200 mL of 0.05 M HCl is mixed with 300 mL of 0.1 M acetic acid (K_a=1.8x10^-5). The pH of the mixture is nearest to (use log2=0.301)

JEE Advanced levelSingle correct optionDifficulty 3 of 3ie091

$200 mL$ of $0.05 M$ $HCl$ is mixed with $300 mL$ of $0.1 M$ acetic acid ( $K_{a} = 1.8 \times 1 0^{- 5}$ ). The pH of the mixture is nearest to (use $lo g 2 = 0.301$ )

After mixing (500 mL):

[HCl] = 10/500 = 0.02 M

and

[HA] = 30/500 = 0.06 M

. The weak acid adds

x \approx K_{a} (0.06) /0.02 = 5.4 \times 1 0^{- 5} M

, negligible against

0.02

. So

[H X^{+}] = 0.02

and

pH = 2 - 0.301 = 1.70

. Treating the weak acid alone would give 2.98.