Calculate the mass of urea (`NH_2CONH_2`) required in making 1.5kg of 0.45 molal aqueous solution.

Options

A. 22.5g
B. 39.4g
C. 44g
D. 32g

Explanation

To calculate the mass of urea (NH₂CONH₂) required to make a 1.5 kg of 0.45 molal aqueous solution, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Molality**:
Molality (m) is defined as the number of moles of solute per kilogram of solvent. Here, we have a 0.45 molal solution, which means there are 0.45 moles of urea in 1 kg of water.

2. **Calculate the Moles of Urea for 1.5 kg of Water**:
Since the solution is 0.45 molal, we can calculate the moles of urea needed for 1.5 kg of water:
\[ \text{Moles of urea} = 0.45 \, \text{mol/kg} \times 1.5 \, \text{kg} = 0.675 \, \text{moles} \]

3. **Find the Molar Mass of Urea**:
The molar mass of urea (NH₂CONH₂) is calculated as follows:
- Nitrogen (N): 14 g/mol × 2 = 28 g/mol
- Carbon (C): 12 g/mol × 1 = 12 g/mol
- Oxygen (O): 16 g/mol × 1 = 16 g/mol
- Hydrogen (H): 1 g/mol × 4 = 4 g/mol
\[ \text{Total molar mass of urea} = 28 + 12 + 16 + 4 = 60 \, \text{g/mol} \]

4. **Calculate the Mass of Urea**:
Now, we can calculate the mass of urea required using the number of moles and the molar mass:
\[ \text{Mass of urea} = \text{Moles of urea} \times \text{Molar mass of urea} \]
\[ \text{Mass of urea} = 0.675 \, \text{moles} \times 60 \, \text{g/mol} = 40.5 \, \text{grams} \]

5. **Final Result**:
Therefore, the mass of urea required to make 1.5 kg of a 0.45 molal aqueous solution is **40.5 grams**.