First slide

Ionization constants of weak acids, PH of weak acids

Question

The dissociation constants of H₂S and HS^–1 are respectively 10^–7 and 10^–13. The P^H of the aqueous solution containing 0.2 mole of H₂S dissolved in 1 lit water is

Easy

A

3
B

4
C

5
D

6

Solution

In case of weak diprotic acid, the H⁺ ions are mainly contributed in the first dissociation step.
$\large \mathop {{H_2}S}\limits_{{C_0} - x} \rightleftharpoons \mathop {H{S^ - }}\limits_{x - y} + \mathop {{H^ + };}\limits_{x + y} {K_{{a_1}}} = {10^{ - 7}}$
$\large \mathop {H{S^ - }}\limits_{x - y} \rightleftharpoons \mathop {{S^{ - 2}}}\limits_y + \mathop {{H^ + };}\limits_{y + x} {K_{{a_2}}} = {10^{ - 13}}$
$\large {K_{{a_1}}} \gg {K_{{a_2}}} \Rightarrow x \gg y$
$\large {K_{{a_1}}} = {10^{ - 7}} = \frac{{\left( {x - y} \right)\left( {x + y} \right)}}{{{C_0} - x}}$
Neglecting x in front of C₀ and y infront of x
$\large \Rightarrow {10^{ - 7}} = \frac{{x \times x}}{{{C_0}}}$
$\large \Rightarrow x = \sqrt {{{10}^{ - 7}} \times 2 \times {{10}^{ - 1}}} = 1.414 \times {10^{ - 4}}$
P^H = 4 - log 1.414 ~ 4.

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