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Law of Mass Action


The rates of reaction (forward or backward) can be written on the basis of the law of mass action proposed by Guldberg and Waage in 1863. According to this law, the rate of reaction at constant temperature is directly proportional to the product of molar concentrations of reacting species, each raised to a power equal to the corresponding stoichiometric coefficient appearing in the chemical reaction.
Taking an example of the reaction

N2O4(g)  2NO2(g)

we have
Rate of forward reaction, rf [N2O4]
or rf = kf[N2O4]

Rate of backward reaction, rb [NO2]2
or rb=kb[NO2]2

where kf and kb are the constants of proportionality. These constants depend only on the temperature of the system.

Expression of Equilibrium Constant


Since at equilibrium,

rate of forward reaction = rate of backward reaction
we will have


where the subscript eq stands for the concentration prevailing at equilibrium. The above expression can be rewritten as


Since kf and kb are constants of proportionality, the ratio kf/kb is also constant and is known as the equilibrium constant (symbol: K). Since for a given reaction kf and kb depend only on the temperature, the equilibrium constant K will also depend only on the temperature of the system. Its value will be independent of the concentrations of reactants (or/and products) taken at the start of the reaction. A given chemical equilibrium may be started by taking either reactants or products or a mixture of reactants and products and whatever may be their initial concentrations, the reaction at equilibrium satisfies the expression of equilibrium constant, i.e. the reaction will be adjusted in such a manner to give the same value of equilibrium constant.

The expression for equilibrium constant can be written directly based on the given reaction. In the numerator, we take the product of molar concentrations of the right-hand species (i.e. products), whereas in the denominator we take the product of molar concentrations of the left-hand species (i.e. reactants) and each concentration term is raised to a power which is the stoichiometric number of the species involved in the reaction.

Expressions for equilibrium constants of a few reactions
 

Reaction

Expression for equilibrium constant

H2(g) + I2(g) 2HI(g)

N2(g) + 3H2(g) 2NH3(g)

2H2O(g) 2H2(g) + O2(g)

2SO2(g) + O2(g) 2SO3(g)

N2O4(g) 2NO2(g)

Keq = [HI]2/[H2][I2]

Keq = [NH3]2/[N2][H2]3

Keq =[H2]2[O2]/[H2O]2

Keq=[SO3]2/[SO2]2{O2]

Keq=[NO2]2/[N2O4]

Expression of Equilibrium Constant


At equilibrium,
rate of forward reaction = rate of backward reaction
we will have

 

where the subscript eq stands for the concentration prevailing at equilibrium. The above expression can be rewritten as
 

Since kf and kb are constants of proportionality, the ratio kf/kb is also constant and is known as the equilibrium constant (symbol: K). Since for a given reaction kf and kb depend only on the temperature, the equilibrium constant K will also depend only on the temperature of the system. Its value will be independent of the concentrations of reactants (or/and products) taken at the start of the reaction. A given chemical equilibrium may be started by taking either reactants or products or a mixture of reactants and products and whatever may be their initial concentrations, the reaction at equilibrium satisfies the expression of equilibrium constant, i.e. the reaction will be adjusted in such a manner to give the same value of equilibrium constant.

The expression for equilibrium constant can be written directly based on the given reaction. In the numerator, we take the product of molar concentrations of the right-hand species (i.e. products), whereas in the denominator we take the product of molar concentrations of the left-hand species (i.e. reactants) and each concentration term is raised to a power which is the stoichiometric number of the species involved in the reaction.

Expressions for equilibrium constants of few reactions
 

Reaction

Expression for equilibrium constant

H2(g) + I2(g) 2HI(g)

N2(g) + 3H2(g) 2NH3(g)

2H2O(g) 2H2(g) + O2(g)

2SO2(g) + O2(g) 2SO3(g)

N2O4(g) 2NO2(g)

Keq = [HI]2/[H2][I2]

Keq = [NH3]2/[N2][H2]3

Keq =[H2]2[O2]/[H2O]2

Keq=[SO3]2/[SO2]2{O2]

Keq=[NO2]2/[N2O4]





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