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

To find the concentration of hydrogen ions in the solution, we can use the expression for the dissociation constant of a weak acid:

$K_a = \frac{[H^+]^2}{[HA] - [H^+]}$

Where:

• $K_a = 2.51 \times 10^{-10}$
• $[HA]$ is the initial concentration of the weak acid (2.00 \times 10^{-3} \ mol \ dm^{-3}$)

Assuming that the dissociation is small, we can approximate: $K_a \approx \frac{[H^+]^2}{[HA]} \\ [H^+]^2 = K_a \times [HA]$

Substituting the known values: $[H^+]^2 = 2.51 \times 10^{-10} \times 2.00 \times 10^{-3}$

Calculating this gives: $[H^+]^2 = 5.02 \times 10^{-13}$

Taking the square root: $[H^+] = \sqrt{5.02 \times 10^{-13}} \approx 7.09 \times 10^{-7} \ mol \ dm^{-3}$

Therefore, the answer is closest to option B: 7.09 \times 10^{-7}.