4 L of 0.02 M aqueous solution of NaCl was diluted by adding 1 L of water. The molality of the resultant solution is……..

Options

A. 0.004
B. 0.008
C. 0.012
D. 0.016

Explanation

To find the molality of the resultant solution after diluting 4 L of a 0.02 M NaCl solution with 1 L of water, we can follow these steps:

### Step 1: Calculate the number of moles of NaCl in the original solution.
The formula to calculate the number of moles is:
\[ \text{Number of moles} = \text{Molarity} \times \text{Volume} \]
Given:
- Molarity (M) = 0.02 M
- Volume (V) = 4 L

Calculating the number of moles:
\[ \text{Number of moles} = 0.02 \, \text{mol/L} \times 4 \, \text{L} = 0.08 \, \text{moles} \]

### Step 2: Find the total volume of the solution after dilution.
The total volume after adding 1 L of water to the original 4 L solution is:
\[ \text{Total Volume} = 4 \, \text{L} + 1 \, \text{L} = 5 \, \text{L} \]

### Step 3: Calculate the molarity of the diluted solution.
Using the formula for molarity:
\[ \text{Molarity} (M) = \frac{\text{Number of moles}}{\text{Total Volume in L}} \]
Substituting the values:
\[ \text{Molarity} = \frac{0.08 \, \text{moles}}{5 \, \text{L}} = 0.016 \, \text{M} \]

### Step 4: Calculate the mass of the solvent (water) in kilograms.
Since we have diluted the solution with 1 L of water, we can convert this volume to mass. The density of water is approximately 1 kg/L.
\[ \text{Mass of water} = 1 \, \text{L} \times 1 \, \text{kg/L} = 1 \, \text{kg} \]

### Step 5: Calculate the molality of the solution.
Molality (m) is defined as the number of moles of solute per kilogram of solvent:
\[ \text{Molality} (m) = \frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}} \]
Substituting the values:
\[ \text{Molality} = \frac{0.08 \, \text{moles}}{1 \, \text{kg}} = 0.08 \, \text{m} \]

### Final Answer:
The molality of the resultant solution is **0.08 m**.

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