Question

Find the values of \(K_{\mathrm{b}}\) for the conjugate bases of the following organic acids: (a) glycolic acid, used by dermatologists as a chemical peel; \(K_{\mathrm{a}}=1.5 \times 10^{-4}\) (b) butyric acid, responsible for the odor of rancid butter; \(K_{\mathrm{a}}=1.5 \times 10^{-5}\)

Short answer

Question: Determine the values of Kb for the conjugate bases of glycolic acid and butyric acid. Answer: The values of Kb for the conjugate bases of glycolic acid and butyric acid are 6.67 × 10^-11 and 6.67 × 10^-10, respectively.

Step-by-step solution

Write down the relationship between \(K_w\), \(K_a\), and \(K_b\).

We know that the ion product of water is related to \(K_a\) and \(K_b\) by the following equation: $$ K_w = K_a \times K_b $$

Find the value of \(K_w\).

\(K_w\) is the ion product constant of water and is equal to \(1.0 \times 10^{-14}\) at 25°C. We can use this value in our calculations.

Calculate the value of \(K_b\) for the conjugate base of glycolic acid.

Now, we have the value of \(K_a\) for glycolic acid (1.5 \(\times\) 10\(^{-4}\)). We can use the relationship to calculate \(K_b\): $$ K_b = \frac{K_w}{K_a} = \frac{1.0 \times 10^{-14}}{1.5 \times 10^{-4}} = 6.67 \times 10^{-11} $$ Therefore, the value of \(K_b\) for the conjugate base of glycolic acid is \(6.67 \times 10^{-11}\).

Calculate the value of \(K_b\) for the conjugate base of butyric acid.

Similarly, we have the value of \(K_a\) for butyric acid (1.5 \(\times\) 10\(^{-5}\)). We can use the relationship to calculate \(K_b\): $$ K_b = \frac{K_w}{K_a} = \frac{1.0 \times 10^{-14}}{1.5 \times 10^{-5}} = 6.67 \times 10^{-10} $$ Therefore, the value of \(K_b\) for the conjugate base of butyric acid is \(6.67 \times 10^{-10}\). In summary, the values of \(K_b\) for the conjugate bases of glycolic acid and butyric acid are \(6.67 \times 10^{-11}\) and \(6.67 \times 10^{-10}\), respectively.