The density of 3 M solution of NaCl is `1.25 "g mL"^(-1)`. Calculate molality of the solution.

Answer

To calculate the molality of a 3 M solution of NaCl with a density of 1.25 g/mL, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the given data**:
- Molarity (M) = 3 M (which means 3 moles of NaCl per liter of solution)
- Density of the solution = 1.25 g/mL

2. **Convert the density to grams per liter**:
- Since 1 mL = 0.001 L, the density in grams per liter (g/L) is:
\[ \text{Density} = 1.25 \, \text{g/mL} \times 1000 \, \text{mL/L} = 1250 \, \text{g/L} \]

3. **Calculate the mass of the solution**:
- For 1 liter of solution, the mass is 1250 g.

4. **Calculate the molar mass of NaCl**:
- The molar mass of NaCl (sodium chloride) is approximately 58.5 g/mol.

5. **Calculate the mass of NaCl in the solution**:
- Since the molarity is 3 M, the mass of NaCl in 1 L of solution is:
\[ \text{Mass of NaCl} = \text{Number of moles} \times \text{Molar mass} = 3 \, \text{mol} \times 58.5 \, \text{g/mol} = 175.5 \, \text{g} \]

6. **Calculate the mass of the solvent (water)**:
- The mass of the solvent (water) can be found by subtracting the mass of the solute (NaCl) from the total mass of the solution:
\[ \text{Mass of water} = \text{Mass of solution} - \text{Mass of NaCl} = 1250 \, \text{g} - 175.5 \, \text{g} = 1074.5 \, \text{g} \]

7. **Convert the mass of water to kilograms**:
- Since molality is expressed in kg of solvent, convert grams to kilograms:
\[ \text{Mass of water in kg} = \frac{1074.5 \, \text{g}}{1000} = 1.0745 \, \text{kg} \]

8. **Calculate the molality (m)**:
- Molality is defined as the number of moles of solute per kilogram of solvent:
\[ \text{Molality} = \frac{\text{Number of moles of NaCl}}{\text{Mass of water in kg}} = \frac{3 \, \text{mol}}{1.0745 \, \text{kg}} \approx 2.79 \, \text{mol/kg} \]

### Final Answer:
The molality of the 3 M NaCl solution is approximately **2.79 mol/kg**.