Question

Find the value of \(K_{b}\) for the conjugate base of the following organic acids. (a) picric acid used in the manufacture of explosives; \(K_{\mathrm{a}}=0.16\) (b) trichloroacetic acid used in the treatment of warts; \(K_{\mathrm{a}}=0.20\)

Short answer

Question: Calculate the base dissociation constant (\(K_b\)) for the conjugate base of (a) Picric acid (\(K_a = 0.16\)) and (b) Trichloroacetic acid (\(K_a = 0.20\)) at 25°C. Use the ion product constant for water (\(K_w = 1.0 \times 10^{-14}\)). Answer: (a) Picric acid: \(K_b = 6.25 \times 10^{-14}\). (b) Trichloroacetic acid: \(K_b = 5 \times 10^{-14}\).

Step-by-step solution

Review the relationship between \(K_a\), \(K_b\), and \(K_w\)

The relationship between the acidic dissociation constant (\(K_a\)), the base dissociation constant (\(K_b\)), and the ion product constant for water (\(K_w\)) is given by: \(K_a \times K_b = K_w\).

Calculate the values of \(K_b\) for each example

Using the given \(K_a\) values and the formula for the relationship between \(K_a\), \(K_b\), and \(K_w\), we can now calculate the values of \(K_b\) for each example. (a) For picric acid, \(K_a = 0.16\). To find the corresponding \(K_b\), we can use the formula: \(K_b = \frac{K_w}{K_a} = \frac{1.0 \times 10^{-14}}{0.16}\) \(K_b = 6.25 \times 10^{-14}\) (b) For trichloroacetic acid, \(K_a = 0.20\). To find the corresponding \(K_b\), we can use the formula: \(K_b = \frac{K_w}{K_a} = \frac{1.0 \times 10^{-14}}{0.20}\) \(K_b = 5 \times 10^{-14}\)

Present the results

The values of \(K_b\) for the conjugate bases of picric acid and trichloroacetic acid are as follows: (a) Picric acid: \(K_b = 6.25 \times 10^{-14}\) (b) Trichloroacetic acid: \(K_b = 5 \times 10^{-14}\)