Q60 / 180 · COMEDK 2023 (Morning Shift) · Chemistry
In a $0.2 \mathrm{~M}$ aqueous solution, lactic acid is $6.9 \%$ dissociated. The value of dissociation constant is
- A$6.5 \times 10^{-4}$
- Correct answerB$9.5 \times 10^{-4}$
- C$3.6 \times 10^{-2}$
- D$1.2 \times 10^{-4}$
Solution
For a weak acid dissociation $HA \rightleftharpoons H^{+} + A^{-}$, the dissociation constant $K_a$ is given by the expression $K_a = \dfrac{c \alpha^2}{1 - \alpha}$.
Given concentration $c = 0.2 \text{ M}$ and degree of dissociation $\alpha = 6.9 \% = 0.069$.
Since $\alpha$ is small, we can approximate $1 - \alpha \approx 1$, so $K_a \approx c \alpha^2$.
Substituting the values: $K_a = 0.2 \times (0.069)^2$.
$K_a = 0.2 \times 0.004761 = 0.0009522$.
Expressing in scientific notation, $K_a = 9.522 \times 10^{-4} \approx 9.5 \times 10^{-4}$.
Answer: $9.5 \times 10^{-4}$
Given concentration $c = 0.2 \text{ M}$ and degree of dissociation $\alpha = 6.9 \% = 0.069$.
Since $\alpha$ is small, we can approximate $1 - \alpha \approx 1$, so $K_a \approx c \alpha^2$.
Substituting the values: $K_a = 0.2 \times (0.069)^2$.
$K_a = 0.2 \times 0.004761 = 0.0009522$.
Expressing in scientific notation, $K_a = 9.522 \times 10^{-4} \approx 9.5 \times 10^{-4}$.
Answer: $9.5 \times 10^{-4}$
Hence, the correct answer is option: 'B'.