range, grain shape, sedimentary structures) of each one and give each a name (choose from glaciofluvial, glaciolacustrine, lodgement till, ablation till, and glaciomarine).
- What are drop stones, and under what circumstances are they likely to form?
- What types of glacial sediments are likely to be sufficiently permeable to make good aquifers?
Media Attributions
- Figure A: © Steven Earle. CC BY.


11.2: What are teachers' rights and responsibilities?
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By Hillary Childress
Note
" A good teacher is like a candle-it consumes itself to light the way for others" http://www.indianchild.com/teachers_quotes.htm
Learning Objectives
- Students should be able to detect signs of Child abuse and child neglect in a classroom.
- Students will know the proper procedure of reporting suspicions of child abuse or nelgect.
- Students will know the 3 types of Child abuse and the statistics on all 3.
Introduction
To a student a teacher can be seen as someone they can tell their deepest darkest secrets too. So what happens when a student tells a teacher some information that might suggest child abuse or neglect? Teachers need to know how to handle child abuse suspicions on the legal and ethical level and how to recognize it. Definitions The lines between child abuse and child neglect can get a little hazy sometimes. The Child Welfare Information Gateway has defined child abuse as “ Any recent act or failure to act on the part of a parent or caretaker which results in death, serious physical or emotional harm, sexual abuse or exploitation; or an act or failure to act which presents an imminent risk or serious harm” ( Child Welfare Information Gateway,2008) There are 3 different types of Child abuse; physical, emotional, and sexual abuse. The Child Welfare Information Gateway also defines the three types of abuse
- Physical-“is non- accidental physical injury as a result of punching, beating, kicking, biting, shaking, throwing, stabbing, choking, hitting, burning, or otherwise harming the child.”(Child Welfare Information Gateway, 2008)
- Emotional- “pattern of behavior that impairs a child’s development of sense of self-worth” (Child Welfare Information Gateway,2008)
- Sexual-“activities by a parent or caregiver such as fondling a child’s genitals, penetration, incest, rape, sodomy, indecent exposure, and exploitation through prostitution or production of pornographic material”( Child Welfare Information Gateway, 2008)
Child abuse can bee seen as causing immediate harm to the child. While child neglect might not cause immediate harm to the child, overtime child neglect can cause physical and developmental harm. Child Neglect it defined as Child Neglect- “the failure of a parent, guardian or other caregiver to provide for a child’s basic needs.” (Child Welfare Information Gateway,2008) Those needs can be put into four catergories physical,medical,educational, and emotional.
Statistics
A teacher needs to know the statistics of child abuse and neglect, once they know the numbers they will see how dyer the situation is and how important it is to know how to respond to child abuse and neglect.The National Child Abuse and Neglect Data System is a federal organization that collects data and statistics on child abuse and neglect every year (U.S. Department of Health and Human Services, 2008). In the year 2006 there was an estimated 3.3 million cases and of those cases over half of them were reported by professionals, such as teachers (U.S Department of Health and Human Services, 2008) in the year 2006 the data showed
- 905,000 victims of Child abuse or neglect
- 51.5% were girls an 48.2% were boys
- 48.8% were white,22.8% were African-America, and 18.4 were Hispanic
The data that was collected also showed the child neglect was more common than child abuse, in years past the NCANDs reported that child abuse was more prevalent that child neglect. In 2006 the data showed
- 64.1% were victims of neglect
- 16% were victims of physical abuse
- 8.8% were victims of sexual abuse
- 6.6% were victims of emotional abuse
Detecting Child Abuse or Neglect
As teachers we spend and average of 7 hours, 5 days a week with our students. So besides their parents, we are the people that the children spend most of their time with, this allows us to create a relationship of trust with our students.The relationship that is created is one that is so strong that a teacher will do anything to protect their students.So by knowing how to detect abuse and neglect teachers are better prepared to protect their students. We also get to know our students behavioral patterns, and if it changes occur. A dramatic change can in behavior can be a warning sign of child abuse or neglect (Coleman). According to Dr. Coleman, a child psychologist some other warning signs of child abuse or neglect both physical and emotional. They are as follows(Coleman).
- Bruises, lumps, welts
- Repeated broken bones
- Burns
- Shyness around adults
- Is often absent
- Frequent accidents-such as wetting their pants
- Lack of concentration
- Poor academic performance
- High aggression
- Early arrival to school and reluctance to leave
- Unsociable
When it comes to detecting the possibility of child neglect the warning signs can be a lot more apparent and can be easily seen by the outer appearance of the child. Some of the things to look for if a teacher suspects a child is being neglected are as follows (Duncan, 2001)
- Child appears to always be hungry
- Unorganized train of thought
- Child appears to suffer from medical and dental neglect
- Child comes to class in clothes that appear dirty and worn
Reporting Suspicions of Child Abuse or Neglect
When teachers suspect child abuse or neglect they sometimes hesitate to report it, this may be because of a fear that the parents of the child may retaliate against the child, or they feel that even if it is reported nothing will be done. As teachers those we are mandated to report any suspicions of child abuse or neglect. This is stated in the Child Abuse Prevention and Treatment Act(CAPTA) if a teacher fails to report any suspicions they can face disciplinary action up to and including termination and criminal liabilities(Smith, 2007). When a teacher suspects that a child is being abused in most school the teacher will file a report for the principal once the report is filled it is normally given to the guidance counselor who will be the one to contact the local depart of Child Protective Services(CPS)(Citizens Information). The website also states that if a child confides in a child that the teacher should record the conversations. The teacher also needs to have the child’s basic information such as; name , address, phone number, details about the suspected abuse, and information about the potential perpetrator(Duncan, 2001). The CPS will determine in the information is substantial enough for an investigation. The CPS will normally send the mandated reporter a letter, but a family’s right to privacy is still of importance. So a mandated reporter might know that the CPS investigated but may not know the findings or results of the investigation (Duncan, 2001).
Conclusion
So in conclusion teachers have not only a legal responsibility but an ethical responsibility to protect their students. Teachers should pay attention to students’ behavior and create strong relationships with their students. If this happens, I feel that we will see a huge drop in numbers of children dying from child abuse and neglect. Every child deserves a happy and safe childhood and as educators we can help ensure that they are happy and healthy.
Reference
Child Welfare Information Gateway.(2008).What is child abuse and neglect?.Retrieved February 7, 2009, From Child Welfare Inofrmation Gateway. Web site: www.childwelfare.gov/pubs/factsheets/whatiscan.cfm
Children’s Bureau.(2008).NCANDS Survey Instrument.Retri ved February 7, 2009, from Department of Health and Human Services. Web site: www.acf.hhs.gov/programs/cb/systems/ncands/survey.htm
Coleman, M. What should you do when you suspect child abuse. Retrived February 7, 2009, from Scholastic.com. Web site: content.scholastic.com/browse/aticle.jsp?id=4435
Duncan,N. When should teachers report abuse? Retrived February 7, 2009,from Children’s Voice Article.Web site: www.cwla.org/articles/cv0111teachers.htm
Smith,S.(2007). Mandatory reporting of child abuse and neglect. Retrived February 7, 2009, from Smith Law firm. Web site: www.smith-lawfirm.com/mandatory_reporting.htm
(2008).Reporting child abuse are primary and post primary leve. Retrived February 7, 2009, from Citizens Information.Web site: http://www.citizensinformation.ie/categories/education/primary-and-post-primary-education/attendance-and-discipline-in-schools/child_abuse
Quote Provided by: http://www.indianchild.com/teachers_quotes.htm


7.3: Improving Infrastructure Resiliency
Infrastructure resiliency is the capability to restore infrastructure to its original state after a disruption occurs. Improved resiliency can be achieved with planning for disruptions and having resources available to respond to disruptions. Figure 7.3.1 illustrates the various time periods. Prior to an incident or disaster, preparations can be made. At the time of an incident, the infrastructure performance degrades, especially as failures propagate through associated components. In extreme cases, the infrastructure performance may degrade to closure (so I would equal zero in Figure 7.3.1). A recovery period ensues until the infrastructure returns to normal performance.
Table 7.3.1 lists some strategies to improve resiliency along with technical, organizational, social and economic examples. The strategies are:
- Robustness may refer to facility design and construction but also includes good planning for emergencies and rehearsals.
- Redundancy includes strategies such as back-up power and lifeline resources such as food and water.
- Resourcefulness involves the resources that can be mobilized in response to an event.
- Rapidity is the speed at which restoration can occur.
Table 7.3.1: Technical, Organization, Social and Economic Dimensions of Infrastructure Resiliency. Source: O’Rourke, 2007. Redrawn and altered by Authors
| Strategy | Technical | Organizational | Social | Economic |
| Robustness | Appropriate building codes and construction procedures | Emergency operations planning and practice | Degree of community preparedness | Regional economic diversification for supply |
| Redundancy | Capacity for technical substitutions | Alternative sites for managing emergency operations | Availability of Housing options for disaster victims | Investment in backup systems |
| Resourcefulness | Availability of equipment and materials for response | Capacity to improvise and innovate | Capacity to address lifeline needs | Capacity to improvise |
| Rapidity | Restoration time | Reduced Reaction Time | Time to restore lifeline services | Time to regain capacity |
As an example of resiliency planning, consider an electricity utility. The utility can insure redundancy in transmission lines and power generation sources. Individual facilities can be design and built to withstand significant stresses. With major storms forecast, crews with equipment and supplies can be pre-positioned to respond to any outages rapidly. While the utility may still see disruptions, all of these activities will improve the resiliency of the utility.
Another example is planning for evacuation effectively. Figure 7.3.2 shows a 2005 evacuation of Houston due to forecast hurricane. During this evacuation, roadway lanes in to the city have been reversed to increase the available capacity. Unfortunately, the traffic volumes resulted in major traffic jams. Improved entry controls onto the highway could eliminate this type of jam.
Climate change and sea level rise are two factors that are increasing the importance of infrastructure resiliency. As average sea level increases, the likelihood of flooding increases. A variety of new strategies may be required, as with the response to Hurricane Sandy that flooded portions of the New York subway system.
Finally, the use of scenario analysis (as described in Chapter 6) may be useful for planning. A regular session to consider possible risks, preparedness, and documentation of procedures can be extremely useful.


24.1: Introduction
There are many groups of unrelated organisms that are referred to as ‘fungus’ or ‘mold’. Formerly, these groups were all believed to have been related, sharing the characteristics of being heterotrophic eukaryotes, generally with cell walls, usually decomposers or parasites, and often with the storage carbohydrate glycogen. These organisms were placed into groups ending with “-mycota”, meaning fungus. On closer inspection, we find that these groups differ on many important life history traits and very few of them actually belong to the true Fungi. However, if you take a mycology course, you will most likely study these unrelated organisms, as well. Similarly, fungi are still studied under the umbrella of botany as a relic of past classification, but they are more closely related to animals than they are to plants.
Fungus-Like Organisms
Myxogastria (formerly Myxomycota): Plasmodial Slime Molds
Myxomycetes (members of the Myxogastria) are fungus-like organisms called slime molds, but they are not members of Kingdom Fungi. In their feeding stage, myxomycetes form one large amoeba with many nuclei and no cell wall. This amoeba moves over damp, decaying material looking for bacteria to engulf and digest. When it dries out or runs out of food, it begins to make fruiting structures called sporangia (sporangium, singular). Inside these sporangia, the myxomycete will undergo meiosis, wall off individual nuclei and make haploid spores for aerial dispersal. Dispersal by spores, heterotrophism, and glycogen as a storage carbohydrate originally classified this group within Kingdom Fungi, but this is the end of the similarities. The spores have cell walls made of cellulose , like plants. When these spores land, they will germinate into haploid cells (called swarm cells) that will fuse together to form a diploid amoeba. This means that, unlike true Fungi, they have a diplontic life cycle.
Observe the slime molds on display. If possible, make a wet mount of a small sample. If there are motile cells (cells that are actively moving around), look for the presence of 2 flagella. This also distinguishes myxomycetes from Kingdom Fungi, where only one flagellum is present. If a mature amoeba is present, can you see cytoplasmic streaming occurring?
Draw what you see and make observations below. Label the name, function, and ploidy of any identifying structures.
Other Slime Molds: Dictyostelia and Protostelia
Quite on theme for fungal classification, there are several different groups of unrelated organisms that are called slime molds. The two mentioned above, Dictyostelia and Protostelia, represent cellular slime molds and are relatively closely related to the plasmodial slime molds. Unlike the plasmodial slime molds, these groups exist as individual amoebae until it is time to leave the area. In the Dictyostelia, the amoebae assemble together to form elaborate fruiting structures where only some of the individuals will become spores and the rest will die. They are studied for this altruistic behavior.
Oomycota -- The Water Molds
Oomycetes are also fungus-like organisms with cell walls made of cellulose . Similar to myxomycetes, they have motile spores with 2 flagella. However, one of these flagella is "normal"-looking (called a whiplash flagellum) and the other is ornamented. This strange characteristic puts organisms into a group called the heterokonts (meaning "different flagella"). Like us, true Fungi are part of the opisthokonts (opisth- meaning rear, -kont meaning flagellum).
Also similar to myxomycetes, oomycetes have a diplontic life cycle . What does this mean?
Kingdom Fungi - The True Fungi
Though many heterotrophic decomposers and parasites are fungus-like, an organism must be in Kingdom Fungi to be considered a true fungus. In addition to genetic relationships, organisms are classified into Kingdom Fungi based on the following traits:
- Eukaryotic
- Heterotrophic by absorption
- Morphology: Unicellular or a thallus composed of hyphae . If present, motile cells have only a single, whiplash flagellum (like us).
- Cell walls: Chitin
- Storage carbohydrate: Glycogen
- Life cycle: Haplontic (though this one gets a bit weird)
- Ecology: Many fungi are decomposers, primarily in terrestrial ecosystems. Other groups of fungi live in symbiosis with other organisms as parasites, mutualists, or commensalists.
Determining the ancestry and relatedness of groups of fungi is surprisingly difficult. DNA sequencing has led to continual rearrangements of the fungal tree of life and, at the time of writing, there is no one agreed upon picture of the history of fungi that the author is aware of. However, there are a few major groups that Kingdom Fungi is commonly broken into, and these will be discussed in the following section.
The image below is from an open-access publication (doi.org/10.1128/ mBio.01739-16) and presents one possible hypothesis for the relationships between groups of fungi. This hypothesis is called a phylogeny and is based on genetics, as well as physiological and morphological features. No single phylogeny is currently accepted by all mycologists.
Chytrids: includes Chytridiomycota and Blastocladiomycota from the above phylogeny
Chytrids comprise the oldest lineages of fungi. Unlike any other group within this kingdom, they are aquatic and have swimming spores (zoospores) with a single flagellum. Though many in this group are harmless decomposers, the most famous of the chytrids is Batrachochytrium dendrobatidis , a fungus that infects the skin of amphibians. This chytrid is contributing to a worldwide decline in many amphibian species (though there are numerous other contributing factors), particularly frogs.
If available view specimens of chytrids under the dissecting and compound microscopes. What features can you find?
Zygomycetes: includes all of the non-flagellated, early diverging fungi above, except Glomeromycotina
The zygomycetes are composed of at least two distinct lineages of fungi that all share a common structure during sexual reproduction, the zygosporangium . This is a large, ornamented, orange-to-brown structure where both fertilization and meiosis occur. Zygomycetes have no septations in their hyphae, which is referred to as being coenocytic . These fungi are commonly found on high-sugar substrates, such as rotting fruits or molding bread, or as insect parasites. Zygomycetes can reproduce asexually by producing mitosporangia (shown below), making haploid spores by mitosis.
Above are three mature zygosporangia produced during sexual reproduction of Rhizopus stolonifer . In the center of the image, two compatible mycelia (+ and -) have connected together and are currently forming gametangia. They will flood these gametangia with haploid nuclei, which will fuse within the zygosporangium to create diploid zygotes. Each of these will immediately undergo meiosis to produce haploid spores.
View specimens of zygomycetes available in lab and record your observations below. Which features would help you identify this group?
Glomeromycota: listed as Glomeromycotina in the fungal phylogeny
This single lineage within Kingdom Fungi forms relationships with the roots of almost all land plant species and thalli of the earliest plant lineages, who evolved before roots. This mycorrhizal (myco- meaning fungus, rhiza meaning root) relationship has existed for 400 million years and was likely involved in the movement of plants onto land. Glomeromycetes are called endomycorrhizal because the fungal hyphae enter inside of plant cells. The fungus enters the plant tissue, usually through the roots, and penetrates the cell walls of the cortex cells in the root. However, they hyphae do not go through the plasma membrane. Instead, they form highly branched, tree-like structures called arbuscles . This provides a large amount of surface area for the plant and fungus to interact with each other. How are they interacting?
These images are from an open access paper (doi: 10.1038/srep29733) studying fungal colonization of plant cells. In the image on the right, the fungal tissue was stained with a fluorescent dye. In the lower two (B and C), fungal hyphae were stained dark and are forming arbuscules within the plant cell walls.
Because it is a heterotroph, the fungus takes sugars from the plant. The fungal hyphae extend beyond the plant roots into the soil, where it can absorb water and nutrients that are transferred to the plant. Each partner gains a benefit from this relationship, so this is called a mutualistic symbiosis, or mutualism .
A symbiotic relationship refers to a shared relationship between at least two organisms of different species. This relationship can benefit both parties, as above, only benefit one, potentially causing harm to the other. What would you call this last type of symbiosis?
View a mycorrhizal root tip under the compound microscope, either as a prepared slide or from a fresh sample. If from a fresh sample, use 5% KOH + Phloxine B or Cotton Blue to stain the fungal tissue. Draw what you see below and label any distinguishing features of both the plant and fungus.
The Dikarya: Ascomycota and Basidiomycota
These two groups of fungi are referred to as the dikarya because some portion of their life cycle is dikaryotic . When two compatible mating types meet, they fuse together and begin the process of fertilization with plasmogamy (fusion of the cytoplasm). However, the nuclei do not fuse. Instead, a new mycelium is formed with two different haploid nuclei in each cell, making the ploidy n + n (as opposed to diploid, 2n). This state is called dikaryotic. Karyogamy (fusion of the nuclei) does not occur until the fungus is about to make spores. The two nuclei fuse and the zygote immediately undergoes meiosis, forming haploid spores.
Which type of life cycle would you classify this as and why?
Though there are microscopic species and life stages in each group (including the yeast you saw earlier), members of the Ascomycota and Basidiomycota both form macroscopic fruiting bodies.
Fungi make a diversity of fruiting structures, structures in which meiosis occurs to form spores. In the microfungi, you saw zygomycetes making their fruiting structures: zygosporangia. In the macrofungi, you will learn three different types of ascocarps and the anatomy of a basidiocarp, otherwise known as a mushroom. These structures are analogous to fruits produced on a tree. The rest of the fungal body (or, the rest of the tree, in this analogy) is the mycelium, buried within the substrate and busily acquiring food. Note: The mycelium is not the equivalent of the roots of the tree, but of the entire tree, including the roots, stems, and branches.
Ascomycota -- The Sac Fungi
This group of fungi is when the life cycle starts to get particularly strange and the fungus forms something called a dikaryon (di- meaning two, karyo- meaning nucleus). When two different hyphal bodies fuse, they do not fuse their nuclei, only the cytoplasm. The result is a single fungal body with two separate types of nuclei floating around inside it. Because it is neither haploid (n), nor truly diploid (2n), this condition is called being dikaryotic (n+n).
Ascomycota are distinguished from other groups of fungi by the following characteristics:
- Production of ascospores (usually 8) within an ascus , a normally elongate, sac-like structure
- Hyphae with simple septations
- The mycelium is primarily haploid. When two haploid (n) mycelia of the correct mating types meet, they can form a dikaryotic (n+n) fruiting body called an ascocarp .
There are three different types of ascocarps:
- Apothecium - a (usually) cup-shaped fruiting body with asci lining the interior of the cup. Two exceptions are Helvella and Morchella (morels), where the cup has been inverted, no longer looking like a cup, and the asci cover the now-exterior surface.
- Perithecium - a round fruiting body with a long neck, much like a bottle, with the asci inside the bottom of the bottle. Microscopic and quite similar to a Fucus conceptacle.
- Cleistothecium - a spherical, enclosed fruiting body packed with rounded asci. These are also microscopic and can be beautifully ornamented.
Above is the spore producing surface of an apothecium. The long asci each contain 8 ascospores.
Basidiomycota -- The Club Fungi
Basidiomycota are the other group of dikaryotic fungi. This group includes the mushroom-forming species of fungi, as well as two groups of (mostly) plant parasites , delightfully referred to as the rusts and the smuts.
Basidiomycota are distinguished from other groups of fungi by the following characteristics:
- Basidiospores (usually 4) produced from a basidium --a normally squat, roundish structure with prongs called sterigmata that spores are produced on.
- Hyphae with complex septations. These specialized septations look like they are surrounded by parentheses and help the mycelium maintain its dikaryotic state.
- Clamp connections can sometimes be seen, though are only obvious in certain genera.
- The mycelium is primarily dikaryotic. The haploid spores germinate and must find another germinating spore of the correct mating type to form a dikaryotic mycelium. This can then produce fruiting bodies called basidiocarps , or as we commonly call them, mushrooms.
The image above shows the spore producing surface of a basidiomycete, Coprinus . The dark football-shaped structures are the haploid basidiospores . They sit atop small projections called sterigmata ( sterigma , singular) that emerge from the top of the basidium . In most mushrooms, each basidium produces four basidiospores.


<IP_ADDRESS>: The Ability to Adhere to Host Cells and Resist Physical Removal
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Learning Objectives
- Briefly describe 3 different mechanisms by which bacteria can adhere to host cells and colonize and state how this can promote colonization.
- State an advantage for bacteria in being able to switch the adhesive tips of their pili.
- Define biofilm and state at least 3 benefits associated with bacteria living as a community within a biofilm.
Highlighted Bacterium
- Read the description of Neisseria memingitidis andmatch the bacterium with the description of the organism and the infection it causes.
One of the body's innate immune defenses is the ability to physically remove bacteria from the body through such means as the constant shedding of surface epithelial cells from the skin and mucous membranes, the removal of bacteria by such means as coughing, sneezing, vomiting, and diarrhea, and bacterial removal by bodily fluids such as saliva, blood, mucous, and urine. Bacteria may resist this physical removal by producing pili, cell wall adhesin proteins, and/or biofilm-producing capsules. In addition, the physical attachment of bacteria to host cells can also serve as a signal for the activation of genes involved in bacterial virulence. This process is known as signal transduction.
Using Pili (fimbriae) to Adhere to Host Cells
As seen in Unit 1, pili enable some organisms to adhere to receptors on target host cells (Figure \(\PageIndex{5}\).2.1) and thus colonize and resist flushing by the body. Pili are thin, protein tubes originating from the cytoplasmic membrane and are found in virtually all Gram-negative bacteria, but not in many Gram-positive bacteria.
The pilus has a shaft composed of a protein called pilin. At the end of the shaft is the adhesive tip structure having a shape corresponding to that of specific glycoprotein or glycolipid receptors on a host cell (Figure \(\PageIndex{5}\).2.3). Because both the bacteria and the host cells have a negative charge, pili may enable the bacteria to bind to host cells without initially having to get close enough to be pushed away by electrostatic repulsion. Once attached to the host cell, the pili can depolymerize and enable adhesions in the bacterial cell wall to make more intimate contact. There is also evidence that the binding of pili to host cell receptors can serve as a trigger for activating the synthesis of some cell wall adhesins.
Bacteria are constantly losing and reforming pili as they grow in the body and the same bacterium may switch the adhesive tips of the pili in order to adhere to different types of cells and evade immune defenses (Figure \(\PageIndex{2}\).2.3). E. coli , for example, is able to make over 30 different types of pili.
One class of pili, known as type IV pili, not only allows for attachment but also enable a twitching motility. They are located at the poles of bacilli and allow for a gliding motility along a solid surface such as a host cell. Extension and retraction of these pili allows the bacterium to drag itself along the solid surface (Figure \(\PageIndex{4}\)). In addition, bacteria can use their type IV pili to "slingshot" the bacterium over a cellular surface. In this case, as the pili contract they are thought to become taut like a stretched rubber band. When an anchoring pilus detaches, the taut pili "slingshot" the bacterium in the opposite direction (Figure \(\PageIndex{5}\)). This motion typically alternates with the twitching motility and enables a more rapid motion and direction change than with the twitching motility because the rapid slingshotting motion reduces the viscosity of the surrounding biofilm.
This enables bacteria with these types of pili within a biofilm to move around a cellular surface and find an optimum area on that cell for attachment and growth once they have initially bound. Bacteria with type IV pili include Pseudomonas aeruginosa, Neisseria gonorrhoeae, Neisseria meningitidis , and Vibrio cholerae .
Examples of bacteria using pili to colonize:
1. To cause infection, Neisseria gonorrhoeae must first colonize a mucosal surface composed of columnar epithelial cells. Pili allow for this initial binding and, in fact, N. gonorrhoeae is able to rapidly lose pili and synthesize new ones with a different adhesive tip, enabling the bacterium to adhere to a variety of tissues and cells including sperm, the epithelial cells of the mucous membranes lining the throat, genitourinary tract, rectum, and the conjunctiva of the eye. Subsequently, the bacterium is able to make more intimate contact with the host cell surface by way of a cell wall adhesin called Opa (see below).
2. The pili of Neisseria meningitidis allow it to adhere to mucosal epithelial cells in the nasopharynx where it is often asymptomatic. From there, however, it sometimes enters the blood and meninges and causes septicemia and meningitis. Type IV pili are thought to help the bacterium cross the blood brain barrier.
Click on this link, read the description of Neisseria meningitidis , and be able to match the bacterium with its description on an exam.
3. Uropathogenic strains of Escherichia coli can produce pili that enable the bacterium to adhere to the urinary epithelium and cause urinary tract infections. They also produce afimbrial adhesins (see below) for attachment to epithelial cells. Enteropathogenic E. coli (EPEC) use pili to adhere to intestinal mucosal cells.
- To view an electron micrograph E. coli with pili , see Dennis Kunkel's Microscopy at the University of Hawaii-Manoa.
- To view electron micrographs of enteropathogenic E. coli (EPEC) adhering to intestinal cells, see Donnenberg Lab Images at the University of Maryland Medical School.
4. Pili of
Vibrio cholerae
allow it to adhere to cells of the intestinal mucosa and resist the flushing action of diarrhea.
5. Pili of
Pseudomonas aeruginosa
allow it to initially colonize wounds or the lung.
Using Adhesins to Adhere to Host Cells
Adhesins are surface proteins found in the cell wall of various bacteria that bind to specific receptor molecules on the surface of host cells and enable the bacterium to adhere intimately to that cell in order to colonize and resist physical removal (Figure \(\PageIndex{6}\)). Many, if not most bacteria probably use one or more adhesins to colonize host cells.
For example:
1. Streptococcus pyogenes (see electron micrograph) (group A beta streptococci) produce a number of adhesins
a. Protein F that binds to fibronectin , a common protein on epithelial cells. In this way it is able to adhere to the lymphatics and mucous membranes of the upper respiratory tract and cause streptococcal pharyngitis (strep throat).
b. Lipoteichoic acid binds to fibronectin on epithelial cells.
c. M-protein also functions as an adhesin.
2. The tip of the spirochete Treponema pallidum contains adhesins that are able to bind to fibronectin on epithelial cells.
Scanning electron Micrograph of T. pallidum adhering to a host cell by its tip.
3. The tip of the spirochete Borrelia burgdorferi contains adhesins that can bind to various host cells.
4. Escherichia coli O157 utilizes a type 3 secretion system to inject effector proteins into intestinal epithelial cells. Some of these cause polymerization of actin at the cell surface and this pushes the host cell cytoplasmic membrane up to form a pedestal. Another effector protein inserts into the membrane of the pedestal to serve as a receptor molecule for E. coli adhesins (Figure \(\PageIndex{7}\)).
5. Helicobacter pylori use a type 4 secretion system to inject effector proteins into stomach epithelial cells to induce these host cells to display more receptors on their surface for H. pylori adhesins.
6. Bordetella pertussis produces several adhesins (Figure \(\PageIndex{8}\)):
a. Filamentous hemagglutinin is an adhesin that allows the bacterium to adhere to galactose residues of the glycolipids on the membrane of ciliated epithelial cells of the respiratory tract.
b. Pertussis toxin also functions as an adhesin. One subunit of the pertussis toxin remains bound to the bacterial cell wall while another subunit binds to the glycolipids on the membrane of ciliated epithelial cells of the respiratory tract.
c.
B. Pertussis
also produces an adhesin called pertactin that further enables the bacterium to adhere to cells.
7. Neisseria gonorrhoeae produces an adhesin called Opa (protein II) that enables the bacterium to make a more intimate contact with the host cell after it first adheres with its pili. Like with adhesive tips of pili, N. gonorrhoeae has multiple alleles for Opa protein adhesins enabling the bacterium to adhere to a variety of host cell types.
8. Staphylococcus aureus uses protein A as an adhesin to adhere to various host cells. It also helps the bacterium to resist phagocytosis.
Using Biofilms to Adhere to Host Cells
Many normal flora bacteria produce a capsular polysaccharide matrix or glycocalyx to form a biofilm on host tissue. Biofilms are groups of bacteria attached to a surface and enclosed in a common secreted adhesive matrix, typically polysaccharide in nature. Many pathogenic bacteria, as well as normal flora and many environmental bacteria, form complex bacterial communities as biofilms.
Bacteria in biofilms are often able to communicate with one another by a process called quorum sensing and are able to interact with and adapt to their environment as a population of bacteria rather than as individual bacteria. By living as a community of bacteria as a biofilm, these bacteria are better able to:
- resist attack by antibiotics;
- trap nutrients for bacterial growth and remain in a favorable niche;
- adhere to environmental surfaces and resist flushing;
- live in close association and communicate with other bacteria in the biofilm; and
- resist phagocytosis and attack by the body's complement pathways.
Biofilms are, therefore, functional, interacting, and growing bacterial communities. Biofilms even contain their own water channels for delivering water and nutrients throughout the biofilm community.
- Electron micrograph of a biofilm of Haemophilus influenzae from Biomedcentral.com
- Photomicrograph of a biofilm with water channels from Centers for Disease Control and Prevention Rodney M. Donlan: "Biofilms: Microbial Life on Surfaces"
- Biofilm of Pseudomonas aeruginosa from the Ausubel Lab, Department of Molecular Biology, Massachusetts General Hospital
- Scanning electron micrograph of Staphylococcus aureus forming a biofilm in an indwelling catheter courtesy of CDC.
- Biofilm of Staphylococcus aureus from Montana State University
For example:
1. Streptococcus mutans , and Streptococcus sobrinus , two bacteria implicated in initiating dental caries, break down sucrose into glucose and fructose. Streptococcus mutans can uses an enzyme called dextransucrase to convert sucrose into a sticky polysaccharide called dextran that forms a biofilm enabling the bacteria to adhere to the enamel of the tooth and initiate plaque formation.
This dextran mesh traps the S. mutans and S. sobrinus , along with other bacteria and debris, and forms plaque. S. mutans and S. sobrinus also ferment glucose in order to produce energy. The fermentation of glucose results in the production of lactic acid that is released onto the surface of the tooth and initiates decay.
- Scanning electron micrograph of Streptococcus growing in the enamel of a tooth .© Lloyd Simonson, author. Licensed for use, ASM MicrobeLibrary .
- Scanning electron micrograph of dental plaque .© H. Busscher, H. van der Mei, W. Jongebloed, R Bos, authors. Licensed for use, ASM MicrobeLibrary .
2. Most children suffering from chronic ear infection (otitis media) have a biofilm of bacteria in their middle ear. This biofilm contains bacteria such as Streptococcus pneumoniae , Haemophilus influenzae , and Moraxella catarrhalis and enables the bacteria to chronically colonize the middle ear as well as resist body defenses and antibiotics.
3. Planktonic Pseudomonas aeruginosa uses its polar flagellum to move through water or mucus and make contact with a solid surface such as the body's mucous membranes. It then can use pili and cell wall adhesins to attach to the epithelial cells of the mucous membrane. Attachment activates signaling and quorum sensing genes to eventually enable the population of P. aeruginosa to start synthesizing a polysaccharide biofilm composed of alginate. As the biofilm grows, the bacteria lose their flagella to become nonmotile and secrete a variety of enzymes that enable the population to obtain nutrients from the host cells. Eventually the biofilm mushrooms up and develops water channels to deliver water and nutrients to all the bacteria within the biofilm. As the biofilm begins to get too crowded with bacteria, quorum sensing enables some of the Pseudomonas to again produce flagella, escape the biofilm, and colonize a new location ( See Figs. 9A-9H ).
Many chronic and difficult-to-treat infections are caused by bacteria in biofilms. Within biofilms, bacteria grow more slowly, exhibit different gene expression than free planktonic bacteria, and are more resistant to antimicrobial agents such as antibiotics because of the reduced ability of these chemicals to penetrate the dense biofilms matrix. Biofilms have been implicated in tuberculosis, kidney stones, Staphylococcus infections, Legionnaires' disease, and periodontal disease. It is further estimated that as many as 10 million people a year in the US may develop biofilm-associated infections as a result of invasive medical procedures and surgical implants.
- Scanning electron micrograph of Listeria growing on a stainless steel surface . © Amy Lee Wong, author. Licensed for use, ASM MicrobeLibrary .
- Scanning electron micrograph of Pseudomonas growing on bronchial mucosa . © Hiroyuki Kobayashi, author. Licensed for use, ASM MicrobeLibrary .
- Scanning electron micrograph of Staphylococcus aureus forming a biofilm in an indwelling catheter courtesy of CDC.
- Article and computer-generated model of biofilm formation courtesy of NIH.
YouTube movie and animation: What are Biofilms?
Exercise: Think-Pair-Share Questions
Pseudomonas aeruginosa , a common cause of serious respiratory infections on people with cystic fibrosis, produces a single polar flagellum, can secrete a polysaccharide slime composed of alginate, and is able to produce both pili and cell wall adhesins. How could each of these factors contribute to the bacterium's pathogenosis and in what order might they be used?
Summary
- One of the body's innate immune defenses is the ability to physically remove bacteria from the body.
- Bacteria may resist physical removal by producing pili, cell wall adhesin proteins, and/or biofilm-producing capsules that enable bacteria to adhere to host cells.
- At the end of the shaft of a bacterial pilus is an adhesive tip structure having a shape corresponding to that of specific receptor on a host cell for initial attachment. Bacteria can typically make a variety of different adhesive tips enabling them to attach to different host cell receptors.
- Cell wall adhesins are surface proteins found in the cell wall of various bacteria that bind tightly to specific receptor molecules on the surface of host cells. Bacteria can typically make a variety of different cell wall adhesins enabling them to attach to different host cell receptors.
- Biofilms are groups of bacteria attached to a surface and enclosed in a common secreted adhesive matrix, typically polysaccharide in nature. Many pathogenic bacteria, as well as normal flora and many environmental bacteria, form complex bacterial communities as biofilms.
- Many chronic and difficult-to-treat infections are caused by bacteria in biofilms.


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-
abortion
-
any pregnancy loss before 20 weeks' gestation.
-
childhood mortality
-
death of a child under 5 years of age
-
community health nurse
-
provide education and health promotion outside the hospital setting, directly to the public
-
community-based nursing
-
delivery of nursing care in the community
-
error of omission
-
treatment or an assessment by a nurse that is not performed
-
family-centered care
-
set of principles that guide health-care delivery according to the strengths and needs of the person, family, and community, promoting involvement of the family in informed decision making
-
female genital mutilation and cutting (FGM/C)
-
removal of all or part of the external female genitalia for nonmedical reasons
-
fetal mortality
-
intrauterine demise of the fetus at any gestational age
-
infant mortality
-
death of an infant before their first birthday
-
maternal mortality
-
death of a person while pregnant or within 42 days of birth or termination of pregnancy that was not accidental
-
maternal-fetal conflict
-
when maternal interests and fetal interests are incompatible
-
risk management
-
identifying risk factors by analyzing processes and procedures and implementing programs to address risk and prevent patient harm
-
stem cells
-
undifferentiated cells that can renew themselves and develop into different types of cells


6.2.1: Developmental Disabilities at Home
In some cases, a person with a developmental disability may reside in a long-term care facility or group home. Workers in those environments help to provide care and support for the person. Other times, a family who has a member with a developmental disability may decide to care for their family member within the home. They may need to have extra help doing so. This is where the very important role of a Home Health Care Aide/Personal Care Aide comes in. They may help to provide assistance with completion of ADLs, provide supervision, teach positive coping skills to the patient and family, and serve as a source of respite (relief for the family) during times of high stress or high life demands. Their role is to help the family and patient in meeting their needs. They will provide emotional support in addition to completing physical care and home care tasks. Two of the most important roles providing care within the home are to help the person be as independent as possible and to always promote self–determination (making choices and plans for oneself).
Multiple choice:
1. Which of the following is the best explanation for what respite means?
a). A nurse administering extra medication for the patient to help them sleep.
b). Providing relief for the family by providing supervision and personal care for the patient so the family can rest and do other activities.
c). Putting the patient in a room by him/herself with a TV to keep them occupied.
d). Giving the patient extra time to put their shoes on.
- Answer
-
1. B
FEEDBACK :
1. Providing respite for a family means providing relief and assistance for a family who cares for a patient. Respite activities may include providing assistance with completion of ADLs, light housekeeping, emotional support, and providing companionship to the patient.
Caring for a Child with a Developmental Disability
Caring for a child with a developmental disability is the same as caring for any other child in the sense that they have the same basic needs. They need food, water, safety, love, a sense of belonging within their family and community, social interaction, and to develop a sense of independence and self-determination.
Unlike other children the same age, they may require additional care. They may not achieve the same developmental milestones, or they may achieve them at a later date than other children their same age. They may need extra help in school, or have additional members on their home health care team to help meet their needs. With extra support and treatment interventions, children with developmental disabilities can lead full and productive lives, filled with joy and happiness, just like any other children.
1. Children with developmental disabilities have the same needs as other children, although they may require additional care and take longer to reach developmental milestones.True or False? ________
- Answer
-
1. True
FEEDBACK :
1. All people, regardless of disability have similar needs: food, water, safety, love, a sense of belonging within the family and community, social interaction, and to develop a sense of independence and self-determination. While people with developmental disabilities may need additional care, support, and time to achieve goals and to meet daily living needs, they can still lead full and productive lives.
Caring for an Adult with a Developmental Disability
Caring for an adult with a developmental disability is the same as caring for any other adult in the sense that they have the same basic needs. They need food, water, safety, love, a sense of belonging within their family and community, social interaction, and to develop a sense of independence and self-determination. Unlike other adults at the same age, they may require additional care. They may not be able to do the same things as other adults their age. For example, they may not be able to live independently, or go to work, or have a family of their own. Or, they may be able to do many of these things, but need some additional support.
It is very important to remember that just because the adult may have impairments, they are not children. Even if they need to have complete care, they should be treated as an adult. They should be provided with opportunities to socialize with other adults, to make choices, and to be as independent and self-reliant as possible. Always treat adults with developmental disabilities as adults, not children.
Another aspect of working with adults with a developmental disability is to be aware that many also have sexual desires and needs, just like any other adult. Just because a person has a disability does not mean that they are incapable of sexual or emotional intimacy.   Always be respectful of times needed for privacy.
1. If an adult requires complete care, they should be treated and spoken to as one would a child. True or False? ___________
2. Adults with developmental disabilities have sexual interests and needs just like any other adult. True or False? ___________
- Answer
-
1. False
2. True
FEEDBACK :
1. Regardless of the amount of care needed, all adults should be treated as adults, and not children. Home Health Aides/Personal Care Aides should take care to treat all adults, regardless of impairment as adults and provide respect for each individual.
2. While people with disabilities may need to make adjustments during sexual intimacy, this does not mean that they are not capable of sexual relationships, that they do not desire them or that they do not have sexual feelings. Always be respectful of times needed for privacy.


1.
(a) Sc: [Ar]4
s
2
3
d
1
; (b) Ti: [Ar]4
s
2
3
d
2
; (c) Cr: [Ar]4
s
1
3
d
5
; (d) Fe: [Ar]4
s
2
3
d
6
; (e) Ru: [Kr]5
s
2
4
d
6
3.
(a) La: [Xe]6
s
2
5
d
1
, La
3
+
: [Xe]; (b) Sm: [Xe]6
s
2
4
f
6
, Sm
3
+
: [Xe]4
f
5
; (c) Lu: [Xe]6
s
2
4
f
14
5
d
1
, Lu
3
+
: [Xe]4
f
14
5.
Al is used because it is the strongest reducing agent and the only option listed that can provide sufficient driving force to convert La(III) into La.
9.
The CaSiO
3
slag is less dense than the molten iron, so it can easily be separated. Also, the floating slag layer creates a barrier that prevents the molten iron from exposure to O
2
, which would oxidize the Fe back to Fe
2
O
3
.
15.
E
° = −0.6 V,
E
° is negative so this reduction is not spontaneous.
E
° = +1.1 V
17.
(a)
(b)
(c)
(d)
(e)
(f)
19.
(a)
(b)
(c) In acid solution between pH 2 and pH 6,
forms
which is in equilibrium with dichromate ion. The reaction is
At other acidic pHs, the reaction is
(d)
(e)
(f)
21.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
23.
As CN
−
is added,
As more CN
−
is added,
25.
(a) Sc
3+
; (b) Ti
4+
; (c) V
5+
; (d) Cr
6+
; (e) Mn
4+
; (f) Fe
2+
and Fe
3+
; (g) Co
2+
and Co
3+
; (h) Ni
2+
; (i) Cu
+
27.
(a) 4, [Zn(OH)
4
]
2−
; (b) 6, [Pd(CN)
6
]
2−
; (c) 2, [AuCl
2
]
−
; (d) 4, [Pt(NH
3
)
2
Cl
2
]; (e) 6, K[Cr(NH
3
)
2
Cl
4
]; (f) 6, [Co(NH
3
)
6
][Cr(CN)
6
]; (g) 6, [Co(en)
2
Br
2
]NO
3
29.
(a) [Pt(H
2
O)
2
Br
2
]:
(b) [Pt(NH
3
)(py)(Cl)(Br)]:
(c) [Zn(NH
3
)
3
Cl]
+
:
(d) [Pt(NH
3
)
3
Cl]
+
:
(e) [Ni(H
2
O)
4
Cl
2
]:
(f) [Co(C
2
O
4
)
2
Cl
2
]
3−
:
31.
(a) tricarbonatocobaltate(III) ion; (b) tetraaminecopper(II) ion; (c) tetraaminedibromocobalt(III) sulfate; (d) tetraamineplatinum(II) tetrachloroplatinate(II); (e)
tris-
(ethylenediamine)chromium(III) nitrate; (f) diaminedibromopalladium(II); (g) potassium pentachlorocuprate(II); (h) diaminedichlorozinc(II)
33.
(a) none; (b) none; (c) The two Cl ligands can be
cis
or
trans
. When they are
cis
, there will also be an optical isomer.
37.
39.
[Co(H
2
O)
6
]Cl
2
with three unpaired electrons.
41.
(a) 4; (b) 2; (c) 1; (d) 5; (e) 0
43.
(a) [Fe(CN)
6
]
4−
; (b) [Co(NH
3
)
6
]
3+
; (c) [Mn(CN)
6
]
4−
45.
The complex does not have any unpaired electrons. The complex does not have any geometric isomers, but the mirror image is nonsuperimposable, so it has an optical isomer.
47.
No. Au
+
has a complete 5
d
sublevel.


6.2: Venn Diagrams
A Venn Diagram in some ways improves on an Euler diagram by having a blank form that we can shade and X to create each of our propositions. We’ll see later how this allows us to do our analysis of inferences.
Blank form:
We have two overlapping circles, labels for each circles, space outside of both circles, and room for putting X’s and shading in all of these regions.
Let’s put number labels on each of these regions:
Let’s make this more concrete so we can discuss each region.
1) Is the region of Shrimp that are not People.
2) Is the region of things that are both Shrimp and People (you won’t find any).
3) Is the region of things that are People and not Shrimp.
4) Is the region of non-shrimp and non-people (Tubas, Cars, Bananas, etc.)
Okay, so how do we diagram each of our standard form categorical propositions?
The first rule to note is that all universal propositions are diagrammed using Shading and all particular propositions are diagrammed using X’s .
We shade in region 1 because there are no Chickens that are not Winged (at least that’s what our proposition claims).
We shade in region 2 because the proposition claims that there are no Robots that are also Conscious Beings.
NOW WE SWITCH TO X’S INSTEAD OF SHADING
We put one X in region 2 because the proposition claims that there is at least one Donkey that is also a Stubborn Thing.
We put one X in region 1 because the proposition claims that there is at least one Horse that is not a Tame Animal.
Using Venn Diagrams for Inferences
Any immediate inference will be apparent in a Venn diagram.
What’s an immediate inference, you ask?
It’s an inference from one proposition directly (immediately) to another inference.
Let’s look at the following inference:
No dogs are cows, so it follows that
it is false that there is some dog that is a cow.
Compare our two diagrams:
Do you see how, if we overlapped them, they wouldn’t fit together?
This is how we know that if the first proposition is true, the second one must be false.
These are Contradictories , so of course if one is true, then the other is false.
This inference, therefore, doesn’t work. It’s an Invalid inference.
Let’s try another:
Some dog is a mammal,
so it follows that some mammal is a dog
Notice how the two diagrams are identical:
If they’re claiming the exact same thing, then obviously one implies or entails the other. What it means for each proposition to be true is for the same state of the world to obtain (to be the case).
Therefore, this inference is Valid .
This type of inference (switching the subject and predicate) is called Conversion and it only works for E and I Propositions. Try to do it for an A or O proposition and you’ll find that it doesn’t work.
And another type of inference that often arises:
Some paintings are beautiful,
so it follows that some paintings are not beautiful.
Let’s look at the two diagrams.
Notice how the information contained in the second diagram is not contained in the first diagram . Immediate inferences only work (and in fact all deductive inferences only work) if the information contained in the conclusion is already contained in the premises.
If in the move from premises to conclusion, we have to change our diagram (add new information), then the inference is invalid
(at minimum there is a hidden assumption,
at worst the inference simply doesn’t work).
So, to recap, there are three kinds of inference here:
1. Invalid inferences because the diagrams are incompatible.
2. Valid inferences because the diagrams are the same (or sometimes because the conclusion is represented in the diagram in some way).
3. Invalid inference because the conclusion introduces new information (changes the diagram).
Conversion, Obversion, Contraposition
Let’s talk briefly about three kinds of immediate inferences one can draw in Categorical Logic. These are in addition to the inferences we can draw using the square of opposition.
Conversion
Conversion is the switching of the subject and predicate.
So, “No Apples are Bananas” converts to “No Bananas are Apples.”
And, “Some Frisbees are round things” converts to “Some round things are frisbees.”
This only works for E and I propositions. We can remember this by looking at the middle vowels of the word Conv E rs I on.
Obversion
Obversion is when you change the quality of the proposition from negative to affirmative or affirmative to negative, and then you replace the predicate with its complement.
So, “No Apples are Bananas” obverts to “All Apples are non-Bananas.”
And, “Some Frisbees are round things” obverts to “Some Frisbees are not non-round things.”
Obversion works for every form of categorical proposition.
What’s a complement, you ask?
A complement of class/kind/category X is whatever isn’t a member of X.
The complement of birds is the set of all non-birds .
The complement of people identical to Lakshmi is the set of all things not identical to Lakshmi.
The complement of animals that are going to get eaten is the set of all things that aren’t animals that are going to get eaten .
We form complements by introducing a negation (non, not, n’t, etc.) into the term. Usually, you can just put a “non-” in front of the term, but, as you can see, that isn’t always easy.
The important thing to remember is that your description should cover everything that isn’t in the group (all non-existent things, all imaginary things, all real things, everything). So don’t make the complement of “people identical to Sven” by writing “People not identical to Sven.”
Contraposition
Obversion is when you switch the subject and predicate of the proposition, and then you replace each with its complement.
So, “All Apples are Bananas” obverts to “All non-Bananas are non-Apples.”
And, “Some Frisbees are round things” obverts to “Some non-round things are non-Frisbees.”
This only works for E and I propositions. We can remember this by looking at the middle vowels of the word Contr A p O sition.


6.3: Creating the Introduction, Step 1- Grab Attention
“It was a pleasure to burn.” —Ray Bradbury, Fahrenheit 451
“It was the best of times, it was the worst of times.” —Charles Dickens, A Tale of Two Cities
“Mr. and Mrs. Dursley, of number four Privet Drive, were proud to say that they were perfectly normal, thank you very much.” —J.K. Rowling, Harry Potter and the Sorcerer’s Stone
Well-known authors often admit that the opening line of a book is possibly the most important one in the entire book. Authors, like any other profession, need to make a living to maintain their lifestyle. This requires them to sell copies of their books, so authors must possess the capability to hook a reader within only one or two short lines to entice further reading. Most people, when searching for a new book, look first at the covers, and then to the first line of the story, and if it sufficiently grabs their attention, they continue perusing the pages. However, if those first lines fall flat, the book gets closed, set down, and likely forgotten forever.
A similar phenomenon occurs within the first few seconds of a speech. The first words uttered or the first actions that may communicate a message to an audience become absolutely critical. Borrowing from the previous analogy of a speaker to an author, imagine picking up a book that began with, “Hi, everyone. My name is Stephen King, and today, I’d like to share a really scary story with you about homicidal clowns.” Such a book promises little excitement, and most people would likely put it down without hesitation. In a similar light, a speaker who gets up before an audience and “warms up” with a casual greeting, small talk, and an awkward announcement of the topic tends to put off most audiences’ attention spans. Considering that the average human transient attention span (temporary response to a stimulus) lasts around 8 seconds (Dukette & Cornish , 2009), a speaker has an extremely brief window of time in which to grab the audience’s attention and, subsequently, sustain it for the duration of the speech. In fact, the shorter the time the speaker has to speak, the more important this initial attention getter becomes. If given a limited amount of time to speak, don’t waste it on anything that does not further the purpose for speaking.
To grab an audience’s attention, try using one of the several time-honored techniques that continue to work today, despite all the various advances in technology. These include quotations, stories, rhetorical questions, shocking or unexpected information, and compelling visual aids or demonstration.
Quotations
A great quotation related to the speech topic often provides wisdom from a well-respected source that says something valuable or profound in much fewer words than most people can manage using many more. Choose quotes that demonstrate elegance, eloquence, or clever wit, yet make sure they remain relevant to the topic. Avoid using fun or humorous quotations for the sake of it, for this may make the audience feel cheated. Consider pulling quotations from websites, like BrainyQuote.com or GoodReads.com , works of literature, poetry, film, or even from personal acquaintances. Quotes can work especially great at the beginning and ending of speeches.
Home Stories
Providing a story or a narrative helps speakers frame the topic for the audience. Stories provide speakers with a way to personalize a topic by helping audience members identify with the characters, events, or places within the story. Also, stories can entertain and engage, further reinforcing the idea of using an attention getter at the beginning of a speech. Stories can present “what if” scenarios that give the audience a hypothetical situation that illustrates the main point of the speech. Stories can also come in the form of real-life anecdotes based on personal experiences, those of others, or even events portrayed in fictional works like television, film, or literature. Select a story for both its relevance to the topic, but more importantly, its ability to resonate, or strike a familiar chord, with the audience.
Knowing the audience in advance becomes critically important when selecting the perfect story to illustrate or frame a point.
Home Asking Questions
“According to the U.N., roughly 734 million people live on less than two dollars a day. Could you?” This rhetorical question , or question designed to evoke a thought or emotive response from an audience, requires no answer. Starting a speech with a question like the one above immediately cuts to the point, while simultaneously provides the audience concrete information and gets them to think about the main idea of the speech. Delivering a rhetorical question effectively requires skill, though, so inexperienced public speakers should avoid using them until they gain a bit more experience. Deliver the question slowly, deliberately, and follow it with a brief pause that allows the audience to consider what they heard. Too short a pause, and the audience does not have adequate time to think, while too long a pause runs the risk of having the audience actually start responding to the question. Finding the right balance of time takes skill, but once perfected, gives the speaker a powerful opening tool for grabbing attention. In addition to this deft use of a pause, the speaker should also follow up the question by explaining how the rest of the speech will address the nature of the question.
Home In a quick poll the speaker poses a question that requires little commitment from the audience, other than raising a hand. For example, using the topic above, the speaker might start by saying, “Can I get a quick show of hands for everyone in this room who currently has a job?” Gaining a small showing of audience involvement like this provides a highly effective way to grab attention, and the critically thinking speaker can combine this technique with the rhetorical question to further drive home an important point. For example, following the question above, the speaker could say, “Now, keep your hand up if you make less than two dollars a day at your job, just like the other 734 million people in the world who make this wage or less, according to the U.N.” Such strategies have risks though, especially when they backfire, such as when audience members do not raise their hands as expected, or when a speaker ends up with more audience involvement than previously desired. Use discretion, and always have a backup plan.
Unexpected Information
“Just how big is a billion? To put this in perspective, let us look at a single second. Now, let’s figure out how much time passes in one billion seconds. Any guesses? It takes more than 31 years. If you started counting to one billion when Orson Welles’ War of the Worlds radio broadcast convinced some Americans that aliens had invaded the country in 1938, you’d finish counting around the time Neil Armstrong took his first step on the moon .” Using a set of statements like this to arrive at an unexpected conclusion would provide a great segue to kick off a speech explaining a concept like the federal deficit, especially if the speaker wished to put into perspective the scope of the federal budget. Statements such as these stimulate audience members’ curiosity and keep them listening for more useful information. Another way of approaching this, but also combining the technique with gaining audience involvement, would occur if the speaker asked every other male in the room to raise his hand and then asked every third female in the room to raise her hand as well. Then, the speaker could explain to the audience that, according to the Damon Runyon Cancer Research Foundation , the statistics show that the people with their hands in the air represent the odds of receiving a positive diagnosis for some form of cancer. While sobering and somewhat macabre, such involvement causes the audience to feel invested and personally related to the topic from that point forward.
Visual Aids and Demonstrations
Chapter 10 will discuss the impact of visual aids in much more detail. Suffice to say, visual aids can provide a speaker with powerfully gripping opening techniques. Additionally, demonstrations may provide an audience with a visually compelling reason to listen as well. A student delivering an informational speech on the martial art of tai chi may walk slowly and deliberately out into the center of the room, take a deep breath, and, in silence, begin performing various forms and poses inherent to the art. Without saying a word, such a demonstration effectively captures an audience’s interest to hear more.
Refer to Current or Historical Events
“Last week we noted the founding of this great college in 1886, with a big celebration in the campus commons. The first students to graduate were nursing students, and they received their diplomas in 1890. Since then, there have been thousands of nurses who got their education right here.”
The above example refers to both the past and the present. A nursing student attending this college might use this as a good attention getter for a speech about some element of nursing or the medical field. Generic yet personal, it immediately engages the audience and brings them personally closer to the topic and its relevance.


4.3: Hard and Soft Acids and Bases
The Hard and Soft Bases Concept (HSAB)
The hard and soft acid and base concept (HSAB) can be conceived as a refinement of the Lewis-acid and base concept. Its most useful feature is that it can make predictions about the strength of the acid-base interactions. It can also estimate if the interactions are more ionic or more more covalent.
4.2.1 Visual representation of a unpolarized atom and an atom polarized in an electric field.
Let us first clarify what is meant by hard and soft, respectively. These terms refer to the polarizability of the electrons in an atom or a molecule (Fig. 4.2.1). An atom is soft when its electrons are easily polarizable. This means that the electron cloud easily deforms in an electric field. Easy deformation is consistent with the term “soft”. In an electric field the negatively charged electrons are attracted to the positive pole of the electric field. Therefore, the electron cloud distorts toward the positive end of the electric field, and the atom is polarized. Vice versa, when the electron cloud is not easily polarizable, we say the atom is hard. What is then meant by a hard and a soft acid or base? A hard or soft acid is a hard or soft Lewis acid, and a hard or soft base is a hard or soft Lewis base. As mentioned previously, the HSAB concept is useful because it make statements about the strength of the acid-base interactions, and thus the strength of the bonds. It can also make statements on whether the bonding is more covalent or more ionic (Fig. 4.2.2).
Generally, hard-hard interactions, meaning the interactions between a hard acid and a hard base, tend to be strong. The bonding is more likely ionic. Soft-soft interactions also tend to be strong, but they are more likely covalent. Hard-soft interactions tend to be weak.
Why are soft-soft and hard-hard interactions strong, while hard-soft interactions are weak? To answer this question, we must first understand what makes and acid or base hard or soft. Generally, we can say that the more delocalized the electrons are, the softer the species. For a single atom or ion this means that the larger the atom or ion is the softer the species. The larger the atom size, the more delocalized are its valence electrons. The size of a neutral atom is defined by its position in the periodic table. Generally, the higher the period, the softer the atom (Fig. 4.2.3).
For ions, also the charge plays a role. For cations, a higher positive charge makes a cation harder, for anions a higher negative charge makes the anion softer (Fig. 4.2.4).
The size of the donor/acceptor atom is not the only factor that determines the hardness. Also the ability of the species to make π-bonding is important. Species that have orbitals suitable for π-bonding tend to be soft even if size arguments suggest that they are hard. This is because π-bonding increases electron delocalization (Fig. 4.2.5).
For example, transition metals have d-orbitals available which are suitable for π-bonding with ligands, while alkali metals do not. Therefore, a relatively small transition metal cation such as Cu + is softer than large alkali metal ions such as Cs + . For anions π-bonding is also important. For instance, CN - anions are soft bases even though the donor carbon atom is small because the CN - ligand has π-orbitals available for π-bonding with Lewis acids.
So back to the question: Why are soft-soft and hard-hard interactions strong, but hard-soft interactions weak? This essentially boils down to rule 2 of the orbital overlap criterion (see chapter 3 on MO theory). Two small orbitals have typically good overlap, and two large orbitals also have good orbital overlap, and thus the interaction is strong. However, large and small orbitals tend to have weak orbital overlap, and thus the bonding weak.
Now to the question of why soft-soft interactions tend to be more covalent, while hard-hard interactions tend to be more ionic. The answer has to do with the fact that in smaller atoms the energy differences between atomic orbitals tends to be larger compared to large atoms. As a consequence, it is statistically more likely that the HOMO and LUMO of two soft species have more similar energies compared to two hard species. When the HOMO and LUMO of a Lewis acid and a Lewis base are similar in energy, then the bonding is more covalent. When they are significantly different, then the bonding is more ionic.
Let us illustrate this by two qualitiative examples. Lithium oxide is made of O 2- anions and Li + cations. If we view the ionic bonding between the O 2- and the Li + ions as an extreme case of a polar, dative bond, then oxide anion acts as a Lewis base, and the Li + ion acts as a Lewis acid. How can the high ionicity be explained? Both the Li + and the O 2- are small ions, thus they are both hard. The small size also implies that the energy differences between the atomic orbitals are large. Because of this, it is unlikely that the highest occupied atomic orbital of the O 2- ion has a similar energy than the lowest unoccupied atomic orbital of the Li + ion. Due to the large energy difference, the bonding MO will be localized almost completely at the O 2- anion, and the bonding will be ionic (Fig. 4.2.7).
An example of a compound with strong soft-soft-interactions is silver iodide. While AgI is considered an ionic compound, the interactions have a significantly stronger covalent character. The soft nature of Ag + is readily understood from the fact that Ag + is a period 5 transition metal ion with low positive charge, and d-orbitals available for π-bonding. Iodine is a period 6 element, thus iodide is quite soft. Because Ag and I are elements of period 5 and 6, respectively, their orbital energy differences are significantly smaller than those of O and Li which are period 2 elements. Thus, the HOMO of I - and the LUMO of Ag + are naturally closer in energy resulting in a more covalent interaction (Fig. 4.2.8).
We should be aware that we need to treat these considerations with caution. For example, B-O bonds are fairly covalent bonds despite the fact that B and O are both quite hard. The HOMO of the donor and the LUMO of the acceptor of hard species are not necessarily much different. Other parameters such as electronegativity differences also weigh in and must be taken into account to correctly predict the nature of the chemical bond.
Examples - Bases
To get a feeling for correctly estimating the hardness of a species let us consider a few examples. Let us start with some bases.
What statements about hardness can you make for the series F - , Cl - , Br - , I - (Fig. 4.2.9). They are all halogenide ions with the same negative charge. The size increases from fluoride to chloride, to bromide to iodide. Thus, the softness should increase in the same order. F - is a small ion with a small negative charge and should be be hard, I is a very heavy element therefore I - is very soft. Cl - and Br - are moderately hard, and soft ions, respectively.
Next, consider the series H 2 O, OH - , O 2- , CH 3 O - , and PhO - . All of the species contain small O donor atoms, so all of them should be considered hard. The OH - ion is somewhat softer than the H 2 O because of the negative charge that increases the size of the donor O atom. For the same reason O 2- is somewhat softer than OH - . CH 3 O - is somewhat softer than O 2- because of the positive inductive effect of the methyl group. The phenolate ion is the softest because the negative charge at O can be delocalized in the aromatic ring. The delocalization of the negative charge leads to a greater polarizability, and thus softness. We could also think about if F - would likely be harder or softer than H 2 O. F is a little smaller than O, but F carries a negative charge, so the case is ambiguous.
Next, let us look at the series NH 3 , CH 3 NH 2 , and PhNH 2 (Fig. 4.2.11). The N donor atom is a small, little polarizable atom, thus the species should be regarded hard. N is somewhat larger than O though, which means that NH 3 is somewhat softer than H 2 O. CH 3 NH 2 would be a bit softer than NH 3 because the positive inductive effect of the methyl group, and aniline would be a bit softer than methyl amine because of possibility to delocalize the lone pair at N in the aromatic ring.
What about H 2 S, alkyl thiols and di alkyl thiols (4.2.12)? The S donor atom is in the 3rd period, and large enough to be considered soft. The softness would be expected to somewhat increase from H 2 S to R-SH to R-S-R because of the positive inductive effect of the alkyl group.
The next example is a phospine of the general formula PR 3 (4.2.13). Like sulfur, phosphorus is a period 3 donor atom, and phosphines are generally soft.
Lastly, let us look at carbon monoxide and cyanide (Fig. 4.2.14). At first glance these species appear like hard bases because of the small carbon donor atoms. However, they are actually quite soft because of their ability to use their π and π* orbitals in π-bonding with Lewis acids, in particular transition metal ions. We will look closer at this issue later when we discuss the bonding in transition metal complexes in detail.
Example - Acids
Now let us think about the hardness of acids.
In the series H + , Li + , Na + , K + : Are these hard or soft acids and how does the hardness change within this series (Fig. 4.2.15)? The answer is: All alkali metal cations are considered hard acids, even the relatively large K + cation in the 4th period. This is because alkali metal cations have only s-valence orbitals and thus a lack of orbitals suitable for π-bonding. Within the series H + is the hardest and K + is the softest because the ionic radius increases with increasing period.
Similarly, the earth alkaline metals Be 2 + , Mg 2 + , and Ca 2 + are hard cations with the hardness decreasing from Be 2 + to Ca 2 + . Due the the 2+ charge earth alkaline metal cations are expected harder than alkali metal cations of the same period, for example Be 2 + should be estimated harder than Li + .
In the next series BF 3 , BCl 3 , B(CH 3 ), and BH 3 the hardness declines from BF 3 to BH 3 (Fig. 4.2.17). BCl 3 is a softer than BF 3 because of the smaller electronegativity of Cl versus F. The more electronegative F withdraws more electron density from the boron making it smaller, and thus harder. Because of the positive inductive effect, the B(CH 3 ) 3 is softer than BCl 3 . The BF 3 and BCl 3 molecules are considered hard acids overall, the B(CH 3 ) 3 is an intermediate case. At first glance, it would appear that BH 3 is harder than B(CH 3 ) 3 , nonetheless it acts more like a soft acid, possibly because of the hydride-like character of the compound.
Next let us consider the transition metal ion series Fe 2 + , Fe 3 + , Co 2 + , Co 3 + , Rh 3 + , Ir 3 + (Fig. 4.2.18). These cations have the ability to make π-bonding, but because of the higher 2+ and 3+ charge respectively, none of them are soft. All period 4 cations with a 3+ charge, namely Fe 3 + and Co 3 + are hard acids, the Fe 2 + and Co 2 + ions are at the borderline between hard and soft due to their lower charge. Rh 3 + and Ir 3 + are also at the borderline. They have a higher positive charge, but are in period 5 and 6, respectively. Rh 3 + would be expected to be harder than Ir 3 + because it is in a lower period.
Ti 4 + and Si 4 + are both hard acids (Fig. 4.2.19). Generally, all ions with a charge of +4 or higher are hard acids.
What about the last series Cu + , Cd 2 + , Hg 2 + , Pd 2 + , and Pt 2 + (Fig,. 4.2.20)? Think about it. They are all considered soft acids. Cu + is a relatively low period 4 element, but has only a 1+ charge, and has d-orbitals for π-bonding. Hg 2 + , Pd 2 + , and Pt 2 + have a somewhat higher 2+ charge, but are period 5 and 6 elements, and also have d-orbitals for π-bonding. Pt 2 + would be expected softer than Pd 2 + because of its higher period.
Quantitative Measures for Hardness
Note that there is a quantitative measure for the Hardness of a Lewis acid and Lewis base. For the time being, it is enough to recognize that such a quantitative scale exists, and focus instead on the qualitative understanding of the concept and how it can be useful in explaining some observable phenomena.
The HSAB Concept and Solubilities
Because the HSAB concept can estimate the strength of the interactions between Lewis acids and Lewis bases, it can also estimate a number of other properties that derive from this strength of interactions. For example, it can be used to estimate solubilities. When the Lewis acid-base interaction between cation and anion is strong we would expect low solubility, when the interaction is weak then we would expect high solubility.
For example, it is know that the solubility of silver halogenides in water increases from AgI to AgBr to AgCl to AgF (Fig. 4.2.23). This is in accordance with the HSAB concept. Ag + is considered soft, and thus it would make the strongest interactions with the softest anion, the iodide I - . Ag + would make the weakest interactions with F - , because it is the hardest.
What would be our expectations for the lithium halogenides (Fig. 4.2.24)? In this case, we would expect the solubility to decline from LiI to LiBr, to LiCl, to LiF. Why? This is because Li + is a hard cation, and thus the strongest interactions should result with F - . Consequently, LiF would have the lowest solubility. I - is the softest anion, thus it should make the weakest interactions with Li + .Consequently, the LiI would have the highest solubility. Is this what we observe experimentally? The experimentally greatest observed solubility is that of LiBr, followed by LiCl, followed by LiI. LiF has the lowest solubility. We can see that the LiI solubility is not what we expected. Instead of having the highest solubility, it has the second-lowest solubility. We can see here the limitations of the HSAB concept. There are also other factors that determine solubility, in particular solvation enthalpy. I - has a very low hydration enthalpy, which explains the lower than expected LiI solubility. In a way, the HSAB concept is able to explain the low hydration enthalpy of I - because it is based on the strength of interaction between I - and water. The water is a hard acid and therefore interacts only weakly with a soft base like I - . This can serve as an explanation for the low hydration enthalpy.
Another good example to illustrate the effects of solvation enthalpy on solubility is the solubility of the silver halogenides in liquid ammonia (not aqueous ammonia). It is actually reversed, the AgF has the smallest solubility , and the AgI has the highest solubility. The HSAB interaction between Ag + and the halogenide ions are the same no matter of the solvent. Therefore, they cannot serve as an explanation. Rather, we can argue that the reverse enthalpies of solvation in liquid ammonia compared to liquid water are responsible for the inverse behavior. From the standpoint of HSAB, the ammonia molecules are already significantly softer than the water molecules, therefore interactions with the soft anions become significantly stronger.
The HSAB Concept and Stability
The HSAB concept can also be used to estimate thermodynamic stabilities of compounds, such as decomposition points, melting points etc. Generally, the greater the acid-base interactions the greater the expected thermodynamic stability. Let us do couple of exercises to practice this concept.
What order of thermodynamic stability would you expect for the alkali oxides (Fig. 4.2.25)? The answer is: The stability declines with increasing period of the alkali metal. Why? The oxide anion is considered a hard base due to its relatively small radius. Thus, the strongest interactions are expected with the Li + which is the hardest alkali metal, and the weakest interactions would be expected for the Cs + which is the softest alkali metal. This is in line with experimental observations. Only Li gives Li 2 O when burned in O 2 , Na gives sodium peroxide and the remaining alkali metals give superoxides.
We can ask the same question for the earth alkaline oxides (Fig. 4.2.26). Similarly, the stability of BeO is the highest because Be has the highest hardness. BaO has the lowest stability because Ba 2 + is the softest earth alkali cation. Ba gives barium peroxide instead of barium oxide when burned in O 2 .
The HSAB Concept and Acidity
The HSAB concept can also explain Brønsted acidity. How?
Let us look at the series H 2 O, H 2 S, and H 2 Se (Fig. 4.2.27). The Brønsted acidity increases from H 2 O to H 2 S to H 2 Se. Why? H + is a hard acid, and therefore the strongest interactions would be expected with the hardest base, the oxide ion, and the weakest interactions would be expected with the softest base, the Se 2 - anion. Therefore, H 2 Se loses a proton most easily, making it the strongest acid. For H 2 O the acidity is the smallest because the interactions between H + and O 2- are the greatest.
Let us go to a somewhat more complicated example (Fig. 4.2.28). The acidity of perchloric acid, chloric acid, chlorous acid, and hypochlorous acid declines from HClO 4 to HClO 3 to HClO 2 to HClO. In this case all protons are bound to oxygen, so we cannot argue as before. However, we can argue that the negative charge in the anions of the acids is most delocalized in the case of the perchloric acid because the greatest number of resonance structures can be drawn for perchloric acid. Because the negative charge is most delocalized, the electron is most polarizable, and thus the softest. For the hypochloric acid we have the opposite case. There is no electron delocalization possible and only one resonance structure can be drawn for the hypochlorite anion. It is therefore the hardest, interacting the strongest with the proton.
Lastly, let us think about the relative basicity of NH 3 , PH 3 , and AsH 3 (Fig. 4.2.29)? The N atom is the hardest base, and the interactions with protons are the strongest. Therefore, NH 3 is the strongest base. AsH 3 is the weakest base because As is the softest atom making the weakest interactions with protons.
Dr. Kai Landskron ( Lehigh University ). If you like this textbook, please consider to make a donation to support the author's research at Lehigh University: Click Here to Donate .