Equilibria: Chemistry 9701 (Cambridge International AS & A Level)

A gaseous equilibrium is established in a sealed, rigid container of fixed volume:

$\text{X(g)} + \text{Y(g)} \rightleftharpoons 2\text{Z(g)} \qquad \Delta H = -114\ \text{kJ mol}^{-1}$

With no other change made to the system, the temperature of the container is then lowered.

Which row correctly describes the effect on the position of equilibrium and on the value of $K_c$?

Phosphorus pentachloride decomposes reversibly at high temperature:

$\text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g)$

A chemist places $0.400\ \text{mol}$ of $\text{PCl}_5(g)$ in an evacuated $2.00\ \text{dm}^3$ container and allows the system to reach dynamic equilibrium at constant temperature. At equilibrium, $0.280\ \text{mol}$ of $\text{PCl}_5(g)$ remains.

(a) Write the expression for $K_c$ for this equilibrium. [1]

(b) Calculate the equilibrium concentration, in $\text{mol dm}^{-3}$, of $\text{PCl}_5$, $\text{PCl}_3$ and $\text{Cl}_2$. [3]

(c) Calculate $K_c$ for this equilibrium, including its units, to 3 significant figures. [2]

Bromine and chlorine gases react reversibly to form bromine monochloride:

$\text{Br}_2(g) + \text{Cl}_2(g) \rightleftharpoons 2\text{BrCl}(g)$

Since $\text{Br}_2$, $\text{Cl}_2$ and $\text{BrCl}$ are all gases, this is a homogeneous equilibrium: every species present is in the same (gaseous) phase. A gaseous equilibrium mixture of $\text{Br}_2$, $\text{Cl}_2$ and $\text{BrCl}$ is established in a sealed container at constant temperature. At equilibrium, the total pressure is $200\ \text{kPa}$, and the mole fractions of $\text{Br}_2$, $\text{Cl}_2$ and $\text{BrCl}$ are $0.20$, $0.20$ and $0.60$ respectively.

(a) Calculate the partial pressure, in kPa, of each of the three gases at equilibrium. [3]

(b) Write the expression for $K_p$, and use your answers to (a) to calculate its value. State whether $K_p$ has units, explaining your reasoning. [3]

(c) State and explain the effect, if any, on the value of $K_p$ of increasing the total pressure at constant temperature. [2]

Lactic acid (2-hydroxypropanoic acid), $\text{CH}_3\text{CH(OH)COOH}$, is a weak monobasic acid with $K_a = 1.4\times10^{-4}\ \text{mol dm}^{-3}$ at 298 K.

(a) Calculate the pH of a $0.200\ \text{mol dm}^{-3}$ solution of lactic acid, stating clearly any assumption you make. [4]

(b) A buffer solution is prepared containing $0.100\ \text{mol dm}^{-3}$ lactic acid and $0.150\ \text{mol dm}^{-3}$ sodium lactate, $\text{CH}_3\text{CH(OH)COONa}$. Calculate the pH of this buffer solution. [3]

(c) A few drops of dilute hydrochloric acid are added to the buffer solution in (b). Explain, in terms of the species present, why the pH of the buffer changes only very slightly. [2]

Lead(II) iodide, $\text{PbI}_2$, is a sparingly soluble ionic solid that establishes the following equilibrium in contact with water:

$\text{PbI}_2(s) \rightleftharpoons \text{Pb}^{2+}(aq) + 2\text{I}^-(aq)$

(a) Write the expression for the solubility product, $K_{sp}$, of $\text{PbI}_2$. [1]

(b) The molar solubility of $\text{PbI}_2$ in pure water at 298 K is $1.5\times10^{-3}\ \text{mol dm}^{-3}$. Calculate $K_{sp}$ for $\text{PbI}_2$, including its units. [3]

(c) Calculate the molar solubility of $\text{PbI}_2$ in a $0.10\ \text{mol dm}^{-3}$ solution of potassium iodide, using your value of $K_{sp}$ from (b). Comment briefly on how this compares with the solubility in pure water. [3]

Solid ammonium chloride decomposes reversibly on heating to form two gases, in a sealed container at constant temperature:

$\text{NH}_4\text{Cl(s)} \rightleftharpoons \text{NH}_3\text{(g)} + \text{HCl(g)}$

This is a heterogeneous equilibrium, since the solid and the two gases are not all in the same phase.

Which expression is correct for $K_c$ of this equilibrium?

Dinitrogen tetroxide dissociates reversibly in the gas phase:

$\text{N}_2\text{O}_4\text{(g)} \rightleftharpoons 2\text{NO}_2\text{(g)}$

$0.0500\ \text{mol}$ of $\text{N}_2\text{O}_4\text{(g)}$ is placed in an evacuated, sealed container and allowed to reach dynamic equilibrium at constant temperature. At equilibrium, $60.0\%$ of the $\text{N}_2\text{O}_4$ originally present has dissociated, and the total equilibrium pressure is $100\ \text{kPa}$.

(a) Write the expression for $K_p$ for this equilibrium. [1]

(b) Calculate the amount, in mol, of $\text{N}_2\text{O}_4\text{(g)}$ and of $\text{NO}_2\text{(g)}$ present at equilibrium, and hence the mole fraction of each gas. [3]

(c) Use your answers to (b) to calculate the partial pressure, in kPa, of each gas at equilibrium. [2]

(d) Calculate $K_p$ for this equilibrium, stating its units. [2]

Methanoic acid reacts reversibly with water:

$\text{HCOOH(aq)} + \text{H}_2\text{O(l)} \rightleftharpoons \text{HCOO}^-\text{(aq)} + \text{H}_3\text{O}^+\text{(aq)}$

According to the Brønsted-Lowry theory, which pair of species is a conjugate acid-base pair?

At $298\ \text{K}$, the ionic product of water is $K_w = [\text{H}^+][\text{OH}^-] = 1.00\times10^{-14}\ \text{mol}^2\ \text{dm}^{-6}$.

(a) Hydrochloric acid, $\text{HCl}$, is a strong monobasic acid that dissociates completely in water. Calculate the pH of a $0.0250\ \text{mol dm}^{-3}$ solution of $\text{HCl}$ at $298\ \text{K}$. [2]

(b) Sodium hydroxide, $\text{NaOH}$, is a strong base that dissociates completely in water. Calculate the pH of a $0.0250\ \text{mol dm}^{-3}$ solution of $\text{NaOH}$ at $298\ \text{K}$, using $K_w$. [3]

(c) The dissociation of water, $\text{H}_2\text{O(l)} \rightleftharpoons \text{H}^+\text{(aq)} + \text{OH}^-\text{(aq)}$, is endothermic. State and explain what happens to the value of $K_w$, and to the pH of pure water, as the temperature is raised above $298\ \text{K}$. Explain why pure water remains neutral at the higher temperature even though its pH is no longer $7.00$. [2]

Iodine, $\text{I}_2$, distributes itself between water and hexane, two immiscible solvents, reaching a partition equilibrium at $298\ \text{K}$:

$\text{I}_2\text{(aq)} \rightleftharpoons \text{I}_2\text{(hexane)}$

(a) Write the expression for the partition coefficient, $K_{pc}$, of iodine between hexane and water. [1]

(b) In one experiment, the equilibrium concentration of iodine in the aqueous layer is $2.50\times10^{-4}\ \text{mol dm}^{-3}$, and in the hexane layer is $2.05\times10^{-2}\ \text{mol dm}^{-3}$. Calculate $K_{pc}$. [2]

(c) In a second experiment at the same temperature, $25.0\ \text{cm}^3$ of aqueous iodine solution of concentration $1.00\times10^{-3}\ \text{mol dm}^{-3}$ is shaken with $10.0\ \text{cm}^3$ of hexane until partition equilibrium is re-established. Given that $K_{pc}$ is unchanged, use conservation of the total amount of iodine to calculate the new equilibrium concentration of iodine in the aqueous layer. [4]