The mass of NaCl required to prepare 0.4 m aqueous solution in 1kg water is

Options

A. 23.4g
B. 25g
C. 28g
D. 14g

Explanation

To find the mass of NaCl required to prepare a 0.4 molal aqueous solution in 1 kg of water, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Molality**:
Molality (m) is defined as the number of moles of solute per kilogram of solvent. The formula is:
\[ m = \frac{\text{number of moles of solute}}{\text{mass of solvent in kg}} \]

2. **Identify Given Values**:
- Molality (m) = 0.4 mol/kg
- Mass of solvent (water) = 1 kg
- Molar mass of NaCl = 58.5 g/mol

3. **Calculate the Number of Moles of NaCl**:
Rearranging the molality formula to find the number of moles of solute:
\[ \text{number of moles of NaCl} = m \times \text{mass of solvent in kg} \]
Substitute the known values:
\[ \text{number of moles of NaCl} = 0.4 \, \text{mol/kg} \times 1 \, \text{kg} = 0.4 \, \text{mol} \]

4. **Calculate the Mass of NaCl**:
Now, we can find the mass of NaCl using the number of moles and the molar mass:
\[ \text{mass of NaCl} = \text{number of moles} \times \text{molar mass} \]
Substitute the values:
\[ \text{mass of NaCl} = 0.4 \, \text{mol} \times 58.5 \, \text{g/mol} = 23.4 \, \text{g} \]

5. **Conclusion**:
The mass of NaCl required to prepare a 0.4 molal aqueous solution in 1 kg of water is **23.4 grams**.