Law of Mass Action:
In an attempt to correlate the rate of a chemical reaction and the concentration of the reactants a relationship is suggested by C. M. Guldberg and P. wage known as the law of mass action.
According to this law- ‘The rate of a chemical reaction at a particular temperature is directly proportional to the products of the molar concentration of the reactants at any given time.’
The molar concentration i.e. number of moles per litre is also called active mass. e.g. molar concentration of A is expressed as [A].
Let us consider a reaction between the species A and B, represented as
A + B ——> Products
According to law of mass action,
r (rate of reaction) α [A] [B]
Or, r (rate of reaction) = k [A] [B]
Where, [A] and [B] = molar concentration of A and B respectively.
k = constant, called rate constant
If [A] = [B] = 1, then,
r (rate of reaction) = k
Thus, the rate constant of a reaction at a given temperature is the rate of the reaction when the molar concentration of each reactant is unity (i.e. one).
For a general reaction,
aA + bB + cC ——-> Products
The law of mass action may be written as:
r (rate of reaction) = k [A]a [B]b [C]c
Therefore, the law of mass action may be restated as:
‘The rate of a chemical reaction at a particular temperature is directly proportional to the products of the molar concentration of the reactants with each concentration terms raised to the power equal to the number of molecules of the respective reactants taking part in the reaction.’
Note– a, b, c in the above equation is called stoichiometric coefficient of A, B, and C respectively.
Law of Mass Action and Equilibrium Constant:
Let us consider a reversible reaction,
aA + bB ——> cC + dD
Therefore, from law of mass action,
Rate of forward reaction, rf α [A]a [B]b
rf = kf [A]a [B]b
Similarly,
Rate of backward reaction, r b α [C]c [D]d
r b = kb [C]c [D]d
At equilibrium, the rate of forward reaction is equal to the rate of backward reaction. Therefore,
kf [A]a [B]b = kb [C]c [D]d
Or, kf / kb = [C]c [D]d / [A]a [B]b
Or, Kc = [C]c [D]d / [A]a [B]b
The above equation is called law of chemical equilibrium. Thus, the equilibrium constant is the ratio between the products of molar concentration of the products to that of the reactants with each conc. term raised to the power equal to its stoichiometric coefficient in the balanced equation at a constant temperature.