Answer
Equilibrium constant of overall reaction is the product of equilibrium constants of another two reactions.
Work Step by Step
Equilibrium constant$(K_{c})$ ,for a chemical reaction present in equilibrium,is expressed by the concentrations of products raised to their stoichiometric coefficients divided by the concentrations of the reactants raised to their stoichiometric coefficients which is written by law of mass action.
Consider two chemical reactions and write expression for equilibrium constants-
$A(g) + 2B(g) = 3C(g)$
$K_{1}=\frac{[C]^{3}}{[A][B]^{2}}$
$3C = D(g)$
$K_{2}=\frac{[D]}{[C]^{3}}$
Sum up above two reactions to get the overall reaction and write expression of equilibrium constant for overall reaction-
$A(g) + 2B(g) = D(g)$
$K_{overall} = \frac{[D]}{[A][B]^{2}}$
We express the equilibrium constant expression of overall reaction using equilibrium constants of other reaction-
$K_{overall} = \frac{[D]}{[A][B]^{2}}$
$K_{overall}=(\frac{[C]^{3}}{[A][B]^{2}})\times(\frac{[D]}{[C]^{3}})$
$K_{overall} = K_{1}\times K_{2}$
Therefore equilibrium constant of overall reaction is the product of equilibrium constants of another two reactions.
