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Law of Mass Action & Equilibrium Constant

“The rate at which a substance reacts is directly proportional to its active mass and rate of a chemical reaction is directly proportional to product of active masses of reactants each raised to a power equal to corresponding stoichiometric coefficient appearing in the balanced chemical equation”.

Fore reaction aA + bB \rightleftharpoons cC + dD

Rate of reaction ∝ [A]a.[B]b

or rate of reaction = K[A]a[B]b

where K is rate constant or velocity constant of the reaction at that temperature.

Unit of rate constant (K) 

K = \frac{Rate\ of\ reaction}{[A]^a[B]^b}=\frac{molL^-^1 s^-^1}{(molL^1^)^a^+^b } = (molL^-^1)^1\ ^t^o\ ^n\ s^-^1 

(where n is order of reaction.)

For unit concentration of reactants rate of the reaction is equal to rate constant or specific reaction rate.

Note:

 Active mass is the molar concentration of the reacting substances

actually participating in the reaction.

Hence,

Active mass = number of moles/volume in litres

Active mass of solid is taken as unity.

Also, Active mass of reactant (a) = Conc. × activity coefficient

i.e. a = Molarity × f                        for dilute solution f = 1 

Applying Law of mass action for general reversible reaction

aA + bB \rightleftharpoons cC + dD

Rate of forward reaction \alpha [A]a[B]b

or Rf = Kf [A][B]b

Similarly for backward reaction               

Rb = Kb[C][D]d

At equilibrium Kf[A]a[B]b = Kb[C]c[D]d

\Rightarrow \frac{K_f}{K_b} =\frac{[C]^c[D]^d}{[A]^a[B]^b} =K_c

The above equation is known as equilibrium equation and Kc is known as equilibrium constant.

Equilibrium constant for the reverse reaction is the inverse of the equilibrium constant for the reaction in the forward direction.

\Rightarrow K_f =\frac{1}{K_b}

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