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State the law of mass action and derive the expression for equilibrium constant for a general reaction.

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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
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