Write the equilibrium constant expression for: (a) \(\mathrm{SiCl}_{4}(l)+2 \mathrm{H}_{2} \mathrm{O}(g)\) \(\rightleftarrows \mathrm{SiO}_{2}(s)+4 \mathrm{HCl}(g)\) (b) \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{CO}_{2}(g) \rightleftarrows \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(l)\) (c) \(\mathrm{MnO}_{2}(s)+4 \mathrm{H}^{+}(a q)+2 \mathrm{Cl}^{-}(a q)\) \(\rightleftarrows \mathrm{Mn}^{2+}(a q)+\mathrm{Cl}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)\) (d) \(\mathrm{I}_{2}(s) \rightleftarrows \mathrm{I}_{2}(g)\) (e) \(\mathrm{TiCl}_{4}(g)+2 \mathrm{Mg}(s) \rightleftarrows \mathrm{Ti}(s)+2 \mathrm{MgCl}_{2}(s)\) (f) \(\mathrm{Ni}(\mathrm{OH})_{2}(s) \rightleftarrows \mathrm{Ni}^{2+}(a q)+2 \mathrm{OH}^{-}(a q)\)

Step by step solution

01

Write the equilibrium constant expression for reaction (a)

\( K_a = \frac{[\text{SiO}_2][\text{HCl}]^4}{[\text{SiCl}_4][\text{H}_2\text{O}]^2} \) Note that there's no need to include the solid substances (SiCl4 and SiO2) in the equilibrium constant expression, as their concentrations are considered constant due to their phase. So we can rewrite it as: \( K_a = \frac{[\text{HCl}]^4}{[\text{H}_2\text{O}]^2} \) (b) H2(g) + CO2(g) \(\rightleftarrows\) CO(g) + H2O(l)

02

Write the equilibrium constant expression for reaction (b)

\( K_b = \frac{[\text{CO}][\text{H}_2\text{O}]}{[\text{H}_2][\text{CO}_2]} \) (c) MnO2(s) + 4H+(aq) + 2Cl-(aq) \(\rightleftarrows\) Mn2+(aq) + Cl2(g) + 2H2O(l)

03

Write the equilibrium constant expression for reaction (c)

\( K_c = \frac{[\text{Mn}^{2+}][\text{Cl}_2]}{[\text{H}^+]^4[\text{Cl}^-]^2} \) Ignore the solid substances (MnO2) and liquid substances (H2O) in the equilibrium constant expression. (d) I2(s) \(\rightleftarrows\) I2(g)

04

Write the equilibrium constant expression for reaction (d)

\( K_d = \frac{[\text{I}_2]}{[\text{I}_2]} \) Ignore the solid substances (I2) in the equilibrium constant expression.

05

Simplify K_d expression

\( K_d = 1 \) (e) TiCl4(g) + 2Mg(s) \(\rightleftarrows\) Ti(s) + 2MgCl2(s)

06

Write the equilibrium constant expression for reaction (e)

\( K_e = \frac{[\text{Ti}][\text{MgCl}_2]^2}{[\text{TiCl}_4][\text{Mg}]^2} \) Ignore the solid substances (Mg, Ti, and MgCl2) in the equilibrium constant expression. Therefore, the equilibrium constant is not dependent on their concentrations.

07

Simplify K_e expression

\( K_e = \frac{1}{[\text{TiCl}_4]} \) (f) Ni(OH)2(s) \(\rightleftarrows\) Ni2+(aq) + 2OH-(aq)

08

Write the equilibrium constant expression for reaction (f)

\( K_f = \frac{[\text{Ni}^{2+}][\text{OH}^-]^2}{[\text{Ni(OH)}_2]} \) Ignore the solid substances (Ni(OH)2) in the equilibrium constant expression.

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