Calculate the pH for each of the following solutions at 25^∘...

Calculate the $\mathrm{pH}$ for each of the following solutions at $25^{\circ} \mathrm{C}$ :
(a) $0.10 M \mathrm{NH}_{3},$ (b) $0.050 M \mathrm{C}_{5} \mathrm{H}_{5} \mathrm{N}$ (pyridine). $(K_{\mathrm{b}}$ for pyridine $=1.7 \times 10^{-9}$.)

Key Concepts

Weak Base Equilibrium

This concept explains that weak bases only partially react with water to generate hydroxide ions (OH–) and their corresponding conjugate acids, establishing an equilibrium between the base, water, and the products. The equilibrium is governed by the base’s dissociation constant (Kb), which quantitatively characterizes the extent of the reaction.

Base Dissociation Constant (Kb)

Kb is a numerical value that represents the strength of a base in water. It is defined by the equilibrium concentrations of the products (hydroxide ions and the conjugate acid) divided by the equilibrium concentration of the base. A higher Kb indicates a stronger base, while a lower Kb signifies a weaker base, which is critical in calculating the concentration of hydroxide ions in solution.

ICE Table Setup

The ICE (Initial, Change, Equilibrium) table is a systematic approach used to calculate the equilibrium concentrations in a chemical reaction. For weak bases, it helps in setting up the initial concentrations, determining the changes that occur as the base reacts with water, and then solving for the unknown equilibrium concentrations using the Kb expression.

Approximations in Equilibrium

When dealing with weak bases that have very small Kb values, the change in concentration (often denoted as x) is usually much smaller than the initial concentration. This allows the assumption that the initial concentration remains nearly unchanged, thereby simplifying the algebra involved in solving the equilibrium expression.

pH and pOH Relationship

In aqueous solutions at 25°C, the pH is related to the pOH by the equation pH + pOH = 14. After calculating the concentration of hydroxide ions from the Kb equilibrium, the pOH can be determined using the negative logarithm of the hydroxide ion concentration, and then converted to pH, which is essential for assessing the basicity of the solution.

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