Question

Mercury(I) oxide decomposes into elemental mercury and elemental oxygen: \(2 \mathrm{Hg}_{2} \mathrm{O}(s) \rightleftharpoons 4 \mathrm{Hg}(l)+\mathrm{O}_{2}(g)\). (a) Write the equilibrium-constant expression for this reaction in terms of partial pressures. (b) Suppose you run this reaction in a solvent that dissolves elemental mercury and elemental oxygen. Rewrite the equilibrium- constant expression in terms of molarities for the reaction, using (solv) to indicate solvation.

Short answer

(a) The equilibrium constant expression in terms of partial pressures for the given reaction is: \[K_P = \frac{P_{\mathrm{Hg}}^4 \times P_{\mathrm{O}_2}}{P_{\mathrm{Hg}_2\mathrm{O}}^2}\] (b) The equilibrium constant expression in terms of molarities for the given reaction in a solvent is: \[K_C = \frac{[\mathrm{Hg(solv)}]^4 \times [\mathrm{O_2(solv)}]}{[\mathrm{Hg_2O(solv)}]^2}\]

Step-by-step solution

(a) Equilibrium constant expression in terms of partial pressures

To write the equilibrium constant expression for the decomposition reaction of Mercury(I) oxide in terms of partial pressures, we can use the formula for K_P, the equilibrium constant for gases in terms of partial pressures: \[K_P = \frac{(\text{Partial pressure of products})^{\text{stoichiometric coefficients}}}{(\text{Partial pressure of reactants})^{\text{stoichiometric coefficients}}}\] For the given reaction: \[2 \mathrm{Hg}_2\mathrm{O}(s) \rightleftharpoons 4\mathrm{Hg}(l) + \mathrm{O}_2(g)\] The equilibrium constant expression in terms of partial pressures can be written as: \[K_P = \frac{P_{\mathrm{Hg}}^4 \times P_{\mathrm{O}_2}}{P_{\mathrm{Hg}_2\mathrm{O}}^2}\] Keep in mind that since Mercury(I) oxide is a solid and elemental mercury is a liquid, their partial pressures are not included in the equilibrium constant expression. The only relevant partial pressure is for elemental oxygen gas.

(b) Equilibrium constant expression in terms of molarities

To rewrite the equilibrium constant expression in terms of molarities, we can use the formula for K_C, the equilibrium constant for the reaction in terms of concentrations: \[K_C = \frac{[\text{Products}]^{\text{stoichiometric coefficients}}}{[\text{Reactants}]^{\text{stoichiometric coefficients}}}\] Let's use the (solv) notation for solute concentrations. For the given reaction in a solvent: \[2 \mathrm{Hg}_2\mathrm{O}(s) \rightleftharpoons 4\mathrm{Hg(solv)} + \mathrm{O}_2(solv)\] The equilibrium constant expression in terms of molarities can be written as: \[K_C = \frac{[\mathrm{Hg(solv)}]^4 \times [\mathrm{O_2(solv)}]}{[\mathrm{Hg_2O(solv)}]^2}\] Since Mercury(I) oxide is still a solid in the solvent, its concentration remains constant and does not appear in the equilibrium constant expression. The only relevant concentrations are for solvated elemental mercury and elemental oxygen.

Key concepts

Equilibrium Constant

In chemical reactions, not all reactants are completely converted to products. Instead, a dynamic equilibrium is established where the forward and backward reactions occur at the same rate. The equilibrium constant, denoted as either \(K_P\) for gases or \(K_C\) for solutions, quantifies this balance.
The expression for the equilibrium constant is derived based on the reaction's stoichiometry. For reactions involving gases, partial pressures are used in \(K_P\), while concentrations expressed as molarity are used in \(K_C\). A larger equilibrium constant means the reaction favors the products at equilibrium, while a smaller one indicates that reactants are favored.
In the decomposition reaction of mercury(I) oxide, the focus is on products that are either gases or dissolved in a solvent, as these contribute to the equilibrium expression.

Partial Pressures

Gases exert pressure when they occupy a container. This pressure is known as partial pressure in the context of a mixture of gases, and each gas contributes to the total pressure proportionally to its amount present.
In the equilibrium constant expression for gases, such as \(K_P\), partial pressures replace concentrations. Only gaseous components appear in the expression. For example, in the mercury(I) oxide decomposition, the solid and liquid forms do not factor into the equilibrium expression since their partial pressures, by definition, are not applicable.
Partial pressures are crucial for reactions involving gases because they directly affect the position of equilibrium and the value of \(K_P\). Adjusting the volume or temperature of the system can change these pressures, thereby shifting the equilibrium position.

Molarity

Molarity is a measure of the concentration of a solute in a solution and is defined as moles of solute per liter of solution. It's a fundamental concept in chemistry for describing how "crowded" a solute is within a solution.
In reactions carried out in a solvent, equilibrium constants are expressed in terms of molarity, denoted \(K_C\).
This involves solute concentrations—such as our dissolved elemental mercury and oxygen. Molarity helps us to predict how changes in concentration of the solutes will affect the equilibrium of the system.

• Higher molarity implies more solute per unit volume.
• Lower molarity may mean either less solute or a greater volume.

Understanding molarity is essential for interpreting solvation effects on chemical equilibrium.

Mercury Compound Reactions

Mercury compounds exhibit unique behaviors because mercury can exist in multiple oxidation states, influencing their reactivity and equilibrium states.
The decomposition of mercury(I) oxide is a classic reaction where heating causes the solid compound to yield liquid mercury and gaseous oxygen.
This particular reaction, when placed in a solvent system, focuses on the dissolved species, allowing mercury and oxygen to participate in further chemical processes or analysis.

• Mercury(I) oxide is stable as a solid, making it energetically favorable to decompose only upon energy input.
• The resulting mercury and oxygen, when solvated, engage differently depending on the solvent utilized.

Understanding the behavior of mercury in such reactions is vital for applications in chemical synthesis and industrial processes.