An aqueous solution buffered by benzoic acid (C6 H5. COOH ) and sodium benzoate (C6 H5 COOHNa) i

step 1 Okay, so we're given a pH of 3 .10 and a concentration of HA, which is equal to .200M. So we're

An aqueous solution buffered by benzoic acid (C6 H5. COOH )...

An aqueous solution buffered by benzoic acid $\left(\mathrm{C}_{6} \mathrm{H}_{5}\right.$ $\mathrm{COOH}$ ) and sodium benzoate $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOHNa}\right)$ is 0.0500 $\mathrm{M}$ in both compounds. Given that benzoic acid's $K_{\mathrm{a}}$ equals $6.4 \times 10^{-5},$ what is the pH of the solution?

An aqueous solution buffered by benzoic acid $\left(\mathrm{C}_{6} \mathrm{H}_{5}\right.$
$\mathrm{COOH}$ ) and sodium benzoate $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOHNa}\right)$ is
0.0500 $\mathrm{M}$ in both compounds. Given that benzoic acid's
$K_{\mathrm{a}}$ equals $6.4 \times 10^{-5},$ what is the pH of the solution?

Key Concepts

pKa and Logarithmic Relationship

The pKa is the negative logarithm of the acid dissociation constant, calculated as pKa = -log(Ka). This value simplifies the comparison of acid strengths and is directly used in the Henderson-Hasselbalch equation to determine the pH of buffer solutions. It underscores the logarithmic nature of the pH scale, which compresses wide ranges of acidity into a manageable numerical scale.

Acid Dissociation Constant (Ka)

The acid dissociation constant, Ka, quantifies the extent to which a weak acid dissociates into its ions in solution. It reflects the strength of the acid; a small Ka indicates that the acid dissociates only slightly, meaning it is a weak acid. Ka is vital for understanding acid-base equilibria in buffered solutions.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation provides a relationship between the pH of a buffer solution, the pKa of the weak acid, and the ratio of the concentrations of the conjugate base to the acid. It is a fundamental tool for calculating the pH of buffer systems and for designing buffers with particular pH values.

Buffer Solution

A buffer solution is one that resists changes in its pH when small amounts of acid or base are added. It typically consists of a weak acid and its conjugate base (or a weak base and its conjugate acid), working together to neutralize added H+ or OH– ions, thereby maintaining a relatively stable pH.

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