Question

Consider a buffer solution where [weak acid] \(>\) [conjugate base]. How is the \(\mathrm{pH}\) of the solution related to the \(\mathrm{p} K_{\mathrm{a}}\) value of the weak acid? If [conjugate base] > [weak acid], how is pH related to \(\mathrm{P} K_{\mathrm{a}}\) ?

Short answer

In summary, when the concentration of the weak acid is greater than its conjugate base in a buffer solution, the pH of the solution is less than the pKa value. Conversely, when the concentration of the conjugate base is greater than the weak acid, the pH of the solution is greater than the pKa value. This relationship is derived from the Henderson-Hasselbalch equation: \[ pH = pKa + log \frac{[\text{conjugate base}]}{[\text{weak acid}]}\]

Step-by-step solution

Recall the Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is used to determine the pH of a buffer solution: \[ pH = pKa + log \frac{[\text{conjugate base}]}{[\text{weak acid}]}\] where pH is the acidity of the solution, pKa refers to the combined dissociation constant of the weak acid, and the concentrations of the conjugate base and weak acid are given in moles per liter.

Determine the relationship between pH and pKa when [weak acid] > [conjugate base]

Given the condition [weak acid] > [conjugate base], we will use the Henderson-Hasselbalch equation: \[ pH = pKa + log \frac{[\text{conjugate base}]}{[\text{weak acid}]}\] We know that [weak acid] > [conjugate base], so the ratio \(\frac{[\text{conjugate base}]}{[\text{weak acid}]}\) is less than 1. Since the logarithm of a value less than 1 is negative (log x < 0 if 0 < x < 1), we have: \[ pH = pKa + log(\text{negative value})\] Therefore, when [weak acid] > [conjugate base], the pH of the solution is less than the pKa value.

Determine the relationship between pH and pKa when [conjugate base] > [weak acid]

Given the condition [conjugate base] > [weak acid], we will use the Henderson-Hasselbalch equation: \[ pH = pKa + log \frac{[\text{conjugate base}]}{[\text{weak acid}]}\] We know that [conjugate base] > [weak acid], so the ratio \(\frac{[\text{conjugate base}]}{[\text{weak acid}]}\) is greater than 1. Since the logarithm of a value greater than 1 is positive (log x > 0 if x > 1), we have: \[ pH = pKa + log(\text{positive value})\] Therefore, when [conjugate base] > [weak acid], the pH of the solution is greater than the pKa value.

Key concepts

Buffer Solution

A buffer solution is a special type of solution that resists changes in pH when small amounts of acid or base are added. It consists of a mixture of a weak acid and its conjugate base. This composition allows the solution to neutralize added acids or bases.

Key features of a buffer solution include:

• Maintaining a relatively constant pH.
• Containing both a weak acid and its conjugate base in equilibrium.
• Being crucial in biological systems to maintain stable pH conditions.

The most common type of buffer in biochemistry is a phosphate buffer, which is vital for many biological processes.

Weak Acid

A weak acid is an acid that only partially dissociates in solution. Unlike strong acids, which release all their hydrogen ions, weak acids release them slowly and are in equilibrium with their conjugate bases.

Characteristics of a weak acid include:

• Incompletely ionizing in solution.
• Having a higher pH than strong acids.
• Possessing a measurable pKa value.

Examples include acetic acid and citric acid. The partial dissociation of weak acids is key to their role in buffer solutions.

Conjugate Base

The conjugate base is the species that remains after a weak acid has donated a proton. In a buffer solution, the conjugate base works alongside the weak acid to counteract pH changes.

Understanding conjugate bases:

• Formed when a weak acid loses a hydrogen ion.
• Able to react with hydrogen ions to form the weak acid again.
• Helps stabilize the pH in buffer solutions.

An example is acetate, which is the conjugate base of acetic acid. Conjugate bases play essential roles in maintaining the desired pH levels within buffers.

pH

pH is a measure of the acidity or basicity of a solution. It is calculated as the negative logarithm of the hydrogen ion concentration.

Key aspects of pH include:

• Scale ranges from 0 to 14, with 7 as neutral.
• Below 7 indicates acidic solutions, above 7 indicates basic solutions.
• Essential for reactions, biological processes, and environmental science.

The pH of buffer solutions is determined using the Henderson-Hasselbalch equation, which relates pH to pKa and the concentrations of a weak acid and its conjugate base.

pKa

The pKa value is a key concept in understanding acid strength. It is the negative logarithm of the acid dissociation constant ( K_a ), representing the acid's tendency to donate protons.

Features of pKa include:

• Lower pKa value indicates a stronger acid.
• Used to predict the pH of buffer solutions via the Henderson-Hasselbalch equation.
• Helps in understanding the equilibrium between weak acids and their conjugate bases.

The pKa is crucial for designing buffer solutions that require specific pH ranges, making it a critical aspect of many chemical and biological applications.