The equivalent conductance of 1M benzoic acid is `12.8 ohm^(-1) cm^(2)` and if the conductance of benzoate ion and `H^+` ion at infinite dilution are `42 ohm^(-1) cm^(2)` and `288.42 ohm^(-1) cm^(2)` respectively . Then its degree of dissociation is

Answer

To find the degree of dissociation (α) of benzoic acid, we can use the formula:

\[ \alpha = \frac{\Lambda_{eq}}{\Lambda_{eq}^{\infty}} \]

where:
- \(\Lambda_{eq}\) is the equivalent conductance of the solution (given as 12.8 ohm\(^{-1}\) cm\(^{2}\)),
- \(\Lambda_{eq}^{\infty}\) is the equivalent conductance at infinite dilution.

### Step 1: Calculate the equivalent conductance at infinite dilution

The equivalent conductance at infinite dilution for benzoic acid (C₆H₅COOH) can be expressed as the sum of the conductances of its ions:

\[ \Lambda_{eq}^{\infty} = \Lambda_{C_6H_5COO^-} + \Lambda_{H^+} \]

Given:
- \(\Lambda_{C_6H_5COO^-} = 42 \, \text{ohm}^{-1} \text{cm}^2\)
- \(\Lambda_{H^+} = 288.42 \, \text{ohm}^{-1} \text{cm}^2\)

Now, substitute the values:

\[ \Lambda_{eq}^{\infty} = 42 + 288.42 = 330.42 \, \text{ohm}^{-1} \text{cm}^2 \]

### Step 2: Calculate the degree of dissociation (α)

Now, we can substitute \(\Lambda_{eq}\) and \(\Lambda_{eq}^{\infty}\) into the formula for α:

\[ \alpha = \frac{12.8}{330.42} \]

Calculating this gives:

\[ \alpha = 0.0387 \]

### Step 3: Convert α to percentage

To express the degree of dissociation as a percentage, we multiply by 100:

\[ \alpha \times 100 = 0.0387 \times 100 = 3.87\% \]

### Final Answer

Thus, the degree of dissociation of benzoic acid is:

\[ \alpha = 3.87\% \]

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