2,4,6-Trichlorophenol is a weak monoprotic acid, with $K_a = 2.51 \times 10^{-5} \: mol \: dm^{-3}$ at 298 K - AQA - A-Level Chemistry - Question 9 - 2017 - Paper 3

To determine the concentration of hydrogen ions from the weak acid 2,4,6-trichlorophenol in solution, we apply the formula for weak acids:

$K_a = \frac{[H^+][A^-]}{[HA]}$

In the case of a monoprotic acid, we can assume that:

• $[H^+] = [A^-]$
• $[HA]$ is approximated as the initial concentration minus dissociation, which is relatively small.

Given the initial concentration of 2,00 \times 10^{-3} mol dm$^{-3}$:

• Let $x = [H^+] = [A^-]$.
• Thus, we have: $K_a = \frac{x^2}{(2.00 \times 10^{-3} - x)} \approx \frac{x^2}{2.00 \times 10^{-3}}$ (assuming $x$ is small compared to the initial concentration).

Now substituting in the values:

$2.51 \times 10^{-5} = \frac{x^2}{2.00 \times 10^{-3}}$

Rearranging gives:

$x^2 = 2.51 \times 10^{-5} \times 2.00 \times 10^{-3}$

Calculating $x^2$:

$x^2 = 5.02 \times 10^{-8}$

Taking the square root:

$x = \sqrt{5.02 \times 10^{-8}} \approx 7.09 \times 10^{-4} \: mol \: dm^{-3}$

Thus, the concentration of hydrogen ions is approximately:

$\mathbf{7.09 \times 10^{-4} \: mol \: dm^{-3}}$.