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 by adding 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:
\[ \text{Moles} = \text{Molarity} \times \text{Volume (in L)} \]
Given:
- Molarity (M) = 0.02 M
- Volume (V) = 4 L

Calculating the moles:
\[ \text{Moles of NaCl} = 0.02 \, \text{M} \times 4 \, \text{L} = 0.08 \, \text{moles} \]

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

### Step 3: Calculate the molarity of the resultant solution.
Using the dilution formula \(M_1V_1 = M_2V_2\):
- \(M_1 = 0.02 \, \text{M}\)
- \(V_1 = 4 \, \text{L}\)
- \(V_2 = 5 \, \text{L}\)

We need to find \(M_2\):
\[ 0.02 \, \text{M} \times 4 \, \text{L} = M_2 \times 5 \, \text{L} \]
\[ 0.08 = M_2 \times 5 \]
\[ M_2 = \frac{0.08}{5} = 0.016 \, \text{M} \]

### Step 4: Convert molarity to molality.
To find molality (m), we need to know the mass of the solvent (water) in kilograms. Since we added 1 L of water, and the density of water is approximately 1 kg/L, we have:
\[ \text{Mass of water} = 1 \, \text{kg} \]

Now, we can calculate molality using the formula:
\[ \text{Molality (m)} = \frac{\text{moles of solute}}{\text{mass of solvent (in kg)}} \]
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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