If the equilibrium constant for the reaction H2+ (1)/(2) O2 ⇌H2 O is K, the equilibrium constant

step 1 problem number 109 because this equation is a case of double reverse reaction so the answer will

If the equilibrium constant for the reaction H2+ (1)/(2) O2...

If the equilibrium constant for the reaction $\mathrm{H}_{2}+$ $\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}$ is $K,$ the equilibrium constant for the reaction $2 \mathrm{H}_{2} \mathrm{O} \rightleftharpoons 2 \mathrm{H}_{2}+\mathrm{O}_{2}$ at the same temperature is $(a) 1 / K$ $(b) 1 /(2 K)$ $(c) 2 K$ $(d) K^{2}$ $(e) 1 / K^{2}$

If the equilibrium constant for the reaction $\mathrm{H}_{2}+$ $\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}$ is $K,$ the equilibrium constant for the reaction $2 \mathrm{H}_{2} \mathrm{O} \rightleftharpoons 2 \mathrm{H}_{2}+\mathrm{O}_{2}$ at the same temperature is
$(a) 1 / K$
$(b) 1 /(2 K)$
$(c) 2 K$
$(d) K^{2}$
$(e) 1 / K^{2}$

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Key Concepts

Law of Mass Action

This principle defines the equilibrium constant in terms of the concentrations (or pressures) of the products and reactants at equilibrium. It provides the mathematical framework for calculating equilibrium constants by establishing that the ratio of the product of concentrations of the products to that of the reactants, each raised to the power of their stoichiometric coefficients, remains constant under given conditions.

Reversing a Reaction

When a chemical reaction is reversed, the equilibrium constant of the reverse reaction becomes the reciprocal of the equilibrium constant for the forward reaction. This relationship is fundamental for understanding how equilibrium positions change when the direction of the reaction is flipped.

Scaling Reaction Stoichiometry

Changing the coefficients in a balanced chemical equation by a factor alters the equilibrium constant by raising it to the corresponding power. This scaling rule is crucial when comparing the equilibrium constants of reactions that are stoichiometrically modified versions of one another, as it demonstrates that the equilibrium constant is not simply multiplied by the same factor but exponentiated based on the change in the stoichiometric coefficients.

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