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# What is the law of mass action?

The law of mass action states that the rate of a reaction depends on the concentration of its reactants raised to their stoichiometric coefficients. This law allows the equilibrium concentrations of reactants and products of a reversible chemical reaction to be related to each other. In other words, state the formula for the equilibrium constant.

The law of mass action was enunciated by the Norwegian chemists (and also brothers-in-law) Cato M. Guldberg (1836-1902) and Peter Waage (1833-1900) in 1864. This is one of the fundamental laws of chemistry, since we allows the final equilibrium concentrations to be calculated from the initial quantities.

In addition to this, the law of mass action also allows us to understand in a simple way the effects that changes in the concentrations of any of the species have on the equilibrium. In other words, it allows us to understand how Le Chatelier’s principles work.

Despite being called the “law of mass action,” it does not actually refer to the masses of reactants and products, but rather to their concentrations. The reason it is called the law of mass action and not the law of action of concentrations is because concentration used to be called “active mass.”

## The Law of Mass Action and the Equilibrium Constant

According to the law of mass action, when reversible reactions reach equilibrium it is not because the reaction stops. Rather, equilibrium is reached when the rate of the forward reaction is made equal to the rate of the reverse reaction. When that happens, all chemical species are produced and consumed at the same rate, so their concentrations become constant (stop changing).

Guldberg and Waage discovered that the rates of both reactions (the direct and the inverse) depend on the molar concentration (in mol / L) of their reactants raised to the stoichiometric coefficients. From these observations they were able to find the formula for the equilibrium constant.

By this law, for any reversible chemical reaction that reaches equilibrium,

“… the relationship between the product of the molar concentrations of the products raised to their stoichiometric coefficients and the product of the molar concentrations of the reactants raised to their stoichiometric coefficients is constant at a given temperature.”

This constant is called the “equilibrium constant” and is represented by the symbol K c .

### The equilibrium constant formula

Let’s see what the above statement looks like in the form of a mathematical equation. Let be any reversible chemical reaction like the one presented below, where A and B are the reactants, C and D the products, and a, b, c and d are the respective stoichiometric coefficients of the balanced reaction:

For a generic reaction like this, the equilibrium constant is given by:

where [A], [B], [C], and [D] are the molar concentrations of A, B, C, and D at equilibrium.

### The equilibrium constant in pressures

The above formula for the equilibrium constant applies to any chemical reaction in which all substances are in the same phase (that is, they are all in the aqueous phase, or in the gas phase, for example). However, in the case of gas phase reactions, it is more convenient to work with pressures than with concentrations.

Where p A , p B , p C and p D are the partial pressures of A, B, C and D respectively, and a, b, c and d remain the stoichiometric coefficients. In this case, K P is called the equilibrium pressure constant, and it is related to K C by means of the following formula:

where R is the universal constant for ideal gases and T is the absolute temperature in Kelvin.

### Reactions involving more than one phase

Sometimes a chemical reaction involves the formation of a solid as a precipitate from a solution, or the formation of a liquid from reactants that react in the gas phase. In these cases, the reaction is not happening all in the same phase, so we must modify the formula for the equilibrium constant.

Fortunately, the modifications are very simple. The only thing that we must take into account when writing the formula for the equilibrium constant is that the pure substances that appear as solids or liquids should not be taken into account. If necessary, we put a 1 instead.

In conclusion, the law of mass action allows us to write the formula for the equilibrium constant both in concentrations and in partial pressures. Knowing one of the two, we can find the other from the first.

Finally, we must be careful and review the phase in which all chemical species are found, to know whether or not we should include them in the equilibrium constant.

## Examples of the use of the law of mass action

In the following examples we show how to use the law of mass action to write the formulas for the equilibrium constants for different types of chemical reactions.

### Equilibria of reactions in the gaseous state

#### Example 1: The decomposition of N 2 O 4 in the gas phase

2 O 4 is a brown gas that decomposes according to the following reaction:

For this reaction, the equilibrium constants in concentrations and pressures are given by:

#### Example 2: The oxidation of carbon monoxide

Carbon monoxide is a very toxic gas that can be converted to carbon dioxide by reacting with oxygen according to the following reaction:

For this reaction, the equilibrium constants in concentrations and pressures are given by:

### Acid-base equilibria in aqueous phase

#### Example 3: Self-protolysis of water

The ionic balance of water, also known as the water self-protolysis reaction, is a reversible reaction between two water molecules in a liquid state . The reaction is:

When writing the equilibrium constant for this reaction, we must take into account that, in this case, the only reactant is a pure liquid whose concentration is practically constant. For this reason, it is not included in the formula for the equilibrium constant:

This is a very important equilibrium constant that receives its own name (constant of the ionic product of water) and its own symbol (K W. The W refers to water in English, which is called water ). However, it is an equilibrium constant in concentrations like any other.

### Solubility equilibria

#### Example 4: The solubility equilibrium of silver chloride

When we prepare a saturated solution, a solubility equilibrium is established. In this case, the equilibrium is that of the dissolution of silver chloride, the reaction of which is given by:

The equilibrium constant for this reaction (and for all dissolution reactions) does not include silver chloride (AgCl) as it is a solid. In addition, as in the case of water, these constants also receive a special name which is “solubility product constant”, represented as K ps :

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