# 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.

The Law of Mass Action, first expressed by Waage and Guldberg in 1864 (Waage, P.; Guldberg, C. M. Forhandlinger: Videnskabs-Selskabet i Christiana 1864, 35) states that the speed of a chemical reaction is proportional to the quantity of the reacting substances. More formally the change of a product quantity is proportional to the product of reactant activities. In the case of a reaction occurring in a gas phase, the activities are equal to the partial pressures. In the case of a well-stirred aqueous medium, the activities are equal to the concentrations. Therefore, if we have a reaction:

[itex]A + A + B \rightarrow A_2B[itex]

The speed of [itex]A_2B[itex] formation is [itex]\frac{d[A_2B]}{dt} = k \times [A]^2 \times [B][itex] where k is a constant.

A general case is given by a reversible reaction such as:

[itex]A + A + B \leftrightarrow C + D[itex] with

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


Which means C and D are produced by the onward reaction, and consumed by the backward reaction. A consequence of the Mass Action Law is that after a sufficient amount of time, there will be an equilibrium between the two reactions and:

[itex]k_{AB} \times [A]2 \times [B] = k_{CD} \times [C] \times [D][itex] resulting in the following equation, often called Mass Action Law itself

[itex]K = \frac{[C][D]}{[A]^2[B]} = \frac{k_{AB}}{k_{CD}}[itex]

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