The density of `2M` solution of `NaCl` is `1.25 g mL^(-1)`. The molality of the solution is

Options

A. `1.18m`
B. `2.00m`
C. `1.60m`
D. `1.76m`

Answer

To find the molality of a 2M solution of NaCl with a density of 1.25 g/mL, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- Molarity (M) = 2M
- Density (D) = 1.25 g/mL
- Molecular weight of NaCl = 23 (Na) + 35.5 (Cl) = 58.5 g/mol

2. **Convert Density to g/L**:
Since the density is given in g/mL, we can convert it to g/L:
\[ D = 1.25 \, \text{g/mL} \times 1000 \, \text{mL/L} = 1250 \, \text{g/L} \]

3. **Use the Formula for Molality**:
The relationship between molarity (M), density (D), and molality (m) is given by:
\[ m = \frac{M \times 1000}{1000D - M \times \text{Molecular Weight}} \]

4. **Substitute the Values into the Formula**:
Plug in the values we have:
\[ m = \frac{2 \times 1000}{1000 \times 1.25 - 2 \times 58.5} \]

5. **Calculate the Denominator**:
First, calculate \(1000 \times 1.25\):
\[ 1000 \times 1.25 = 1250 \]
Then calculate \(2 \times 58.5\):
\[ 2 \times 58.5 = 117 \]
Now, subtract these two results:
\[ 1250 - 117 = 1133 \]

6. **Calculate the Molality**:
Now substitute back into the equation:
\[ m = \frac{2000}{1133} \approx 1.76 \, \text{molal} \]

### Final Answer:
The molality of the solution is approximately **1.76 molal**.

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