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The Law of Mass Action, first expressed by Waage and Guldberg in 1864 [1], states (in modern language) that the rate of a chemical reaction is proportional to probability that the reacting molecules will be found together in a small volume. Historically, Berthollet was one of the first to develop a theory of mass action.[2] By assumption, the probability of finding one reactant molecule in a small volume is independent of finding another reactant molecule in the same volume; therefore, the probability of finding them both in the same volume is the product of their individual probabilities. Vapours of hydrogen chloride in a beaker and ammonia in a test tube meet to form a cloud of a new substance, ammonium chloride A chemical reaction is a process that results in the interconversion of chemical substances. ...
Probability is the chance that something is likely to happen or be the case. ...
Claude Louis Berthollet Claude Louis Berthollet (December 9, 1748 – November 6, 1822) was a French chemist. ...
The probability is proportional to its chemical activity. Sometimes, the activity may be replaced by molar concentration or partial pressure (in gas phase) without significant error. Activity in chemistry is a measure of how different molecules in a non-ideal gas or solution interact with each other. ...
Thus, the law of mass action can be summarized as
| “ | The rate of a chemical reaction is directly proportional to the product of the effective concentrations of each participating molecule. | ” | Reaction here necessarily refers to a single-step reaction. The law will not usually be valid for reactions that progress through forming of intermediates, though the actual rate law for such reactions can be derived exactly or approximately by applying the law of mass action to each separate step.
Example of a single reaction
Consider the following reaction occurring in the gas phase:
There are three reacting molecules so, assuming the reaction is single step, according to the Law of Mass Action, the rate of forming A2B should be proportional to the probability of finding all three in the same space, which is the product of the probabilities of finding each one in that space. Those probabilities are proportional to their activities, so we may write
![r= k times [A]^2 times [B]](http://upload.wikimedia.org/math/8/2/4/824dd790ff8a5d50b6ea6e6fc39d3a19.png)
where k is the overall proportionality constant. For a closed system (see Mass balance), i.e., if no other reactions are creating or destroying A2B, we may write A mass balance (also called a material balance) is an accounting of material entering and leaving a system. ...
![frac{d[A_2B]}{dt} = k times [A]^2 times [B]](http://upload.wikimedia.org/math/7/1/d/71d5dc2559546561babafb36769f9738.png) .
Example of forward and backward reactions (chemical equilibrium) Similarly, a reversible reaction such as  in a closed system results, assuming the reactions are single-step, in the kinetic rate equation ![frac{d[C]}{dt} = k_{AB} times [A]^2 times [B] - k_{CD} times [C] times [D]](http://upload.wikimedia.org/math/1/4/d/14db24aea368f8a88176ef2a02ca3db6.png) The first term on the right-hand side equals the rate of forming C, i.e., the rate of the forward reaction  . By contrast, the second term is the rate of losing C, i.e., the rate of the backward reaction  .
If the system is at chemical equilibrium, the forward rate must equal the backward rate
![k_{AB} times [A]^2 times [B] = k_{CD} times [C] times [D]](http://upload.wikimedia.org/math/8/0/1/80139fbcaca1a95376919afb59accae1.png) Cross-dividing gives us the equilibrium constant Keq ![K_{eq} = frac{[C][D]}{[A]^2[B]} = frac{k_{AB}}{k_{CD}}](http://upload.wikimedia.org/math/9/8/8/988d25e54c0400a79e15e28ebcde6adf.png) Given the equilibrium constant Keq and the overall amounts of the reacting substances, it is usually possible to determine the final equilibrium concentrations of the individual reacting molecules.
Keq is a constant insofar as the individual rate constants kAB and kCD are; if they change (e.g., with temperature or pH), the equilibrium constant will generally change as well.
The equation for Keq is sometimes referred to as the Mass Action Law. This is incorrect, however; it is merely a consequence of the kinetic rate equations that result from the Law of Mass Action.
A different meaning of the term "mass action" Mass action in science is the idea that a large number of small units (especially atoms or molecules) acting randomly by themselves can in fact have a larger pattern. For example, consider a cloud of gas is moving in a given direction. Individual molecules will move in a semi-random walk, but if taken as a whole, they have direction. In mathematics, computer science, and physics, a random walk, sometimes called a drunkards walk, is a formalisation of the intuitive idea of taking successive steps, each in a random direction. ...
However, this use of the term "mass action" is extremely rare and would not be understood among working scientists. The proper term for such phenomena is "collective behavior" or artificial chemistry. An artificial chemistry is a computer model used to simulate various types of systems. ...
See also A mass balance (also called a material balance) is an accounting of material entering and leaving a system. ...
Chemical equilibrium is the state in which the concentrations of the reactants and products have no net change over time. ...
In chemistry, the equilibrium constant is a quantity characterizing a chemical equilibrium in a chemical reaction. ...
A termite cathedral mound produced by a termite colony: a classic example of emergence in nature. ...
References - ^ Waage, P.; Guldberg, C. M. Forhandlinger: Videnskabs-Selskabet i Christiana 1864, 35
- ^ Levere, Trevor, H. (1971). Affinity and Matter – Elements of Chemical Philosophy 1800–1865. Gordon and Breach Science Publishers. ISBN 2881245838.
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