For H2CO3, K_a2 = 4.7x10^-11 and K_w = 1.0x10^-14. Neglecting the second hydrolysis step of CO3^2- and solving the first-step quadratic exactly, find the pH of 0.100 M Na2CO3 (two decimals).

JEE Main levelNumerical answerDifficulty 2 of 3ia182

For $H X_{2} CO X_{3}$ , $K_{a 2} = 4.7 \times 1 0^{- 11}$ and $K_{w} = 1.0 \times 1 0^{- 14}$ . Neglecting the second hydrolysis step of $CO X_{3} X^{2 -}$ and solving the first-step quadratic exactly, find the pH of $0.100 M$ $Na X_{2} CO X_{3}$ (two decimals).

Numerical answer type, tolerance 0.01.

K_{h} = K_{w} / K_{a 2} = 2.13 \times 1 0^{- 4}

. For

CO X_{3} X^{2 -} + H X_{2} O ⇌ HCO X_{3} X^{-} + OH X^{-}

x^{2} / (0.100 - x) = K_{h}

gives

[OH X^{-}] = 0.00451 M

. So

pOH = 2.346

and

pH = 11.65