Question

The dissociation constant of weak acid HA is \(1.5\times 10^{-5}\). Find the percent dissociation, containing \(0.2\) moles per \(2\) liters of solution.

• A. \(1.22\%\)
• B. \(1.18\%\)
• C. \(1.14\%\)
• D. \(1.26\%\)

Hint:

Use C = 0.1 M and alpha = sqrt(Ka/C), then multiply by 100.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
For a weak acid HA, only a small fraction splits into ions. Ostwald dilution law links the dissociation constant \(K_a\), the concentration \(C\) and the degree of dissociation \(\alpha\).

Step 2: Key Formula:
For small \(\alpha\), \(K_a = C\alpha^2\), so \(\alpha = \sqrt{K_a/C}\). Percent dissociation is \(\alpha \times 100\).

Step 3: Find the concentration:
The amount is \(0.2\) mol in \(2\) L. So
\[ C = \frac{0.2}{2} = 0.1\ \text{M} \]

Step 4: Find the degree of dissociation:
\[ \alpha = \sqrt{\frac{1.5\times 10^{-5}}{0.1}} = \sqrt{1.5\times 10^{-4}} \]
Since \(\sqrt{1.5} = 1.2247\) and \(\sqrt{10^{-4}} = 10^{-2}\),
\[ \alpha = 1.2247\times 10^{-2} \]
This is small compared with 1, so the approximation is fine.

Step 5: Convert to percent:
\[ \text{Percent dissociation} = 1.2247\times 10^{-2}\times 100 \approx 1.22\% \]
Options (B), (C) and (D) are close values that come from arithmetic slips in the square root, so they are wrong.

Final Answer:
The percent dissociation is about 1.22 percent, which is option (A). \[ \boxed{1.22\%} \]