MHT CET · Chemistry · Ionic Equilibrium
Which of the following is NOT a correct mathematical equation for Ostwald dilution law?
- A \(\propto=\sqrt{\frac{\mathrm{K}_{\mathrm{a}}}{\mathrm{c}}}\)
- B \(\mathrm{K}=\frac{\propto^2}{\mathrm{~V}}\)
- C \(\mathrm{K}=\propto^2 \mathrm{c}\)
- D \(\propto=\sqrt{\frac{\mathrm{K}_{\mathrm{a}}}{\mathrm{V}}}\)
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,
\(
\begin{aligned}
& \mathrm{HA}_{(\mathrm{aq})} \rightleftharpoons \mathrm{H}_{(\mathrm{aq})}^{+}+\mathrm{A}_{(\mathrm{aq})}^{-} \\
& \mathrm{C} \quad-\quad- \\
& \mathrm{C}-\mathrm{C} \propto \quad \mathrm{C} \propto \quad \mathrm{C} \propto \\
& \mathrm{K}_{\mathrm{a}}=\frac{\left[\mathrm{H}^{+}\right]\left[\mathrm{A}^{-}\right]}{[\mathrm{HA}]} \\
& \mathrm{K}_{\mathrm{a}}=\frac{\mathrm{C} \propto^2}{1-\propto c}(1-\propto \simeq 1) \\
& \mathrm{K}_{\mathrm{a}}=\mathrm{C} \propto^2 \\
& \propto^2=\frac{\mathrm{K}_{\mathrm{a}}}{\mathrm{C}} \\
& \propto=\sqrt{\frac{\mathrm{K}_{\mathrm{a}}}{\mathrm{C}}}
\end{aligned}
\)
\(
\begin{aligned}
& \mathrm{HA}_{(\mathrm{aq})} \rightleftharpoons \mathrm{H}_{(\mathrm{aq})}^{+}+\mathrm{A}_{(\mathrm{aq})}^{-} \\
& \mathrm{C} \quad-\quad- \\
& \mathrm{C}-\mathrm{C} \propto \quad \mathrm{C} \propto \quad \mathrm{C} \propto \\
& \mathrm{K}_{\mathrm{a}}=\frac{\left[\mathrm{H}^{+}\right]\left[\mathrm{A}^{-}\right]}{[\mathrm{HA}]} \\
& \mathrm{K}_{\mathrm{a}}=\frac{\mathrm{C} \propto^2}{1-\propto c}(1-\propto \simeq 1) \\
& \mathrm{K}_{\mathrm{a}}=\mathrm{C} \propto^2 \\
& \propto^2=\frac{\mathrm{K}_{\mathrm{a}}}{\mathrm{C}} \\
& \propto=\sqrt{\frac{\mathrm{K}_{\mathrm{a}}}{\mathrm{C}}}
\end{aligned}
\)
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