Equivalent conductance of 0.1 M HA (weak acid) solution is 10 `Scm^2` equivalen`t^(–1)` and that at infinite dilution is 200 `Scm^(2)` equivalen`t^(–1)`. Hence pH of HA solution is

Options

A. 1.3
B. 1.7
C. 2.3
D. 3.7

Answer

To find the pH of a 0.1 M solution of a weak acid (HA) given its equivalent conductance, we can follow these steps:

### Step 1: Understand the given data
We have:
- Concentration of the weak acid (HA), C = 0.1 M
- Equivalent conductance of the weak acid solution, λ = 10 S cm² equivalent⁻¹
- Equivalent conductance at infinite dilution, λ₀ = 200 S cm² equivalent⁻¹

### Step 2: Calculate the degree of dissociation (α)
The degree of dissociation (α) can be calculated using the formula:
\[ \alpha = \frac{\lambda}{\lambda_0} \]
Substituting the values:
\[ \alpha = \frac{10}{200} = 0.05 \]

### Step 3: Calculate the concentration of H⁺ ions
For a weak acid HA that dissociates as:
\[ HA \rightleftharpoons H^+ + A^- \]
At equilibrium, the concentration of H⁺ ions can be expressed as:
\[ [H^+] = C \cdot \alpha \]
Substituting the values:
\[ [H^+] = 0.1 \cdot 0.05 = 0.005 \, \text{M} \]

### Step 4: Calculate the pH
The pH is calculated using the formula:
\[ \text{pH} = -\log[H^+] \]
Substituting the concentration of H⁺:
\[ \text{pH} = -\log(0.005) = -\log(5 \times 10^{-3}) = -\log(5) - \log(10^{-3}) \]
Using the logarithmic properties:
\[ \text{pH} = -\log(5) + 3 \]
We know that \(\log(5) \approx 0.698\), so:
\[ \text{pH} = 3 - 0.698 = 2.302 \]

### Conclusion
Thus, the pH of the 0.1 M HA solution is approximately **2.3**.

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