Question

A buffer solution is prepared by mixing 1.000 L of 0.050 M pentafluorobenzoic acidand 1.00 L of 0.060 M sodium pentafluoro benzoate. The K_a of this weak acid is 0.033. Determine the pH of the buffer solution.

Short answer

The pH of the buffer solution is $1.401$.

Step-by-step solution

Understanding the concept of buffer solution.

When the buffer resists any change in pH on addition of any acid or base, then the solution is termed as a buffer.

Writing the formula for pH of buffer solution

On applying the Henderson-Hasselbalch equation, the pH of a buffer solution has the formula as

$pH=pKa+\log \frac{\left[base\right]}{\left[acid\right]}$

Calculating the pKa

We have been given the Ka of the weak acid as.

So, the pKa will be

$$\begin{gathered} pKa=-\log Ka \\ pKa=-\log 0.033 \\ pKa=1.48 \end{gathered}$$

Calculating the pH of buffer solution

The base is sodium pentafluoro benzoate which is in the concentration $0.060$M, while the acid is pentafluorobenzoic acid in concentration $0.050$M.

So, the pH will be as follows:

$$\begin{gathered} pH=pKa+\log \frac{\left[base\right]}{\left[acid\right]} \\ pH=1.48+\log \frac{\left[0.050\right]}{\left[0.060\right]} \\ pH=1.48+\log 0.83 \\ pH=1.48-0.079 \\ pH=1.401 \end{gathered}$$

Therefore, the pH of the buffer solution is obtained as$1.401$.