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 will use Kohlrausch's Law. This law states that the equivalent conductance of an electrolyte at infinite dilution is equal to the sum of the conductances of its constituent ions.

### Step-by-Step Solution:

1. **Identify the ions produced by acetic acid**:
When acetic acid (CH₃COOH) dissociates in water, it produces two ions:
- H⁺ (hydrogen ion)
- CH₃COO⁻ (acetate ion)

2. **Write the equation for equivalent conductance**:
According to Kohlrausch's Law:
\[ \Lambda^\circ_{CH_3COOH} = \Lambda^\circ_{H^+} + \Lambda^\circ_{CH_3COO^-} \]
where:
- \(\Lambda^\circ_{CH_3COOH}\) is the equivalent conductance of acetic acid at infinite dilution,
- \(\Lambda^\circ_{H^+}\) is the conductance of H⁺ at infinite dilution,
- \(\Lambda^\circ_{CH_3COO^-}\) is the conductance of CH₃COO⁻ at infinite dilution.

3. **Substitute the given values**:
From the problem, we know:
- \(\Lambda^\circ_{H^+} = 315 \, \text{mho cm}^2 \text{eq}^{-1}\)
- \(\Lambda^\circ_{CH_3COO^-} = 35 \, \text{mho cm}^2 \text{eq}^{-1}\)

Now substitute these values into the equation:
\[ \Lambda^\circ_{CH_3COOH} = 315 + 35 \]

4. **Calculate the equivalent conductance**:
\[ \Lambda^\circ_{CH_3COOH} = 350 \, \text{mho cm}^2 \text{eq}^{-1} \]

5. **State the final answer**:
The equivalent conductance of acetic acid (CH₃COOH) at infinite dilution is:
\[ \Lambda^\circ_{CH_3COOH} = 350 \, \text{mho cm}^2 \text{eq}^{-1} \]