When `0.6g` of urea dissolved in `100g` of water, the water will boil at `(K_(b)` for water `= 0.52kJ. mol^(-1)` and normal boiling point of water `=100^(@)C)`:

Options

A. `373.052 K`
B. `273.52K`
C. `372.48K`
D. `273.052K`

Explanation

To solve the problem of determining the boiling point of water when 0.6 g of urea is dissolved in 100 g of water, we will follow these steps:

### Step 1: Calculate the number of moles of urea
To find the number of moles of urea, we use the formula:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

The molar mass of urea (NH₂CONH₂) is approximately 60 g/mol.

\[ \text{Number of moles of urea} = \frac{0.6 \, \text{g}}{60 \, \text{g/mol}} = 0.01 \, \text{mol} \]

### Step 2: Convert the mass of water to kilograms
Since the weight of the solvent (water) needs to be in kilograms for the calculation, we convert 100 g to kg:

\[ \text{Weight of water} = 100 \, \text{g} = 0.1 \, \text{kg} \]

### Step 3: Calculate the boiling point elevation (ΔT_b)
Using the formula for boiling point elevation:

\[ \Delta T_b = K_b \cdot \frac{n}{m} \]

Where:
- \( K_b = 0.52 \, \text{K kg/mol} \)
- \( n = \text{number of moles of solute} = 0.01 \, \text{mol} \)
- \( m = \text{mass of solvent in kg} = 0.1 \, \text{kg} \)

Substituting the values:

\[ \Delta T_b = 0.52 \, \text{K kg/mol} \cdot \frac{0.01 \, \text{mol}}{0.1 \, \text{kg}} = 0.052 \, \text{K} \]

### Step 4: Calculate the new boiling point of the solution
The normal boiling point of water (T₀_b) is 100 °C, which is equivalent to 373 K. The boiling point of the solution (T_b) can be calculated as:

\[ T_b = T_0_b + \Delta T_b \]

Substituting the values:

\[ T_b = 373 \, \text{K} + 0.052 \, \text{K} = 373.052 \, \text{K} \]

### Step 5: Convert the boiling point back to Celsius (if needed)
Since the question asks for the boiling point in Celsius, we can convert it back:

\[ T_b = 373.052 \, \text{K} - 273 = 100.052 \, \text{°C} \]

### Final Answer
The boiling point of the solution is approximately **100.052 °C**.

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