Problem 3 - Chemistry: Principles and Reactions

Question

Write the equilibrium equations on which the following \(K_{s p}\) expressions are based. (a) \(\left[\mathrm{Hg}_{2}{\underline{\phantom{xx}}}^{2+}\right]\left[\mathrm{Cl}^{-}\right]^{2}\) (b) \(\left[\mathrm{Pb}^{2+}\right]\left[\mathrm{CrO}_{4}^{2-}\right]\) (c) \(\left[\mathrm{Mn}^{4+}\right]\left[\mathrm{O}^{2-}\right]^{2}\) (d) \(\left[\mathrm{Al}^{3+}\right]^{2}\left[\mathrm{~S}^{2-}\right]^{3}\)

Step-by-Step Solution

Answer

Q: Write the equilibrium equations for each given Ksp expression: a) [Hg2^2+][Cl^-]^2 b) [Pb^2+][CrO4^2-] c) [Mn^4+][O^2-]^2 d) [Al^3+]^2[S^2-]^3 A: a) Hg2Cl2(s) ⇌ Hg2^2+(aq) + 2Cl^-(aq) b) PbCrO4(s) ⇌ Pb^2+(aq) + CrO4^2-(aq) c) MnO2(s) ⇌ Mn^4+(aq) + 2O^2-(aq) d) Al2S3(s) ⇌ 2Al^3+(aq) + 3S^2-(aq)

Step 1: (a) Writing the equilibrium equation for \(\left[\mathrm{Hg}_{2}{ }^{2+}\right]\left[\mathrm{Cl}^{-}\right]^{2}\)

Begin by identifying the ions in the expression. We have Hg\(_{2}^{2+}\) and Cl\(^-\). The exponents in the expression are their respective stoichiometric coefficients from the balanced chemical equation. In this case, the equation will be: \begin{equation} \mathrm{Hg}_{2}\mathrm{Cl}_{2}(s) \rightleftharpoons \mathrm{Hg}_{2}^{2+}(aq) + 2\mathrm{Cl}^{-}(aq) \end{equation}

Step 2: (b) Writing the equilibrium equation for \(\left[\mathrm{Pb}^{2+}\right]\left[\mathrm{CrO}_{4}^{2-}\right]\)

Identify the ions: Pb\(^{2+}\) and CrO\(_4^{2-}\). Write the balanced chemical equation based on the exponents in the expression: \begin{equation} \mathrm{PbCrO}_{4}(s) \rightleftharpoons \mathrm{Pb}^{2+}(aq) + \mathrm{CrO}_{4}^{2-}(aq) \end{equation}

Step 3: (c) Writing the equilibrium equation for \(\left[\mathrm{Mn}^{4+}\right]\left[\mathrm{O}^{2-}\right]^{2}\)

Identify the ions: Mn\(^{4+}\) and O\(^{2-}\). Write the balanced chemical equation based on the exponents in the expression: \begin{equation} \mathrm{MnO}_{2}(s) \rightleftharpoons \mathrm{Mn}^{4+}(aq) + 2\mathrm{O}^{2-}(aq) \end{equation}

Step 4: (d) Writing the equilibrium equation for \(\left[\mathrm{Al}^{3+}\right]^{2}\left[\mathrm{~S}^{2-}\right]^{3}\)

Identify the ions: Al\(^{3+}\) and S\(^{2-}\). Write the balanced chemical equation based on the exponents in the expression: \begin{equation} \mathrm{Al}_{2}\mathrm{S}_{3}(s) \rightleftharpoons 2\mathrm{Al}^{3+}(aq) + 3\mathrm{S}^{2-}(aq) \end{equation}

Key Concepts

Equilibrium Equations

In the realm of chemistry, equilibrium equations play a pivotal role in understanding solubility and reactions in solution. When a solid dissolves in water, it forms ions in a dynamic equilibrium that can be described through these equations. For instance, when Hg₂Cl₂ dissolves, it is represented as \[\text{Hg}_2\text{Cl}_2(s) \rightleftharpoons \text{Hg}_2^{2+}(aq) + 2\text{Cl}^-(aq)\]. The 's' denotes a solid, while 'aq' indicates an aqueous solution, meaning the ions are dispersed in water.

Identifying these equilibrium states requires recognizing the ions in the equilibrium expression. Each ion is usually matched with coefficients based on stoichiometry from a balanced equation. For PbCrO₄, the corresponding equation would be \[\text{PbCrO}_4(s) \rightleftharpoons \text{Pb}^{2+}(aq) + \text{CrO}_4^{2-}(aq)\]. The position of equilibrium can shift in response to various factors like temperature and concentration, impacting how much solid remains versus how much dissolves into ions.

Stoichiometry

At its core, stoichiometry involves calculating relationships between reactants and products in a chemical reaction. It helps predict how substances will react and in what proportions. This is vital in writing equilibrium equations because the coefficients in a balanced equation inform the stoichiometric relationship between ions and molecules.

For example, analyzing the dissolution of MnO₂ involves writing:\[\text{MnO}_2(s) \rightleftharpoons \text{Mn}^{4+}(aq) + 2\text{O}^{2-}(aq)\]. The coefficients (1 for Mn⁴⁺ and 2 for O^2-) indicate that one manganese ion pairs with two oxide ions.

In practice:

• Coefficients show the stoichiometry. For the dissolution of a compound like Al₂S₃, the equation becomes:
• \[\text{Al}_2\text{S}_3(s) \rightleftharpoons 2\text{Al}^{3+}(aq) + 3\text{S}^{2-}(aq)\]
• This equation highlights that two aluminum ions emerge for every three sulfide ions produced in the solution.

Chemical Equilibrium

Chemical equilibrium is a crucial concept that helps explain how reaction rates can equalize in a closed system, where reactants and products form at the same rate. This results in the concentrations staying constant, although not necessarily equal.

In the case of solubility, such as the dissolution of substances like PbCrO₄, the equilibrium is reached when the rate of dissolution of the solid into its ions equals the rate at which the ions recombine to form the solid. The K_sp expression describes this precise balance between solid and solute ion concentrations.

Factors influencing chemical equilibrium include:

• Changes in concentration of ions or reactants.
• Temperature shifts, which can alter solubility and equilibrium position.
• Pressure changes, mainly for gases, though pressure is less impactful in solubility equilibria of solids in liquids.

Understanding these principles aids in predicting the outcomes of dissolving different compounds, adjusting conditions to favor dissolving or precipitating, and facilitating better experimental controls and outcomes in laboratories.