If K1 and K2 are the respective equilibrium constants for...

If $\mathrm{K}_1$ and $\mathrm{K}_2$ are the respective equilibrium constants for the two reactions, $$ \mathrm{XeF}_6(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{~g}) \rightleftharpoons \mathrm{XeOF}_4(\mathrm{~g})+2 \mathrm{HF}(\mathrm{~g}) $$ $\mathrm{XeO}_4(\mathrm{~g})+\mathrm{XeF}_6(\mathrm{~g}) \rightleftharpoons \mathrm{XeOF}_4(\mathrm{~g})+\mathrm{XeO}_3 \mathrm{~F}_2(\mathrm{~g})$ Then equilibrium constant of the reaction $\mathrm{XeO}_4(\mathrm{~g})+$ $2 \mathrm{HF}(\mathrm{g}) \rightleftharpoons \mathrm{XeO}_3 \mathrm{~F}_2(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g})$ will be (a) $\mathrm{K}_1 /\left(\mathrm{K}_2\right)^2$ (b) $\mathrm{K}_1 \cdot \mathrm{~K}_2$ (c) $\mathrm{K}_1 / \mathrm{K}_2$ (d) $\mathrm{K}_2 / \mathrm{K}_1$

If $\mathrm{K}_1$ and $\mathrm{K}_2$ are the respective equilibrium constants for the two reactions,

$$
\mathrm{XeF}_6(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{~g}) \rightleftharpoons \mathrm{XeOF}_4(\mathrm{~g})+2 \mathrm{HF}(\mathrm{~g})
$$

$\mathrm{XeO}_4(\mathrm{~g})+\mathrm{XeF}_6(\mathrm{~g}) \rightleftharpoons \mathrm{XeOF}_4(\mathrm{~g})+\mathrm{XeO}_3 \mathrm{~F}_2(\mathrm{~g})$
Then equilibrium constant of the reaction $\mathrm{XeO}_4(\mathrm{~g})+$ $2 \mathrm{HF}(\mathrm{g}) \rightleftharpoons \mathrm{XeO}_3 \mathrm{~F}_2(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g})$ will be
(a) $\mathrm{K}_1 /\left(\mathrm{K}_2\right)^2$
(b) $\mathrm{K}_1 \cdot \mathrm{~K}_2$
(c) $\mathrm{K}_1 / \mathrm{K}_2$
(d) $\mathrm{K}_2 / \mathrm{K}_1$

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Key Concepts

Manipulation of Equilibrium Reactions

Chemical reactions can be algebraically combined, reversed, or multiplied by a factor, and the equilibrium constant for the overall reaction is adjusted accordingly. When reactions are added, their equilibrium constants are multiplied; when one reaction is reversed, its equilibrium constant becomes its reciprocal; and when a reaction is scaled by a coefficient, the equilibrium constant is raised to the power of that coefficient. This manipulation is analogous to Hess’s Law in thermodynamics.

Equilibrium Constant

An equilibrium constant is a numerical value that expresses the ratio of the concentrations (or partial pressures in the case of gases) of products to reactants at equilibrium, each raised to the power of their respective stoichiometric coefficients. It is a key parameter in determining the position of equilibrium for a chemical reaction.

Reaction Algebra and Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the same regardless of the pathway taken. Similarly, the equilibrium constant for an overall reaction can be derived by appropriately combining the equilibrium constants of individual steps, allowing one to predict the behavior of complex reactions by breaking them down into simpler parts.

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