Which of the following is NOT a correct mathematical equation for Ostwald dilution law?

Which of the following is NOT a correct mathematical equation for Ostwald dilution law?
  1. $\propto=\sqrt{\frac{\mathrm{K}_{\mathrm{a}}}{\mathrm{c}}}$
  2. $\mathrm{K}=\frac{\propto^2}{\mathrm{~V}}$
  3. $\mathrm{K}=\propto^2 \mathrm{c}$
  4. $\propto=\sqrt{\frac{\mathrm{K}_{\mathrm{a}}}{\mathrm{V}}}$

Solution

Ostwald dilution law of weak electrolyte, $\begin{aligned} & \mathrm{HA}_{(\mathrm{aq})} \rightleftharpoons \mathrm{H}_{(\mathrm{aq})}^{+}+\mathrm{A}_{(\mathrm{aq})}^{-} \\ & \mathrm{C} \quad-\quad- \\ & \mathrm{C}-\mathrm{C} \propto \quad \mathrm{C} \propto \quad \mathrm{C} \propto \\ & \mathrm{K}_{\mathrm{a}}=\frac{\left[\mathrm{H}^{+}\right]\left[\mathrm{A}^{-}\right]}{[\mathrm{HA}]} \\ & \mathrm{K}_{\mathrm{a}}=\frac{\mathrm{C} \propto^2}{1-\propto c}(1-\propto \simeq 1) \\ & \mathrm{K}_{\mathrm{a}}=\mathrm{C} \propto^2 \\ & \propto^2=\frac{\mathrm{K}_{\mathrm{a}}}{\mathrm{C}} \\ & \propto=\sqrt{\frac{\mathrm{K}_{\mathrm{a}}}{\mathrm{C}}} \end{aligned}$

Asked in: MHT CET 2021 (22 Sep Shift 2)

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