To write a proper citation we recommend following these steps, which will help you maintain accuracy and clarity in acknowledging sources.
Choose Your Citation Style
Find out the name of the citation style you must use from your instructor, the directions for an assignment, or what you know your audience or publisher expects. Then search for your style at the
Purdue Online Writing Lab
(OWL) or use Google or Bing to find your style’s stylebook/handbook and then purchase it or ask for it at a library.
Create In-text Citations
Find and read your style’s rules about in-text citations, which are usually very thorough. Luckily, there are usually examples provided that make it a lot easier to learn the rules.
Example: Style Guides Are Usually Very Thorough
For instance, your style guide may have different rules for when you are citing:
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Quotations rather than summaries rather than paraphrases
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Long, as opposed to short, quotations.
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Sources with one or multiple authors.
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Books, journal articles, interviews and email, or electronic sources.
Determine the Kind of Source
After creating your in-text citation, now begin creating the full bibliographic citation that will appear on the References or Bibliography page by deciding what kind of source you have to cite (book, film, journal article, webpage, etc.).
Example: Using a Style Guide to Create an In-text Citation
Imagine that you’re using APA style and have the
APA style guide rules for in-text citations open in OWL
. In your psychogeography paper, you want to quote the authors of the book The Experience of Nature, Rachel Kaplan and Stephen Kaplan, which was published in 1989. What you want to quote is from page 38 of the book.
Here’s what you want to quote:
“The way space is organized provides information about what one might want to do in that space. A relatively brief glance at a scene communicates whether there is room to roam, whether one’s path is clear or blocked.”
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Skim the headings in the style guide to remind yourself of what its rules concern.
Since it has rules about the length of quotations, you count the number of words in what you want to quote and find that your quote has 38, which is within the range for short quotations (less than 40), according to the APA style guide.According to the rule for short quotations, you see that you’re supposed to introduce the quote by attributing the quote to the author (last name only) and adding the publication date in parentheses. You write:
According to the Kaplans (1989)
, “The way space is organized provides information about what one might want to do in that space. A relatively brief glance at a scene communicates whether there is room to roam, whether one’s path is clear or blocked.”
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Then you notice that the example in the style guide includes the page number on which you found the quotation. It appears at the end of the quote (in parentheses and outside the quote marks but before the period ending the quotation). So you add that:
According to the Kaplans (1989), “The way space is organized provides information about what one might want to do in that space. A relatively brief glance at a scene communicates whether there is room to roam, whether one’s path is clear or blocked”
(p.38)
.
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You’re feeling pretty good, but then you realize that you have overlooked the rule about having multiple authors. You have two and their last names are both Kaplan. So you change your sentence to:
According to
Kaplan and Kaplan
(1989), “The way space is organized provides information about what one might want to do in that space. A relatively brief glance at a scene communicates whether there is room to roam, whether one’s path is clear or blocked” (p.38).
So you have your first in-text citation for your final product:
According to Kaplan and Kaplan (1989), “The way space is organized provides information about what one might want to do in that space. A relatively brief glance at a scene communicates whether there is room to roam, whether one’s path is clear or blocked” (p.38).
Study Your Style’s Rules for Bibliographic Citations
Next, you’ll need a full bibliographic citation for the same source. This citation will appear on the References page or Bibliography page or Works Cited page. (APA style, which we’re using here, requires a page called References.) Bibliographic citations usually contain more publication facts than you used for your in-text citation, and the formatting for all of them is very specific.
Example: Bibliographic Citation Rules Are Very Specific
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Rules vary for sources, depending, for instance, on whether they are books, journal articles, or online sources.
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Sometimes lines of the citation must be indented.
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Authors’ names usually appear last name first.
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Authors’ first names of authors may be initials instead.
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Names of sources may or may not have to be in full.
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Names of some kinds of sources may have to be italicized.
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Names of some sources may have to be in quotes.
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Dates of publication appear in different places, depending on the style.
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Some styles require Digital Object Identifiers (DOIs) in the citations for online sources.
Identify Citation Elements
Figure out which bibliographic citation rules apply to the source you’ve just created an in-text citation for. Then apply them to create your first bibliographic citation.
Example: Using a Style Guide to Create a Bibliographic Citation
Imagine that you’re using APA style and have the
APA style guide rules for bibliographic citations open in OWL
. Your citation will be for the book called The Experience of Nature, written by Rachel Kaplan and Stephen Kaplan and published in 1989.
-
You start by trying to apply OWL’s basic rules of APA style, which tell you your citation will start with the last name of your author followed by his or her first initial, and that the second line of the citation will be indented. So you write:
Kaplan, R. and Kaplan, S
. and remind yourself to indent the second line when you get there.
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Since you have two authors, you look for a rule regarding that situation, which requires a comma between the authors and an ampersand between the names. So you write: Kaplan, R.,
&
Kaplan, S.
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Because you know your source is a book, you look for style guide rules and examples about books. For instance, the rules for APA style say that the publication date goes in parentheses, followed by a period after the last author’s name. And that the title of the book is italicized. You apply the rules and examples and write the publication information you know about your source: Kaplan, R., & Kaplan, S.
(1989). The Experience of Nature.
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Next, you look at the rules and examples of book citations and notice that they show the city where the book was published and the publisher. So you find that information about your source (in a book, usually on the title page or its back) and write: Kaplan, R., & Kaplan, S. (1989). The Experience of Nature.
Cambridge:
Cambridge University Press.
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Congratulations, especially about remembering to indent that line! You have created the first bibliographic citation for your final product.
Repeat the Steps for Creating an In-text Citation and a Bibliographic Citation for Each of Your Sources
Create your bibliographic citation by arranging publication information to match the example you chose in "Study Your Style’s Rules for Bibliographic Citations". Pay particular attention to what is and is not capitalized and to what punctuation and spaces separate each part that the example illustrates.


5.E: Oscillations and Waves (Exercise)
Conceptual Questions
6.1: Period and Frequency in Oscillations
1. If an oscillation occurs more rapidly, how does the period of oscillation change? How does the frequency change?
2. Give examples of natural phenomena that occur with constant frequency (or period) over a length of time.
6.2: Simple Harmonic Motion- A Special Periodic Motion
3. What conditions must be met to produce simple harmonic motion?
4. (a) If frequency is not constant for some oscillation, can the oscillation be simple harmonic motion?
(b) Can you think of any examples of harmonic motion where the frequency may depend on the amplitude?
5. Give an example of a simple harmonic oscillator, specifically noting how its frequency is independent of amplitude.
6. Explain why you expect an object made of a stiff material to vibrate at a higher frequency than a similar object made of a spongy material.
7. As you pass a freight truck with a trailer on a highway, you notice that its trailer is bouncing up and down slowly. Is it more likely that the trailer is heavily loaded or nearly empty? Explain your answer.
8. Some people modify cars to be much closer to the ground than when manufactured. Should they install stiffer springs? Explain your answer.
6.3: Forced Oscillations and Resonance
9. Give additional examples of resonance phenomenon from everyday life.
10. What "damps" the resonance of a forced oscillation? What are the dynamics of "damping" and what physical quantity is involved?
6.4: Waves
11. Give one example of a transverse wave and another of a longitudinal wave, being careful to note the relative directions of the disturbance and wave propagation in each.
12. What is the difference between propagation speed and the frequency of a wave? Does one or both affect wavelength? If so, how?
13. Given a wave of frequency ff traveling with wave speed \(v_{\text {w }}\), what happens to the wave speed if the frequency doubles? What happens to the wavelength?
6.5: Wave Interference- Standing Waves and Beats
14. How does destructive interference occur? What do you see in a destructive interference?
15. Explain how noise-cancelling headphones work in terms of wave interference phenomena.
16. Explain how nodes and antinodes form on standing waves.
17. In the beat phenomenon, the loudness of the sound combined from two sound waves "wobbles" (it increases and decreases over time). Explain how the loudness of the combined sound becomes louder then quieter, even though individual sound waves remain at the same loudness, or amplitude.
6.7: Speed of Sound, Frequency, and Wavelength
18. How do sound vibrations of atoms differ from thermal motion?
19. When sound passes from one medium to another where its propagation speed is different, does its frequency or wavelength change? Explain your answer briefly.
20. For a high-fidelity speaker containing a woofer and a tweeter (see Figure \(\PageIndex{1}\) for example), why is the woofer larger than the tweeter?
6.8: Doppler Effect and Sonic Booms
21. Explain Doppler shift. How does the measured frequency increase or decrease?
22. Due to efficiency considerations related to its bow wake, the supersonic transport aircraft must maintain a cruising speed that is a constant ratio to the speed of sound (a constant Mach number). If the aircraft flies from warm air into colder air, should it increase or decrease its speed? Explain your answer.
23. When you hear a sonic boom, you often cannot see the plane that made it. Why is that?


14.2: Today's Approaches
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- Last updated
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The momentary usage of brain imaging
How are the known brain imaging methods used? What kind of information can be derived using this methods?
fMRI
fMRI is an non-invasive imaging method that pictures active structures of the brain in a high spatial resolution. For that the participant has to lie in a tube and his brain is pictured. While doing a task active structures in the brain of the participant can be recognised on the recordings.
How?
If parts of the brain are active, the metabolism is also stimulated. The blood, that has an important function in the metabolic transport is flowing to the active nerve cells. The haemoglobin in the red blood cells carries oxygen (oxyhaemogliobin) when flowing to the part that is active and that needs oxygen, to consume and work. With consumption the haemoglobin „delivers“ the oxygen (desoxyhaemoglobin). This leads to local changes in the relative concentration of oxyhemoglobin and desoxyhemoglobin and changes in local blood volume and blood flow. While haemoglobin is oxygenated it is diamagnetic (meaning the material tends to leave the magnetic field), but paramagnetic (material tends to migrate into the magnetic field) while desoxygenated. The magnetic resonance signal of blood is therefore slightly different depending on the level of oxygenation.
By being able to detect the magnetic properties mentioned above, the fMRI-scanner is able to determine alterations in blood flow and blood volume, and construct a picture. This picture shows the brain and its activated parts. While the participant is doing a task the researcher can derive, which brain regions are involved. This is an indirect measure, as the metabolism is measured and not the neuronal activity itself. Furthermore this imaging method has good spatial resolution(where the activity occurs) but low temporal resolution (when the activity occurs), as measurements occur after the neuronal activity.
  The electronic activity of the neuronal cells, that is adding can be measured.
The electronic activity is measured by attaching electrodes to the skin of the head. In most cases the electrodes are installed on a cap, that the participant wears. It is very time-consuming to install the cap correctly on the head of the participant, but it is very important for the outcome, that everything is in the right place. To assure the adding of the signals the electrodes have to be installed geometric and in a parallel configuration. This technique is applied to measure the event-related potential (ERP), potential changes. They are correlated temporal to an emotional, sensoric, cognitive or motoric event. In the experiment a certain event has to be repeated again and again. The type ERP then can be extracted and calculated. This method is not only time-consumptive, also a lot of disrupting factors complicate the measuring. Moreover this method has a very high temporal resolution, but a very low spatial resolution. It is hardly possible to measure activity in deeper brain regions or to detect the source of the activity interpreting only the recordings.
Interdisciplinary Approaches
Cognitive Science
Cognitive science is multidisciplinary science. It comprises areas of cognitive psychology, linguistics, neuroscience, artificial intelligence, cognitive anthropology, computer science and philosophy. Cognitive science concentrates to study the intelligent behaviour of humans, which includes perception, learning, memory, thought and language. Research in cognitive sciences are based on naturalistic research methods such as cognitive neuropsychology, introspection, psychological experimentation, mathematical modelling and philosophical argumentation.
In the beginning of the cognitive sciences the most common method was introspection. It meant that the test subject evaluated his or her own cognitive thinking. In these experiments the researchers were using experienced subjects because they had to analyse and report their own cognitive thinking. Problems can occur when the results are interpreted and the subject has different reports from the same action. Obviously a clear separation is needed between the matters that can be studied by introspection and the ones that are not adequate for this method.
Computational modelling in cognitive science means that the mind is seen as a machine. This approach seeks to express theoretical ideas through computational modelling that generate behaviour similar to humans. Mathematical modelling is based on flow charts. The model's quality is very important to ensure the equivalence of the input and results.
Nowadays the researchers in cognitive sciences use often theoretical and computational models. "This does not exclude their primary method of experimentation with human participants. In cognitive sciences it is also important to bring the theories and the experimenting together. Because it comprises so many fields of science it is important to bring together the most appropriate methods from all these fields. The psychological experiments should be interpreted through a theory that expresses mental representations and procedures. The most productive and revealing way to perform research in cognitive sciences is to combine different approaches and methods together. This ensures overall picture from the research area and it comprises the viewpoints of all the different fields." (Thagard, Cognitive Science) Nevertheless Cognitive Science has not yet managed to succeed in bringing the different areas together. Nowadays it is criticised for not establishing a science on its own. Rather few scientist really address themselves as cognitive scientists. Furthermore the basic metaphor of the brain functioning like a computer is challenged as well as the distinctions between their models and nature (cf. Eysenck & Keane, Cognitive Psychology, pp. 519-520). This of course brings up a lot of work for the future. Cognitive Science has to work on better models that explain natural processes and that are reliably able to make predictions. Furthermore these models have to combine multiple mental phenomena. In addition to that a general "methodology for relating a computational model's behaviour to human behaviour" has to be worked out. Hereby the strength of such models can be increased. Apart from that Cognitive Science needs to establish an identity with prominent researchers that avow themselves to Cognitive Science. And finally its biggest goal, the creation of a general unifying theory of human cognition (see Theory Part), has to be reached (cf. ibid, p. 520).
Experimental Cognitive Psychology
Psychological experimentation studies mental functions. This is done with indirect methods meaning reasoning. These studies are performed to find causal relations and the factors influencing behaviour. The researcher observes visible actions and makes conclusions based on these observations. Variables are changed one at a time and the effect of this change is being observed. The benefits of experimental researching are that the manipulated factors can be altered in nearly any way the researcher wants. From this point it is finally possible to find causal relations.
In being the classical approach within the field of cognitive psychology, experimental studies have been the basis for the development of numerous modern approaches within contemporary Cognitive Psychology. Its empirical methods have been developed and verified over time and the gained results were a foundation for many enhancements contributed to the field of psychology.
Taking into consideration the established character of experimental cognitive psychology, one might think that methodological changes are rather negligible. But recent years came up with a discussion concerning the question, whether the results of experimental CP remain valid in the “real world” at all. A major objection is that the artificial environment in an experiment might cause that certain facts and coherences are unintentionally ignored, which is due to the fact that for reasons of clarity numerous factors are suppressed (cf. Eysenck & Keane, Cognitive Psychology, pp. 514–515). A possible example for this is the research concerning attention. Since the attention of the participant is mainly governed by the experimenter’s instructions, its focus is basically determined. Therefore "relatively little is known of the factors that normally influence the focus of attention" (ibid, p. 514). Furthermore it turns out to be problematic that mental phenomena are often examined in isolation. While trying to make the experimental setup as concise as possible (in order to get clearly interpretable results) one decouples the aspect at issue from adjacent and interacting mental processes. This leads to the problem that the results turn out to be valid in the idealised experimental setting only but not in “real life”. Here multiple mental phenomena interact with each other and numerous outer stimuli influence the behaviour of mental processes. The validity gained by such studies could only be characterised as an internal validity (which means that the results are valid in the special circumstances created by the experimenter) but not as an external validity (which means that the results stay valid in changed and more realistic circumstances) (cf. ibid, p. 514). These objections lead to experiments which have been developed to refer closer to "real life". According to these experiments "real-world" phenomena like 'absent-mindedness', 'everyday memory' or 'reading' gain importance. Nevertheless the discussion remains whether such experiments really deliver new information about mental processes. And whether these 'everyday phenomenon studies' really become broadly accepted greatly depends on the results current experiments will deliver.
Another issue concerning experimental setups in cognitive psychology is the way individual differences are handled. In general the results from an experiment are generated by an analysis of variance. This causes that results which are due to individual differences are averaged out and not taken into further consideration. Such a procedure seems to be highly questionable, especially if put into the context of an investigation of Bowers in 1973, which showed that over 30% of the variance in such studies are due to individual differences or their interaction with the current situation (cf. ibid, p. 515). Based on such facts one challenge for future experimental cognitive psychology is the analysis of individual differences and finding way to include knowledge about such differences in general studies.
Cognitive Neuroscience
Another approach towards a better understanding of human cognition is cognitive neuroscience. Cognitive neuroscience lies at the interface between traditional cognitive psychology and the brain sciences. It is a science whose approach is characterised by attempts to derive cognitive level theories from various types of information, such as computational properties of neural circuits, patterns of behavioural damage as a result of brain injury or measurements of brain activity during the execution of cognitive tasks (cf. www.psy.cmu.edu). Cognitive neuroscience helps to understand how the human brain supports thought, perception, affection, action, social process and other aspects of cognition and behaviour, including how such processes develop and change in the brain over time (cf. www.nsf.gov).
Cognitive neuroscience has emerged in the last decade as an intensely active and influential discipline, forged from interactions among the cognitive sciences, neurology, neuroimaging, physiology, neuroscience, psychiatry, and other fields. New methods for non-invasive functional neuroimaging of subjects performing psychological tasks have been of particular importance for this discipline. Non-invasive functional neuroimaging includes: positron emission tomography (PET), functional magnetic resonance imaging (fMRI), magnetoencephalography (MEG), optical imaging (near infra-red spectroscopy or NIRS), anatomical MRI, and diffusion tensor imaging (DTI) The findings of cognitive neuroscience are directed towards enabling a basic scientific understanding of a broad range of issues involving the brain, cognition and behaviour. (cf. www.nsf.gov).
Cognitive neuroscience becomes a very important approach to understand human cognition, since results can clarify functional brain organisation, such as the operations performed by a particular brain area and the system of distributed, discrete neural areas supporting a specific cognitive representation.  Another importance of cognitive neuroscience is that cognitive neuroscience provides some ways that allow us to "obtain detailed information about the brain structures involved in different kinds of cognitive processing" (Eysenck & Keane, Cognitive Psychology, p. 521). Techniques such as MRI and CAT scans have proved of particular value when used on patients to discover which brain areas are damaged. Before non-invasive methods of cognitive neuroscience were developed localisation of "brain damage could only be established by post mortem examination" (ibid). Knowing which brain areas are related to which cognitive process would surely lead to obtain a clearer view of brain region, hence, in the end would help for a better understanding of human cognition processes. Another strength of cognitive neuroscience is that it serves as a tool to demonstrate the reality of theoretical distinctions. For example, it has been argued by many theorists that implicit memory can be divided into perceptual and conceptual implicit memory; support for that view has come from PET studies, which show that perceptual and conceptual priming tasks affected different areas of the brain (cf. ibid, pp. 521-522). However, cognitive neuroscience is not that perfect to be able to stand alone and answer all questions dealing with human cognition. Cognitive neuroscience has some limitations, dealing with data collecting and data validity. In most neuroimaging studies, data is collected from several individuals and then averaged. Some concern has arose about such averaging because of the existence of significant individual differences. Though the problem was answered by Raichle (1998), who stated that the differ in individual brain should be appreciated, however general organising principles emerge that transcend these differences, a broadly accepted solution to the problem has yet to be found (cf. ibid, p. 522).
Cognitive Neuropsychology
Cognitive Neuropsychology maps the connection between brain functions and cognitive behaviour. Patients with brain damages have been the most important source of research in neuropsychology. Neuropsychology also examines dissociation (“forgetting”), double dissociation and associations (connection between two things formed by cognition). Neuropsychology uses technological research methods to create images of the brain functioning. There are many differences in techniques to scan the brain. The most common ones are EEG (Electroencephalography), MRI and fMRI (functional Magnetic Resonance Imaging) and PET (Positron Emission Tomography).
Cognitive Neuropsychology became very popular since it delivers good evidence. Theories developed for normal individuals can be verified by patients with brain damages. Apart from that new theories could have been established because of the results of neuropsychological experiments. Nevertheless certain limitations to the approach as it is today cannot be let out of consideration. First of all the fact that people having the same mental disability often do not have the same lesion needs to be pointed out (cf. ibid, pp.516-517). In such cases the researchers have to be careful with their interpretation. In general it could only be concluded that all the areas that the patients have injured could play a role in the mental phenomenon. But not which part really is decisive. Based on that future experiments in this area tend to make experiments with a rather small number of people with pretty similar lesion respectively compare the results from groups with similar syndromes and different lesions. In addition to that the situation often turns out to be vice versa. Some patients do have pretty similar lesions but show rather different behaviour (cf. ibid, p.517). One probable reason therefore is that the patients differ in their age and lifestyle (cf. Banich, Neuropsychology, p.55). With better technologies in the future one will be better able to distinguish the cases in which really the various personalities make the difference or in which cases the lesions are not entirely equal. In addition to that the individual brain structures which may cause the different reactions to the lesions will become a focus of research. Another problem for Cognitive Neuropsychology is that their patients are rare. The patients which are interesting for such research have lesions of an accident or suffered during war. But in addition there are differences in the manner of the lesion. Often multiple brain regions are damaged which makes it very hard to determine which of them is responsible for the examined phenomenon. The dependency on chance whether there are available patients will remain in future. Thereby predictions concerning this aspect of the research are not very reliable.  Creative thought or organisational planning are examples (cf. Eysenck & Keane, Cognitive Psychology, p.517). A possible outcome of the research is that those activities rely on parallel processing. This would support the idea of the modification of the information processing theory that will be discussed later on. But if it shows up that a lot of mental processes depend on such parallel processing it would turn out to be a big drawback for Cognitive Psychology since its core is the modularization of the brain and the according phenomena. In this context the risk of overestimation and underestimation has to be mentioned. The latter occurs because Cognitive Psychology often only identifies the most important brain region for the mental task. Other regions that are related thereto could be ignored. This could turn out to be fundamental if really parallel processing is crucial to many mental activities. Overestimation occurs when fibers that only pass the damaged brain region are lesioned, too. The researcher concludes that the respective brain region plays an important role in the phenomenon he analyses even though only the deliverance of the information passed that region (cf. ibid). Modern technologies and experiments here have to be developed in order to provide valid and precise results.
Unifying Theories
A unified theory of cognitive science serves the purpose to bring together all the vantage points one can take toward the brain/mind. If a theory could be formed which incorporates all the discoveries of the disciplines mentioned above a full understanding would be tangible.
ACT-R
ACT-R is a Cognitive Architecture, an acronym for Adaptive Control of Thought–Rational. It provides tools which enable us to model the human cognition. It consists mainly of five components: Perceptual-motor modules, declarative memory, procedural memory, chunks and buffers. The declarative memory stores facts in “knowledge-units”, the chunks. These are transmitted through the modules respective buffers, which contain one chunk at a time. The procedural memory is the only one without an own buffer, but is able to access the contents of the other buffers. For example those of the perceptual-motor modules, which are the interface with the (simulated) outer world. Production is accomplished by predefined rules, written is LISP. The main character behind it is John R. Anderson who tributes the inspiration to Allan Newell.
SOAR
SOAR is another Cognitive Architecture, an acronym for State, Operator And Result. It enables one to model complex human capabilities. Its goal is to create an agent with human-like behaviour. The working principles are the following: Problem-solving is a search in a problem-space. Permanent Knowledge is represented by production rules in the production memory. Temporary Knowledge is represented by objects in the working memory. New Goals are created only if a dead end is reached. The learning mechanism is Chunking. Chunking: If SOAR encounters an impasse and is unable to resolve it with the usual technique, it uses “weaker” strategies to circumvent the dead end. In case one of these attempts leads to success, the respective route is saved as a new rule, a chunk, preventing the impasse to occur again. SOAR was created by John Laird, Allen Newell and Paul Rosenbloom.
Neural Networks
There are two types of neural networks: biological and artificial.
A biological NN consists of neurons which are physically or functionally connected with each other. Since each neuron can connect to multiple other neurons the number of possible connections is exponentially high. The connections between neurons are called synapses. Signalling along these synapses happens via electrical signalling or chemical signalling, which induces electrical signals. The chemical signalling works by various neurotransmitters.
Artificial NN are divided by their goals. One is that of artificial intelligence and the other cognitive modelling. Cognitive modelling NN try to simulate biological NN in order to gain better understanding of them, for example the brain. Until now the complexity of the brain and similar structures has prevented a complete model from being devised, so the cognitive modelling focuses on smaller parts like specific brain regions. NNs in artificial intelligence are used to solve distinct problems. But though their goals differ the methods applied are very similar. An artificial NN consist of artificial neurons (nodes) which are connected by mathematical functions. These functions can be of other functions which in turn can be of yet other functions and so on. The actual work is done by following the connections according to their weights. Weights are properties of the connections defining the probability of the specific route to be taken by the program and can be changed by it, thus optimizing the main function. Hereby it is possible to solve problems for which it is impossible to write a function “by hand”.


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common ion effect
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effect on equilibrium when a substance with an ion in common with the dissolved species is added to the solution; causes a decrease in the solubility of an ionic species, or a decrease in the ionization of a weak acid or base
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complex ion
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ion consisting of a central atom surrounding molecules or ions called ligands via coordinate covalent bonds
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coordinate covalent bond
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(also, dative bond) covalent bond in which both electrons originated from the same atom
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coupled equilibria
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system characterized the simultaneous establishment of two or more equilibrium reactions sharing one or more reactant or product
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dissociation constant
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(
K
d
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formation constant
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(
K
f
) (also, stability constant) equilibrium constant for the formation of a complex ion from its components
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Lewis acid
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any species that can accept a pair of electrons and form a coordinate covalent bond
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Lewis acid-base adduct
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compound or ion that contains a coordinate covalent bond between a Lewis acid and a Lewis base
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Lewis acid-base chemistry
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reactions involving the formation of coordinate covalent bonds
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Lewis base
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any species that can donate a pair of electrons and form a coordinate covalent bond
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ligand
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molecule or ion acting as a Lewis base in complex ion formation; bonds to the central atom of the complex
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molar solubility
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solubility of a compound expressed in units of moles per liter (mol/L)
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selective precipitation
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process in which ions are separated using differences in their solubility with a given precipitating reagent
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solubility product constant (
K
sp
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equilibrium constant for the dissolution of an ionic compound
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