A diprotic acid H2A has K_a1 = 5.0x10^-3 and a negligible K_a2. Calculate the pH of a 0.10 M solution of H2A by solving the quadratic for the first ionisation exactly. Give the answer to two decimal places.

JEE Main levelNumerical answerDifficulty 2 of 3ia028

A diprotic acid $H X_{2} A$ has $K_{a 1} = 5.0 \times 1 0^{- 3}$ and a negligible $K_{a 2}$ . Calculate the pH of a 0.10 M solution of $H X_{2} A$ by solving the quadratic for the first ionisation exactly. Give the answer to two decimal places.

Numerical answer type, tolerance 0.02.

K_{a 1} = x^{2} / (0.10 - x)

gives

x^{2} + 5.0 \times 1 0^{- 3} x - 5.0 \times 1 0^{- 4} = 0

, so

x = 0.0200

M. pH

= - lo g x = 1.70

. Since

α = 20

, the approximation

x ≪ c

would be poor.