At `25^@C` equivalent conductance of a week acid HAc is `16.2 "ohm"^(-1) cm^(2) eq^(-1)`.If the ionic conductances of `Ac^(-)` and `H^(+)`at infinite dilution are respectively `40.9 and 349.8 "ohm"^(-1)cm^(2)eq^(-1).,` calculate the percentage dissociation of the week acid at `25^@C`.

Answer

To solve the problem of calculating the percentage dissociation of the weak acid HAc at 25°C, we will follow these steps:

### Step 1: Identify the Given Data
We have the following information:
- Equivalent conductance of weak acid (HAc), \( \Lambda = 16.2 \, \Omega^{-1} \, \text{cm}^2 \, \text{eq}^{-1} \)
- Ionic conductance of acetate ion, \( \Lambda^0_{\text{Ac}^-} = 40.9 \, \Omega^{-1} \, \text{cm}^2 \, \text{eq}^{-1} \)
- Ionic conductance of hydrogen ion, \( \Lambda^0_{H^+} = 349.8 \, \Omega^{-1} \, \text{cm}^2 \, \text{eq}^{-1} \)

### Step 2: Calculate the Equivalent Conductance at Infinite Dilution for HAc
The equivalent conductance at infinite dilution for the weak acid (HAc) can be calculated using the formula:
\[ \Lambda^0_{\text{HAc}} = \Lambda^0_{\text{Ac}^-} + \Lambda^0_{H^+} \]
Substituting the values:
\[ \Lambda^0_{\text{HAc}} = 40.9 + 349.8 = 390.7 \, \Omega^{-1} \, \text{cm}^2 \, \text{eq}^{-1} \]

### Step 3: Calculate the Degree of Dissociation (α)
The degree of dissociation (α) can be calculated using the formula:
\[ \alpha = \frac{\Lambda}{\Lambda^0_{\text{HAc}}} \]
Substituting the known values:
\[ \alpha = \frac{16.2}{390.7} \approx 0.0415 \]

### Step 4: Calculate the Percentage Dissociation
To find the percentage dissociation, we multiply α by 100:
\[ \text{Percentage Dissociation} = \alpha \times 100 = 0.0415 \times 100 \approx 4.15\% \]

### Final Answer
The percentage dissociation of the weak acid HAc at 25°C is approximately **4.15%**.

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