Q35 / 180 · AIIMS 2010 · Chemistry

What is the $\mathrm{pH}$ of $0.01 \mathrm{M}$ glycine solution? For glycine $K_{a_1}=4.5 \times 10^{-3}$ and $K_{a_2}=1.7 \times 10^{-10}$ at $298 \mathrm{~K}$.

  • A
    3.0
  • B
    10.0
  • Correct answer
    C
    7.06
  • D
    8.2

Solution

Glycine $\mathrm{H}_3 \mathrm{~N}^{+} \mathrm{CH}_2 \mathrm{COO}^{-}$is more acidic than basic. Instead of $K_b$ value, the second given $K_a$ value is corresponding to the $K_b$ value $\left(\because K_a \times K_b=10^{-14}\right)$. Hence, overall ionization constant, $$ \begin{aligned} & K=K_{a_1} \times K_{a_2}=4.5 \times 10^{-3} \times 1.7 \times 10^{-10} \\ & =7.65 \times 10^{-13} \\ & \mathrm{H}^{+}=\sqrt{K C}=\sqrt{7.65 \times 10^{-13} \times 0.01} \\ & =\sqrt{0.765 \times 10^{-14}}=0.87 \times 10^{-7} \mathrm{M} \\ & \mathrm{pH}=-\log \left(0.87 \times 10^{-7}\right)=7.06 \\ & \end{aligned} $$

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

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