At a constant temperature, the equilibrium constant of the reaction `N_(2)(g)+3H_(2)(g)hArr2NH_(3)(g)` is K and that of the reaction `(1)/(2)N_(2)(g)+(3)/(2)H_(2)(g)hArrNH_(3)(g)` is `sqrt(K)`. Explain this difference of K values in spite of the fact that the reactants and products in both the reactions are same.

Explanation

The vlaue of equilibrium constant of a reaction depends upon the mode of writing the balance equation of the reaction.
(i) `N_(2)(g)+3H_(2)(g)hArr 2NH_(3)(g),` Equilibrium constnat, `K=([NH_(3)]^(2))/([N_(2)][H_(2)]^(3))`
(ii) `(1)/(2) N_(2)(g)+(3)/(2) H_(2)(g)hArr NH_(3)(g),`
Equilibrium constant, `K_(1)=([NH_(3)])/([N_(2)]^(1//2)xx[H_(2)]^(3//2))`
Therefore, `K_(1)^(2)=([NH_(3)]^(2))/([N_(2)][H_(2)]^(3))=K or, K_(1)=sqrt(K)`
In both the reactions (i) and (ii), reactants and products are the same, but in the equations of these two reactions, the stoichiometric coefficients of reactants and products are different, resulting in different values of the corresponding equilibrium constant.