Mass action

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For the sociology concept, see mass action (sociology).

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. 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.

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.

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.

1 Example of a single reaction
2 Example of forward and backward reactions (chemical equilibrium)
3 A different definition of mass action
4 See also
5 References

[edit] Example of a single reaction

Consider the following reaction occurring in the gas phase:

$A + A + B \rightarrow A_2B$

There are three reacting molecules so, assuming the reaction is single step, according to the Law of Mass Action, the rate of forming $A 2 B$ 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

$r= k \times [A]^2 \times [B]$

where k is the overall proportionality constant. For a closed system (see Mass balance), i.e., if no other reactions are creating or destroying $A 2 B$ , we may write

$\frac{d[A_2B]}{dt} = k \times [A]^2 \times [B]$ .

[edit] Example of forward and backward reactions (chemical equilibrium)

Similarly, a reversible reaction such as

$A + A + B \rightleftharpoons C + D$

in a closed system results, assuming the reactions are single-step, in the kinetic rate equation

$\frac{d[C]}{dt} = k_{AB} \times [A]^2 \times [B] - k_{CD} \times [C] \times [D]$

The first term on the right-hand side equals the rate of forming C, i.e., the rate of the forward reaction $A + A + B \rightarrow C + D$ . By contrast, the second term is the rate of losing C, i.e., the rate of the backward reaction $A + A + B \leftarrow C + D$ .

If the system is at chemical equilibrium, the forward rate must equal the backward rate

$k_{AB} \times [A]^2 \times [B] = k_{CD} \times [C] \times [D]$

Cross-dividing gives us the equilibrium constant $K e q$

$K_{eq} = \frac{[C][D]}{[A]^2[B]} = \frac{k_{AB}}{k_{CD}}$

Given the equilibrium constant $K e q$ and the overall amounts of the reacting substances, it is usually possible to determine the final equilibrium concentrations of the individual reacting molecules.

$K e q$ is a constant insofar as the individual rate constants $k A B$ and $k C D$ are; if they change (e.g., with temperature or pH), the equilibrium constant will generally change as well.

The equation for $K e q$ 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.

[edit] A different definition of 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.

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".