Question

For each value of \(K_{\mathrm{a}}\), calculate the corresponding value of \(\mathrm{p} K_{\mathrm{a}}\). Which compound is the stronger acid? (a) Acetic acid, \(K_{\mathrm{a}}=1.74 \times 10^{-5}\) (b) Chloroacetic acid, \(K_{\mathrm{a}}=1.38 \times 10^{-3}\)

Short answer

Question: Calculate the pKa values for acetic acid and chloroacetic acid, and determine which one is the stronger acid. Answer: The pKa value for acetic acid is 4.76, and the pKa value for chloroacetic acid is 2.86. Since the pKa value for chloroacetic acid is lower, it is the stronger acid.

Step-by-step solution

Calculate \(\mathrm{p} K_{\mathrm{a}}\) for Acetic Acid

To calculate the \(\mathrm{p} K_{\mathrm{a}}\) for acetic acid, use the formula \(\mathrm{p} K_{\mathrm{a}} = -\log K_{\mathrm{a}}\) and plug in the given \(K_{\mathrm{a}}\) value for acetic acid: \(\mathrm{p} K_{\mathrm{a}}=-\log(1.74 \times 10^{-5})\) Use a calculator to perform the logarithm operation: \(\mathrm{p} K_{\mathrm{a}}=4.76\) So the \(\mathrm{p} K_{\mathrm{a}}\) for acetic acid is 4.76.

Calculate \(\mathrm{p} K_{\mathrm{a}}\) for Chloroacetic Acid

Repeat the process for chloroacetic acid using its \(K_{\mathrm{a}}\) value: \(\mathrm{p} K_{\mathrm{a}}=-\log(1.38 \times 10^{-3})\) Use a calculator to perform the logarithm operation: \(\mathrm{p} K_{\mathrm{a}}=2.86\) So the \(\mathrm{p} K_{\mathrm{a}}\) for chloroacetic acid is 2.86.

Compare the \(\mathrm{p} K_{\mathrm{a}}\) Values to Determine the Stronger Acid

Now, we can compare the \(\mathrm{p} K_{\mathrm{a}}\) values of acetic acid and chloroacetic acid. The lower the \(\mathrm{p} K_{\mathrm{a}}\) value, the stronger the acid: Acetic acid: \(\mathrm{p} K_{\mathrm{a}} = 4.76\) Chloroacetic acid: \(\mathrm{p} K_{\mathrm{a}} = 2.86\) Since the \(\mathrm{p} K_{\mathrm{a}}\) value for chloroacetic acid (2.86) is lower than that of acetic acid (4.76), chloroacetic acid is the stronger acid.