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Equilibrium

Question
CBSEENCH11006362

Apply the law of mass action to a reversible reaction and state the law of chemical equilibrium.

Solution
Let us consider a simple reversible reaction in the state of equilibrium
                     straight A plus straight B rightwards harpoon over leftwards harpoon space space straight C plus straight D
According to the law of mass action.
Rate of the forward reaction open parentheses straight r subscript straight f close parentheses space proportional to space space open square brackets straight A close square brackets space open square brackets straight B close square brackets
or         straight r subscript straight f space equals space straight k subscript straight f open square brackets straight A close square brackets open square brackets straight B close square brackets
where kf is the rate constant for the forward reaction, [A] and [B] are molar concentrations of reactants A and B respectively.
Rate of the backward reaction (rb) ∝ [C] [D] or rb = kb [C] [D]
where kb is the rate constant for the backward reaction, [C] and [D] are molar concentrations of the products C and D respectively.
At equilibrium:
                      Rate of the forward reaction open parentheses straight r subscript straight f close parentheses
                 = Rate of the backward reaction open parentheses straight r subscript straight b close parentheses
                          space space straight k subscript straight f open square brackets straight A close square brackets open square brackets straight B close square brackets space equals space straight k subscript straight b open square brackets straight C close square brackets open square brackets straight D close square brackets
or                       straight k subscript straight f over straight k subscript straight b space equals space fraction numerator open square brackets straight C close square brackets space open square brackets straight D close square brackets over denominator open square brackets straight A close square brackets space open square brackets straight B close square brackets end fraction
                         straight K subscript straight c space equals space straight k subscript straight f over straight k subscript straight b fraction numerator open square brackets straight C close square brackets space open square brackets straight D close square brackets over denominator open square brackets straight A close square brackets open square brackets straight B close square brackets end fraction
The constant straight K subscript straight c is called equilibrium constant and has a constant value at a given temperature. Similarly, for a reaction 2 straight A plus 2 straight B space rightwards harpoon over leftwards harpoon space space straight C plus straight D
straight K subscript straight c space equals space fraction numerator open square brackets straight C close square brackets open square brackets straight D close square brackets over denominator open square brackets straight A close square brackets squared open square brackets straight B close square brackets cubed end fraction
the above represents the complete expression for the law of chemical equilibrium. It may be defined as: For a reversible reaction at equilibrium, the ratio of the products of molar concentration of the products (substance formed) to the products of molar concentration of the reactants with each concentration term raised to a power equal to the number of moles of that substance in the balanced equation is constant at a given temperature.