In a galvanic cell, after running the cell for sometimes, the concentration of the electrolyte is automatically raised to 3 m HCl. Molar conductivity of the 3 m HCl is about `"240 S cm"^(2)" mol"^(-1)` and limiting molar conductivity of HCl is about `"420 cm"^(2)" mol"^(-1)`. If `K_(b)` of water is `"0.52 K kg mol"^(-1)`, calculate the boiling point of the electrolyte at the end of the experiment.

Options

A. 375.6 K
B. 376.3 K
C. 378.1 K
D. 380.3 K

Answer

To solve the problem, we will follow these steps:

### Step 1: Understanding the Dissociation of HCl
HCl dissociates in water as follows:
\[ \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \]

### Step 2: Calculate the Degree of Dissociation (α)
The degree of dissociation (α) can be calculated using the formula:
\[ \alpha = \frac{\Lambda_m}{\Lambda_m^0} \]
where:
- \(\Lambda_m\) is the molar conductivity of the solution (given as 240 S cm² mol⁻¹).
- \(\Lambda_m^0\) is the limiting molar conductivity of HCl (given as 420 S cm² mol⁻¹).

Substituting the values:
\[ \alpha = \frac{240}{420} = 0.5714 \]

### Step 3: Calculate the Van't Hoff Factor (i)
The Van't Hoff factor (i) can be calculated using:
\[ i = 1 + \alpha \]
Substituting the value of α:
\[ i = 1 + 0.5714 = 1.5714 \]

### Step 4: Calculate the Molality (m)
Given that the concentration of HCl is 3 m, we can directly use this value for molality:
\[ m = 3 \, \text{mol/kg} \]

### Step 5: Calculate the Boiling Point Elevation (ΔTb)
The boiling point elevation can be calculated using the formula:
\[ \Delta T_b = i \cdot K_b \cdot m \]
where:
- \(K_b\) is the ebullioscopic constant of water (given as 0.52 K kg mol⁻¹).

Substituting the values:
\[ \Delta T_b = 1.5714 \cdot 0.52 \cdot 3 \]
\[ \Delta T_b = 2.45 \, \text{K} \]

### Step 6: Calculate the New Boiling Point (Tb)
The boiling point of pure water (T₀b) is 100 °C, which is equivalent to 373.15 K. The new boiling point can be calculated as:
\[ T_b = T_{b0} + \Delta T_b \]
Substituting the values:
\[ T_b = 373.15 + 2.45 = 375.6 \, \text{K} \]

### Final Answer
The boiling point of the electrolyte at the end of the experiment is:
\[ \boxed{375.6 \, \text{K}} \]

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