Answer. This law is proposed by Guldberg and Waage in 1869. This law states that "The rate at which a substance reacts is directly proportional to its active mass and the rate of a reaction is directly proportional to the product of the active masses of the reacting substances
Generally an active mass is considered as the molar concentration in units of mol dm-3, expressed as square brackets [ ].
Consider for example, a reversible reaction of the type
kr
A + B <====> C + D
kr
Suppose [A], [B], [C] and [D] are the molar concentrations (mol dm-3) of A, B, C and D substances respectively.
According to Law of Mass Action
Rate of the forward reaction ∞ [A] [B] = kf [A] [B] Similarly,
Rate of the reverse reaction [C] [D] = kr [C] [D]
where kf and kr are the specific rate constant of forward and the reverse reactions respectively.
At equilibrium
Rate of forward reaction = Rate of reverse reaction
K f [A][B] = kr[C][D]
K f = [C] [D]
Kr [A][B]
The equilibrium constant may be represented as
Kc = [C] [D]
[A][B]
Where Kc =
Law of mass action describes the relationship between active mass of the reactants and rate of a reaction.
Derivation of the Expression for Equilibrium Constant
Let us apply the law of mass action for a general reaction.
aA + bB <====> cC + dD
This reaction consists of two reactions; forward and reverse reactions. According to this law, rate of a chemical reaction is directly proportional to the product of the concentrations of its reactants raised to power equal to their stoichiometric coefficient in the balanced chemical equation of the reaction.
Let first discuss the forward reaction. A and B are the reactants for the forward reaction and 'a' and 'b' are their number of moles or stoichiometric coefficient in the equation.
Rate of forward reaction according to law of mass action;
Rate of forward reaction is Rf ∞ [A]a[B]b
Or Rf = kf [A]a[B]b
Where Kf is the rate constant for the forward reaction
Now, discuss the reverse reaction C and D are reactants for reverse reaction having ‘c’ and’d’ stoichiometric coefficients respectively. So according to law of mass action:
Rate of reverse reaction Rr [C]c[D]d r
Or R r = kr [C]c [D]d
Where kr is the rate constant for the reverse reaction. We know that at equilibrium state rates of both the reactions are equal to each other.
Rate of forward .reaction = Rate of reverse reaction
Such as: Rf = Rr and putting the values of Rf and Rr
kf [A]a[B]b = kr [C]c [D]d
By taking the constants on one side and the variables on other side of the equation
K f = [C] c [D] d
Kr [A] a [B]
Now, replace the ratio of both constants with another constant, Kc known as equilibrium constant. The indicates concentration in molar unit
Kc = [C] c [D] d
[A] a [B] b