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

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 1: Understand the definitions
- **Molarity (M)** is defined as the number of moles of solute per liter of solution.
- **Molality (m)** is defined as the number of moles of solute per kilogram of solvent.

### Step 2: Gather the given data
- Molarity (M) = 3 M
- Density of the solution = 1.25 g/mL
- Molar mass of NaCl = 23 g/mol (Na) + 35.5 g/mol (Cl) = 58.5 g/mol

### Step 3: Calculate the mass of the solution
Since the density is given in g/mL, we can convert it to grams per liter:
- Density = 1.25 g/mL = 1.25 g/mL × 1000 mL/L = 1250 g/L

### Step 4: Calculate the mass of the solute in 1 L of solution
Using the molarity, we can find the number of moles of NaCl in 1 L of solution:
- Moles of NaCl = Molarity × Volume = 3 moles/L × 1 L = 3 moles

Now, calculate the mass of NaCl:
- Mass of NaCl = Moles × Molar mass = 3 moles × 58.5 g/mol = 175.5 g

### Step 5: Calculate the mass of the solvent
The total mass of the solution is 1250 g (from the density calculation). To find the mass of the solvent (water), we subtract the mass of the solute from the total mass of the solution:
- Mass of solvent = Total mass of solution - Mass of solute
- Mass of solvent = 1250 g - 175.5 g = 1074.5 g

### Step 6: Convert the mass of the solvent to kilograms
- Mass of solvent in kg = 1074.5 g × (1 kg / 1000 g) = 1.0745 kg

### Step 7: Calculate the molality
Now we can calculate the molality using the formula:
- Molality (m) = Moles of solute / Mass of solvent in kg
- Molality = 3 moles / 1.0745 kg ≈ 2.79 m

### Final Answer
The molality of the solution is approximately **2.79 m**.

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