A solution containing 12.5 g of non - electrolyte substance in 175 g of water gave boiling point elevation of 0.70 K. Calculate the molar mass of the substance. Elevation constant `(K_(b))` for water `"0.52 K kg mol"^(-1)`?

Options

A. 53
B. 65
C. 84
D. 79

Answer

To calculate the molar mass of the non-electrolyte substance based on the given data, we can follow these steps:

### Step 1: Understand the given data
- Mass of the solute (non-electrolyte substance) = 12.5 g
- Mass of the solvent (water) = 175 g
- Boiling point elevation (ΔT) = 0.70 K
- Boiling point elevation constant (K_b) for water = 0.52 K kg mol⁻¹

### Step 2: Use the formula for boiling point elevation
The formula for boiling point elevation is given by:
\[ \Delta T = K_b \times m \]
where:
- \( \Delta T \) is the boiling point elevation,
- \( K_b \) is the boiling point elevation constant,
- \( m \) is the molality of the solution.

### Step 3: Rearrange the formula to find molality
Rearranging the formula to find molality (m):
\[ m = \frac{\Delta T}{K_b} \]

### Step 4: Substitute the known values
Substituting the known values into the equation:
\[ m = \frac{0.70 \, \text{K}}{0.52 \, \text{K kg mol}^{-1}} \approx 1.346 \, \text{mol/kg} \]

### Step 5: Calculate the number of moles of solute
Molality (m) is defined as the number of moles of solute per kilogram of solvent. Thus:
\[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \]
Converting the mass of solvent from grams to kilograms:
\[ \text{mass of solvent} = 175 \, \text{g} = 0.175 \, \text{kg} \]
Now, we can express the number of moles of solute:
\[ \text{moles of solute} = m \times \text{mass of solvent in kg} = 1.346 \, \text{mol/kg} \times 0.175 \, \text{kg} \approx 0.2356 \, \text{mol} \]

### Step 6: Calculate the molar mass of the solute
Molar mass (M) is defined as the mass of the solute divided by the number of moles of solute:
\[ M = \frac{\text{mass of solute}}{\text{moles of solute}} = \frac{12.5 \, \text{g}}{0.2356 \, \text{mol}} \approx 53.06 \, \text{g/mol} \]

### Step 7: Final result
The molar mass of the non-electrolyte substance is approximately 53.06 g/mol.

### Summary
The calculated molar mass of the substance is approximately 53 g/mol, which corresponds to the closest integer option available.

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