Calculate the pH of a buffer solution containing 0.4 M acetic acid and 0.3 M sodium acetate. The pKa of…

Question

Calculate the pH of a buffer solution containing 0.4 M acetic acid and 0.3 M sodium acetate. The pKa of acetic acid is 4.74.

ScanSolve AI Tutor · Accepted Answer

To calculate the pH of the buffer solution, we will use the Henderson-Hasselbalch equation.

Identify the given values.
The buffer solution contains acetic acid ( $\text{CH}_3\text{COOH}$ ) as the weak acid and sodium acetate ( $\text{CH}_3\text{COONa}$ ) as the source of the conjugate base ( $\text{CH}_3\text{COO}^-$ ).
Concentration of weak acid, $[\text{CH}_3\text{COOH}] = 0.4 \, \text{M}$
Concentration of conjugate base, $[\text{CH}_3\text{COO}^-] = 0.3 \, \text{M}$ (since sodium acetate is a strong electrolyte, it dissociates completely)
$\text{pKa}$ of acetic acid $= 4.74$
Write the Henderson-Hasselbalch equation.
$\text{pH} = \text{pKa} + \log_{10}\left(\frac{[\text{conjugate base}]}{[\text{weak acid}]}\right)$
Substitute the values into the equation.
$\text{pH} = 4.74 + \log_{10}\left(\frac{0.3 \, \text{M}}{0.4 \, \text{M}}\right)$
Calculate the ratio and the logarithm.
$\text{pH} = 4.74 + \log_{10}(0.75)$ $\text{pH} = 4.74 + (-0.1249)$ $\text{pH} = 4.74 - 0.1249$ $\text{pH} = 4.6151$
Round the pH to an appropriate number of significant figures (usually two decimal places for pH).
$\text{pH} \approx 4.62$
The pH of the buffer solution is 4.62.

Calculate the pH of a buffer solution containing 0.4 M acetic acid and 0.3 M sodium acetate. The pKa of acetic acid is 4.74.