What is the pH of a 0.125 M solution of the weak base B if ΔH^∘=-28.0 kJ and ΔS^∘=-175 J / K f

step 1 To determine the pH of the solution, we first need to determine the delta G standard, which will

What is the pH of a 0.125 M solution of the weak base B if...

What is the $\mathrm{pH}$ of a $0.125 \mathrm{M}$ solution of the weak base $\mathrm{B}$ if $\Delta H^{\circ}=-28.0 \mathrm{~kJ}$ and $\Delta S^{\circ}=-175 \mathrm{~J} / \mathrm{K}$ for the following equi- librium reaction at $25^{\circ} \mathrm{C}$ ?$$\mathrm{B}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{BH}^{+}(a q)+\mathrm{OH}^{-}(a q)$$

What is the $\mathrm{pH}$ of a $0.125 \mathrm{M}$ solution of the weak base $\mathrm{B}$ if $\Delta H^{\circ}=-28.0 \mathrm{~kJ}$ and $\Delta S^{\circ}=-175 \mathrm{~J} / \mathrm{K}$ for the following equi-
librium reaction at $25^{\circ} \mathrm{C}$ ?$$\mathrm{B}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{BH}^{+}(a q)+\mathrm{OH}^{-}(a q)$$

Key Concepts

pH is the measure of the acidity or basicity of an aqueous solution, defined on a logarithmic scale as the negative logarithm of the hydrogen ion concentration. In the context of a weak base equilibrium, determining the pH helps quantify the extent of base ionization and thus the concentration of hydroxide ions in the solution.

Weak Base Equilibrium

Weak base equilibrium refers to the reversible reaction in which a weak base reacts with water to produce its conjugate acid and hydroxide ions. Since weak bases do not fully ionize in solution, the equilibrium position, typically expressed in terms of a base dissociation constant (Kb), is crucial for predicting the concentration of species at equilibrium.

Gibbs Free Energy and Thermodynamic Relationships

Gibbs free energy (?G°) is a thermodynamic potential that indicates the spontaneity of a reaction under constant temperature and pressure. It relates to the reaction enthalpy (?H°) and entropy (?S°) by the equation ?G° = ?H° - T?S°. This relationship is pivotal in understanding whether a reaction will proceed spontaneously and how temperature influences the equilibrium.

Equilibrium Constant

The equilibrium constant (K) quantifies the ratio of product to reactant concentrations at equilibrium. Through the Gibbs free energy relationship, ?G° = -RT ln K, one can calculate K from known thermodynamic data. This constant is essential for linking the microscopic thermodynamic properties of a reaction to its macroscopic equilibrium behavior, providing the basis for calculations involving the hydroxide ion concentration and hence the pH.

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