Law of Mass Action

Law of Mass Action relates to the rate of a chemical reaction. It states that the rate of a reaction is directly proportional to the concentrations of its reactants. More precisely, the rate of a chemical reaction is directly proportional to the product of its reactant concentrations raised to their respective stoichiometric coefficients at constant temperature and pressure. This implies that an increase in reactant concentration would lead the reaction to move forward at a faster rate. The law of mass action forms the basis for equilibrium constant expression, which helps in quantifying the dynamics of the reaction.

In this article, we will discuss what is meant by the Law of Mass Action, Equilibrium Constant, Chemical Equilibrium, applications of the law and related frequently asked questions.

What is the Law of Mass Action?

The Law of Mass Action states that,

The rate of a chemical reaction is directly proportional to the product of its reactant concentrations raised to the power as their respective stoichiometric coefficients at constant temperature and constant pressure.

Mathematical Expression of the Law of Mass Action

Let us see that how law of mass action can be expressed mathematically. For instance, a chemical reaction is represented as follows,

aA + bB → cC + dD

Derivation of Law of Mass Action

According to the law of mass action,

Rate of reaction ∝ [A]^a[B]^b

Replacing the proportionality sign with equal sign by introducing the proportionality constant (K_f), we get,

Rate of forward reaction = K_f [A]^a[B]^b

K_f is called the velocity constant for forward reaction. The above equation represents the rate of forward reaction. Similarly, rate for backward reaction can be written as,

Rate of backward reaction = K_b[C]^c[D]^d

K_b is called the velocity constant for backward reaction.

Equilibrium constant

Equilibrium constant (K_c) is the ratio of velocity factors for forward reaction (K_f) and backward reaction (K_b). At equilibrium, the rate of forward reaction equals the rate of backward reaction. Mathematically,

Rate of Forward reaction = Rate of Backward reaction

K_f [A]^a[B]^b = K_b[C]^c[D]^d

Rearranging the terms, we get,

K_c = K_f/K_b = [C]^c[D]^d/[A]^a[B]^b

K_c is also called as reaction constant. Another related term is reaction quotient or concentration quotient denoted as Q_c, which is obtained by substituting concentrations of reactants and products at any instant in the expression of K_c.

Concentration Quotient (Q_c) versus Equilibrium Constant (K_c)

The relationship between K_c and Q_c gives information about the direction in which reaction would proceed.

• If Q_c < K_c, the reaction proceeds in forward direction.
• If Q_c = K_c, the reaction is at equilibrium.
• If Q_c > K_c, the reaction proceeds in backward direction.

Law of Mass Action in a Gaseous System

For chemical reactions involving gaseous components, pressure plays more important role than concentration as gases can be more conveniently expressed in terms of pressure. Thus, for a gaseous system, the expression for law of mass action involves partial pressures of the respective components instead of concentrations. For instance, consider a general reversible gaseous reaction as follows:

aA(g) + bB(g) ⇌ cC(g) + dD(g)

The expression for equilibrium constant for the above reaction would be written as follows:

K_eq = (P_C)^c(P_D)^d/(P_A)^a(P_B)^b

where, P_A, P_B, P_C and P_D represent the partial pressures of gases A, B, C, and D respectively at equilibrium.

This formulation in terms of partial pressures is useful for gas phase reactions as pressure is relatively easier to measure for gases and thus shift in equilibrium can be predict based on pressure changes.

Example of Law of Mass Action

Let us see that how law of mass action can be applied to obtain expression for a practical reaction. Consider the following chemical equation which represents the dissociation of ammonium chloride (NH₄Cl) in water.

NH₄Cl (aq) ⇌ NH₄⁺(aq) + Cl^–(aq)

According to law of mass action, equilibrium constant for above reaction would be,

K_eq = [NH₄⁺][Cl^–]/[NH₄Cl]

where, [NH₄⁺] and [Cl^–] are the concentrations of ions and [NH₄Cl] is the concentration of ammonium chloride at equilibrium.

Similarly, one can obtain expression of equilibrium constant for any chemical reaction using the law of mass action.

Chemical Equilibrium

In chemistry, equilibrium is state in dynamics of a chemical reaction when rate of forward reaction equals to the rate of backward reaction. At this state, concentrations of reactants and products remain unchanged over time. It is influenced by a variety of factors such as temperature, pressure (for gases), and concentration. It is quantitatively represented by various constants such as K_f, K_b, K_c and K_p discussed later in this article.

Le Chatelier’s Principle

Le Chatelier’s Principle states that,

When a chemical reaction is disturbed from its equilibrium state by changing conditions such as temperature, pressure, etc., the reaction proceeds in such a direction (forward or backward) so as to counteract the change occurred.

Representation of the Equilibrium Constant

For a chemical reaction that is represented by the following equation,

aA + bB → cC + dD

Equilibrium Constant (K_c) expression is written as follows,

K_c = [C]^c[D]^d/[A]^a[B]^b

K_c is related to concentrations of reactants and products. In a similar expression, when partial pressures of the gaseous components is substituted, it becomes K_p and when mole fractions are substituted, it is called K_x, i.e.

K_p = p_A^a.p_B^b/p_C^cp_D^d

K_x = [X_C]^c[X_D]^d/[X_A]^a[X_B]^b

Relation between K_c, K_p and K_x

The relation between K_p and K_c is given as,

K_p = K_c (RT)^Δng

where,

• K_c = equilibrium constant,
• K_p = equilibrium constant in terms of partial pressures
• R = gas constant
• T = temperature
• Δ_ng = number of gaseous components in products – number of gaseous components in reactants

And, the relation between K_x and K_c is given as,

K_x = K_c(RT/p_T)^Δng

where,

• K_c = equilibrium constant,
• K_x = equilibrium constant in terms of mole fractions,
• R = gas constant,
• T = temperature,
• p_T = total pressure,
• Δ_ng = number of gaseous components in products – number of gaseous components in reactants

Ostwald’s Dilution Law

Ostwald’s Dilution Law is a principle that relates degree of dissociation of a weak electrolyte with equilibrium constant of the dissociation reaction. For instance, consider the chemical equation written as follows,

HA ⇌ H⁺ + A^–

It represents the dissociation reaction of a weak electrolyte HA (weak acid molecule). H⁺ and A^– represent the hydrogen ion and the conjugate base ion, respectively. According to law of mass action, the equilibrium constant for the dissociation reaction would be written as,

K_a = [H⁺][A^–]/[HA]

Ostwald’s Dilution Law states that for a weak electrolyte, the degree of dissociation (α) increases with dilution. Mathematically, it is expressed as:

α = √(K_a/C)

where,

• α = degree of dissociation
• K_a = equilibrium constant of the dissociation reaction
• C = initial concentration of the electrolyte

Applications of the Law of Mass Action

Law of Mass Action has crucial applications in field of chemical equilibrium and beyond, discussed as follows,

• The law is used to determine equilibrium constants for reactions and predicting the direction of reaction under various concentrations of reactants and products.
• The law is also used to determine concentrations of reactants and products at equilibrium.
• The law forms a basis for the expression of rate of reaction in terms of reactant concentrations.
• The law can also be used in design of chemical reactors as it helps to determine amount of product formed by using a defined amount of reactants.
• The law is used in environmental chemistry to predict the amount of pollutants in air, water or soil by determining their equilibrium concentrations.
• The law is also used in surface chemistry to analyze behaviour of processes such as adsorption and catalysis.

FAQs on Law of Mass Action

What do you mean by the Law of Mass Action?

The law of mass action is a law which relates the rate of reaction with the concentration of reactants. It states that the rate of a chemical reaction is directly proportional to the concentrations of its reactants.

What is meant by the equilibrium constant?

Equilibrium constant is the ratio of the product concentrations to the reactant concentrations at equilibrium for a reversible chemical reaction.

How does the Law of Mass Action relate to the Le Chatelier’s principle?

Le Chatelier’s principle defines how a reaction at equilibrium responds to changes in temperature, pressure, or concentration whereas the law of mass action gives a basis for quantitative analysis of changes in reaction rate with changes in reactant or product concentrations.

Does the Law of Mass action apply to irreversible reactions as well?

Yes, the Law holds true for irreversible reactions as well, i.e. the rate of reaction is directly proportional to the concentrations of the reactants.

Are there any limitations to the Law of Mass Action?

Yes, the law doesn’t account for the factors such as reaction mechanisms, catalysts, etc. to determine the rate of reaction.