Law of Mass Action/Law of Equilibrium

(Guldberg-Waage Law)

Statement of LMA

In 1864, two Norwegian chemists Cato Maximillian (C.M) Guldberg (1836–1902) and Peter (P) Waage (1833–1900) studied experimentally a number of equilibrium reactions and put forward their results as a generalization known as law of mass action or equilibrium law.

This law gives a quantitative relationship between the rate of reaction and the active mass (molar concentration) of reacting substances.

The rate of a chemical reaction is directly proportional to the product of the active masses (molar concentrations in mole/dm³) of reacting substances at constant temperature.

OR

At a given temperature, the product of concentrations of the reaction products raised to the respective stoichiometric coefficient in the balanced chemical equation divided by the product of concentrations of the reactants raised to their individual stoichiometric coefficients has a constant value. This is known as the Equilibrium Law or Law of Chemical Equilibrium.

The Molar Concentration in mole/dm³ (mole/litre) of substances is termed as ACTIVE MASS which represented by square brackets; [  ]. Molar concentration of different species is indicated by enclosing these in square bracket and, it is implied that these are equilibrium concentrations.

While writing expression for equilibrium constant, symbol for phases (s, l, g) are generally ignored.

Mathematical Expression of LMA 

 For a general reaction: A + B ⇌ Product ; Law of Mass Action can be written expressed as

Here,

[A]  =Molar concentration of A in mole/dm³                                    

[B]  =Molar concentration of B in  mole/dm³

Importantly, the Equilibrium Law expresses K_c as a relationship between the concentrations of products and reactants in a system at equilibrium and it provides us with a quantifying means to determine the position of the equilibrium.

The magnitude of the equilibrium constant informs us of the relative proportion of products and reactants, providing us information on the extent of the reaction (but not reaction rate). 

Generally the subscript ‘eq’ (used for equilibrium) is omitted from the concentration terms. It is taken for granted that the concentrations in the expression for K_c are equilibrium values.

Active Mass

Active mass represent amount of substance. It may be expressed in two ways:

1.         Active mass in terms of concentration (mol L^-1)

2.         Active mass in terms of partial pressure in atm only for gases.

 

Derivation of Equilibrium Constant (K_c) Expression/LMA Expression

To derive equilibrium constant (K_c), consider a general reversible reaction in which reactants A and B combine to form products C and D. At equilibrium state, the concentrations of A, B, C and D become constant. Let [A], [B], [C] and [D] are the active masses or molar concentrations in mole/dm³ of A, B, C and D at equilibrium state respectively.

According to Law of Mass Action, rate of forward reaction and backward reactions are given as:

Where K_f and K_r are the proportionality constants known as the specific rate constants for forward reaction and specific rate constants for reverse reaction respectively. Their values depend upon the nature of reactants and products.

 Since, at the equilibrium state:                                                                         

                               

 

The ratio K_f/K_r is a constant quantity at any specific temperature, which is known as Equilibrium Constant for the Reaction denoted by K_c (or simply K) where subscript ‘c’ indicates concentrations in mole/dm³.

The above expression is known as Equilibrium Constant Expression or K_c–Expression or Law of Mass Action Expression or LMA-Expression, which is written by placing the active masses of products in the numerator and active masses of reactants in the denominator with each concentration term raised to a power equal to the coefficient of the substance in the balanced equation.

Unit of Kc

1.    The unit of K_c (and K_p) depend on the specific reaction and the unit of K_c (and K_p) varies depending on the terms in its expression.

2.         K_c has dimensions equal to

(concentration)^c+d‒a‒b or (concentration)^{(c+d)‒(a+b)} or (concentration)^∆n or (mol/dm³)^∆n or “mol^{(c+d)‒(a+b)} dm^{‒3[(c+d)‒(a+b)]}”

where ∆n is equal to the total number of moles of products minus the total number of moles of reactants.

3. K_c will be dimensionless (has no unit) only for those reactions for which a + b = c + d signifying that the total number of moles of reactants and products are equal.

4.  In thermodynamics, K_c (and K_p) is defined to have no unit.

Applications of Law of Equilibrium

The law of equilibrium is used to calculate the equilibrium constant of a reversible reaction. The knowledge of K_c is very valuable for a chemist or a manufacturer. [Through the knowledge of K_c, a chemist can control the direction and the extent of chemical reactions by changing the reaction conditions]. Importantly, the Equilibrium Law expresses K_c as a relationship between the concentrations of products and reactants in a system at equilibrium and it provides us with a quantifying means to determine the position of the equilibrium. The magnitude of the equilibrium constant informs us of the relative proportion of products and reactants, providing us information on the extent of the reaction (but not reaction rate). 

K_c is used for:

1. Prediction of direction of reaction

2. Prediction of extent of reaction

1. Prediction of Direction of Reaction

The value of K_c is a valuable aid in predicting the direction of reversible reaction at any stage (in which a reaction will shift in order to achieve the equilibrium) provided the initial concentration of the reagents involved is known). For this purpose, we calculate the reaction quotient Q. The reaction quotient, Q (Q_c with molar concentrations and Q_P with partial pressures) is defined in the same way as the equilibrium constant K_c except that the concentrations in Q_c are not necessarily equilibrium values.

The ratio of initial concentration of products and initial concentration of reactants (not necessarily at equilibrium) is called Reaction Quotient (Q or Q_c). The ratio of non-equilibrium concentrations gives us the reaction quotient, Q or Q_c

If the reaction is not at equilibrium, we can determine which way the reaction is moving by taking the current law of mass action ratio and comparing it to the equilibrium constant i.e. To determine in which direction the net reaction will proceed to achieve equilibrium, we compare the values of Q_c and K_c. There are three possibilities: 

2.  Prediction of Extent of Reactions                              

The reversible reactions proceed in forward direction up to a certain limit and then equilibrium is attained. The Extent of Reaction is the limit up to which reactants are changed to products.

The magnitude of the value of K_c of a reversible reaction predicts the extent of the reaction. The numerical value of the equilibrium constant for a reaction indicates the extent of the reaction.

The magnitude of K_c or K_p is directly proportional to the concentrations of products (as these appear in the numerator of equilibrium constant expression) and inversely proportional to the concentrations of the reactants (these appear in the denominator).

A HIGH VALUE OF K_c IS SUGGESTIVE OF A HIGH CONCENTRATION OF PRODUCTS AND VICE-VERSA.

But it is important to note that an equilibrium does not give any information about the rate at which the equilibrium is reached.

We can make the following generalizations concerning the composition of equilibrium mixtures: