Derive an equation similar to the Henderson–Hasselbalch equation relating the pOH of a buffer to the pKb of its base component.

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Start with the base dissociation equilibrium: \( B + H_2O \rightleftharpoons BH^+ + OH^- \).

Write the expression for the base dissociation constant \( K_b \): \( K_b = \frac{[BH^+][OH^-]}{[B]} \).

Take the negative logarithm of both sides of the \( K_b \) expression: \( -\log K_b = -\log \left( \frac{[BH^+][OH^-]}{[B]} \right) \).

Rearrange the equation to express \( \text{pOH} \): \( \text{pOH} = \text{pKb} + \log \left( \frac{[BH^+]}{[B]} \right) \).

This equation is analogous to the Henderson–Hasselbalch equation, relating \( \text{pOH} \) to \( \text{pKb} \) for a buffer system.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a mathematical relationship that connects the pH of a buffer solution to the concentration of its acidic and basic components. It is expressed as pH = pKa + log([A-]/[HA]), where pKa is the negative logarithm of the acid dissociation constant. This equation is crucial for understanding how buffers maintain pH levels in biological and chemical systems.

pOH and pKb Relationship

The pOH of a solution is a measure of the hydroxide ion concentration, defined as pOH = -log[OH-]. The pKb is the negative logarithm of the base dissociation constant (Kb) and indicates the strength of a base. The relationship between pOH and pKb is essential for deriving a similar equation to the Henderson-Hasselbalch equation, allowing for the analysis of basic buffer systems.

Buffer Solutions

Buffer solutions are mixtures that resist changes in pH when small amounts of acid or base are added. They typically consist of a weak acid and its conjugate base or a weak base and its conjugate acid. Understanding the composition and function of buffers is vital for deriving equations that describe their behavior, such as the one relating pOH to pKb.

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Buffer Solutions

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