Write a chemical equation for an equilibrium system that...

Write a chemical equation for an equilibrium system that would lead to the following expressions $(\mathrm{a}-\mathrm{d})$ for $K$. (a) $K=\frac{\left(P_{\mathrm{H}_{2} \mathrm{~S}}\right)^{2}\left(P_{\mathrm{O}_{2}}\right)^{3}}{\left(P_{\mathrm{SO}_{2}}\right)^{2}\left(P_{\mathrm{H}_{2} \mathrm{O}}\right)^{2}}$ (b) $K=\frac{\left(P_{\mathrm{F}_{2}}\right)^{1 / 2}\left(P_{\mathrm{I}_{2}}\right)^{1 / 2}}{P_{\mathrm{IF}}}$ (c) $K=\frac{\left[\mathrm{Cl}^{-}\right]^{2}}{\left(P_{\mathrm{Cl}_{2}}\right)\left[\mathrm{Br}^{-}\right]^{2}}$ (d) $K=\frac{\left(P_{\mathrm{NO}}\right)^{2}\left(P_{\mathrm{H}_{2} \mathrm{O}}\right)^{4}\left[\mathrm{Cu}^{2+}\right]^{3}}{\left[\mathrm{NO}_{3}^{-}\right]^{2}\left[\mathrm{H}^{+}\right]^{8}}$

Write a chemical equation for an equilibrium system that would lead to the following expressions $(\mathrm{a}-\mathrm{d})$ for $K$.
(a) $K=\frac{\left(P_{\mathrm{H}_{2} \mathrm{~S}}\right)^{2}\left(P_{\mathrm{O}_{2}}\right)^{3}}{\left(P_{\mathrm{SO}_{2}}\right)^{2}\left(P_{\mathrm{H}_{2} \mathrm{O}}\right)^{2}}$
(b) $K=\frac{\left(P_{\mathrm{F}_{2}}\right)^{1 / 2}\left(P_{\mathrm{I}_{2}}\right)^{1 / 2}}{P_{\mathrm{IF}}}$
(c) $K=\frac{\left[\mathrm{Cl}^{-}\right]^{2}}{\left(P_{\mathrm{Cl}_{2}}\right)\left[\mathrm{Br}^{-}\right]^{2}}$
(d) $K=\frac{\left(P_{\mathrm{NO}}\right)^{2}\left(P_{\mathrm{H}_{2} \mathrm{O}}\right)^{4}\left[\mathrm{Cu}^{2+}\right]^{3}}{\left[\mathrm{NO}_{3}^{-}\right]^{2}\left[\mathrm{H}^{+}\right]^{8}}$

Key Concepts

Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations or partial pressures of all reactants and products over time. This concept is fundamental in understanding how a reversible reaction behaves under given conditions.

Equilibrium Constant Expression

The equilibrium constant (K) is an expression that relates the concentrations or partial pressures of the products and reactants in a reversible reaction at equilibrium, each raised to the power of their respective stoichiometric coefficients. This expression quantitatively describes the position of the equilibrium and is crucial in predicting the extent of a reaction.

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationship between the amounts of reactants and products in a chemical reaction, as indicated by the balanced chemical equation. The exponents in the equilibrium constant expression directly reflect these stoichiometric coefficients, ensuring that the mathematical description of the equilibrium aligns with the balanced reaction.

Partial Pressures versus Concentrations

In chemical equilibrium, the state variables can be expressed in terms of concentrations for solutions or partial pressures for gases. The choice depends on the phase of the reactants and products. Understanding how to use partial pressures in K expressions for gases and concentrations for solutes is critical, as it affects the form of the equilibrium constant.

Deriving Chemical Equations from Equilibrium Expressions

Given an equilibrium constant expression, one can work backwards to deduce a balanced chemical equation that would yield that expression. This involves matching the exponents to the stoichiometric coefficients of the reactants and products and ensuring that the form of the expression (using partial pressures for gases and concentrations for ions in solution) corresponds properly to the phases of the substances involved.

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