Q13 / 160 · TS EAMCET 2018 (04 May Shift 2) · Chemistry

Estimate the approximate $\mathrm{p} K_a$ of $0.5 \mathrm{M}$ $\mathrm{CH}_3 \mathrm{COOH}$. Degree of dissociation (ionisation) is $0.15(\log 1.32=0.12)$

  • A
    2.0
  • B
    1.5
  • Correct answer
    C
    1.88
  • D
    0.15

Solution

$\begin{aligned} & \mathrm{CH}_3 \mathrm{COOH} \rightleftharpoons[\mathrm{H}]\left[\mathrm{CH}_3 \mathrm{COO}\right] \\ & \text { C } \\ & 0 \quad 0 \\ & \begin{array}{lll} C(1-\alpha) & \alpha \times C & \alpha \times C \end{array} \\ & K_a=\frac{C \alpha \times c \alpha}{C(1-\alpha)}=\frac{C \alpha^2}{1-\alpha} \\ & =\frac{0.5 \times 0.15 \times 0.15}{1-0.15}=\frac{0.01125}{0.85}=0.0132 \\ & \mathrm{p} K_a=-\log K_a=-\log 0.0132 \Rightarrow \mathrm{p} K_a=1.88 \\ & \end{aligned}$

Hence, the correct answer is option: 'C'.

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