At `18^(@)` C, the conductance of `H^(+) and CH3COO^(-)` at infinite dilution are 315 and 35 mho `cm^(2) eq^(-1)` respectively. The equivalent conductance of `CH_(3)COOH` at infinite dilution is ........ mho `cm^(2) eq^(-1)` .

Options

A. 350
B. 280
C. 30
D. 315

Answer

To find the equivalent conductance of acetic acid (CH₃COOH) at infinite dilution, we can use the known conductance values of its ions at infinite dilution. The dissociation of acetic acid can be represented as:

\[ \text{CH}_3\text{COOH} \rightleftharpoons \text{H}^+ + \text{CH}_3\text{COO}^- \]

### Step-by-Step Solution:

1. **Identify the given values**:
- Conductance of \( \text{H}^+ \) at infinite dilution, \( \lambda_{\text{H}^+} = 315 \, \text{mho cm}^2 \text{eq}^{-1} \)
- Conductance of \( \text{CH}_3\text{COO}^- \) at infinite dilution, \( \lambda_{\text{CH}_3\text{COO}^-} = 35 \, \text{mho cm}^2 \text{eq}^{-1} \)

2. **Write the formula for equivalent conductance**:
The equivalent conductance of a weak acid at infinite dilution can be calculated using the formula:
\[ \lambda_{\text{CH}_3\text{COOH}} = \lambda_{\text{H}^+} + \lambda_{\text{CH}_3\text{COO}^-} \]

3. **Substitute the known values**:
\[ \lambda_{\text{CH}_3\text{COOH}} = 315 + 35 \]

4. **Perform the calculation**:
\[ \lambda_{\text{CH}_3\text{COOH}} = 350 \, \text{mho cm}^2 \text{eq}^{-1} \]

5. **State the final answer**:
The equivalent conductance of acetic acid (CH₃COOH) at infinite dilution is:
\[ \lambda_{\text{CH}_3\text{COOH}} = 350 \, \text{mho cm}^2 \text{eq}^{-1} \]