Question

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) \(K=\frac{\left(P_{\mathrm{NO}}\right)^{2}\left(P_{\mathrm{H}_{2} \mathrm{O}}\right)^{4}\left[\mathrm{Cu}^{2+}\right]^{3}}{\left[\mathrm{NO}_{3}^{-}\right]^{2}\left[\mathrm{H}^{+}\right]^{8}}\)

Short answer

Based on the given expressions for the equilibrium constant K, write the balanced chemical equations for the equilibrium systems: (a) The balanced chemical equation is: $$2\mathrm{SO_{2}} + 2\mathrm{H_{2}O} \rightleftharpoons 2\mathrm{H_{2}S} + 3\mathrm{O_{2}}$$ (b) The balanced chemical equation is: $$\frac{1}{2}\mathrm{F_{2}} + \frac{1}{2}\mathrm{I_{2}} \rightleftharpoons \mathrm{IF}$$ (c) The balanced chemical equation is: $$\mathrm{Cl}_{2} + 2\mathrm{Br}^{-} \rightleftharpoons 2\mathrm{Cl}^{-} + \mathrm{Br}_{2}$$ (d) The balanced chemical equation is: $$2\mathrm{NO}_{3}^{-} + 8\mathrm{H}^{+} + 3\mathrm{Cu}^{2+} \rightleftharpoons 2\mathrm{NO} + 4\mathrm{H}_{2}\mathrm{O} + \mathrm{Cu(NO_3)_2}$$

Step-by-step solution

(a) Identify reactants and products

For (a), the expression for \(K\) is given as \(\frac{\left(P_{\mathrm{H}_{2}\mathrm{~S}}\right)^{2}\left(P_{\mathrm{O}_{2}}\right)^{3}}{\left(P_{\mathrm{SO}_{2}}\right)^{2}\left(P_{\mathrm{H}_{2}\mathrm{O}}\right)^{2}}\). Here, the reactants are \(\mathrm{SO_{2}}\) and \(\mathrm{H_{2}O}\), and the products are \(\mathrm{H_{2}S}\) and \(\mathrm{O_{2}}\).

(a) Construct and balance the chemical equation

Since the exponents in the expression for K represent the stoichiometry, the balanced chemical equation for this system is: $$2\mathrm{SO_{2}} + 2\mathrm{H_{2}O} \rightleftharpoons 2\mathrm{H_{2}S} + 3\mathrm{O_{2}}$$

(b) Identify reactants and products

For (b), the expression for \(K\) is given as \(\frac{\left(P_{\mathrm{F}_{2}}\right)^{1 / 2}\left(P_{\mathrm{I}_{2}}\right)^{1 / 2}}{P_{\mathrm{IF}}}\), and the reactants are \(\mathrm{F}_{2}\) and \(\mathrm{I}_{2}\), while the product is \(\mathrm{IF}\).

(b) Construct and balance the chemical equation

Based on the stoichiometry given by the exponents, the balanced chemical equation for this system is: $$\frac{1}{2}\mathrm{F_{2}} + \frac{1}{2}\mathrm{I_{2}} \rightleftharpoons \mathrm{IF}$$

(c) Identify reactants and products

For (c), the expression for \(K\) is given as \(K=\frac{\left[\mathrm{Cl}^{-}\right]^{2}}{\left(P_{\mathrm{Cl}_{2}}\right)\left[\mathrm{Br}^{-}\right]^{2}}\). The reactants are \(\mathrm{Cl}_{2}\) and \(2\mathrm{Br}^{-}\), and the products are \(2\mathrm{Cl}^{-}\).

(c) Construct and balance the chemical equation

The balanced chemical equation for this system is: $$\mathrm{Cl}_{2} + 2\mathrm{Br}^{-} \rightleftharpoons 2\mathrm{Cl}^{-} + \mathrm{Br}_{2}$$

(d) Identify reactants and products

For (d), the expression for \(K\) is given as \(K=\frac{\left(P_{\mathrm{NO}}\right)^{2}\left(P_{\mathrm{H}_{2}\mathrm{O}}\right)^{4}\left[\mathrm{Cu}^{2+}\right]^{3}}{\left[\mathrm{NO}_{3}^{-}\right]^{2}\left[\mathrm{H}^{+}\right]^{8}}\). The reactants are \(2\mathrm{NO}_{3}^{-}\), \(8\mathrm{H}^{+}\), and \(3\mathrm{Cu}^{2+}\), while the products are \(2\mathrm{NO}\), \(4\mathrm{H}_{2}\mathrm{O}\), and \(\mathrm{Cu(NO_3)_2}\).

(d) Construct and balance the chemical equation

The balanced chemical equation for this system is: $$2\mathrm{NO}_{3}^{-} + 8\mathrm{H}^{+} + 3\mathrm{Cu}^{2+} \rightleftharpoons 2\mathrm{NO} + 4\mathrm{H}_{2}\mathrm{O} + \mathrm{Cu(NO_3)_2}$$