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MHT CET · Chemistry · Ionic Equilibrium

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

  1. A \(\propto=\sqrt{\frac{\mathrm{K}_{\mathrm{a}}}{\mathrm{c}}}\)
  2. B \(\mathrm{K}=\frac{\propto^2}{\mathrm{~V}}\)
  3. C \(\mathrm{K}=\propto^2 \mathrm{c}\)
  4. D \(\propto=\sqrt{\frac{\mathrm{K}_{\mathrm{a}}}{\mathrm{V}}}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\propto=\sqrt{\frac{\mathrm{K}_{\mathrm{a}}}{\mathrm{V}}}\)

Step-by-step Solution

Detailed explanation

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