8g of NaOH is dissolved in 18g of `H_(2)O`. Mole fraction of NaOH in solution and molality (in mol `kg^(-1)`) of the solutions respectively are:

Options

A. 0.2,11.11
B. 0.167,11.11
C. 0.2, 22.20
D. 0.167, 22.20

Explanation

To solve the problem of finding the mole fraction of NaOH in the solution and the molality of the solution, we can follow these steps:

### Step 1: Calculate the number of moles of NaOH
To find the number of moles of NaOH, we use the formula:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

Given:
- Mass of NaOH = 8 g
- Molar mass of NaOH = 40 g/mol

\[ \text{Number of moles of NaOH} = \frac{8 \, \text{g}}{40 \, \text{g/mol}} = 0.2 \, \text{mol} \]

### Step 2: Calculate the number of moles of water (H₂O)
Using the same formula for water:

Given:
- Mass of water = 18 g
- Molar mass of water = 18 g/mol

\[ \text{Number of moles of water} = \frac{18 \, \text{g}}{18 \, \text{g/mol}} = 1 \, \text{mol} \]

### Step 3: Calculate the mole fraction of NaOH
The mole fraction of NaOH (X_NaOH) can be calculated using the formula:

\[ X_{\text{NaOH}} = \frac{n_{\text{NaOH}}}{n_{\text{NaOH}} + n_{\text{H}_2O}} \]

Substituting the values we found:

\[ X_{\text{NaOH}} = \frac{0.2}{0.2 + 1} = \frac{0.2}{1.2} \approx 0.167 \]

### Step 4: Calculate the molality of the solution
Molality (m) is defined as the number of moles of solute per kilogram of solvent:

\[ m = \frac{n_{\text{solute}}}{\text{mass of solvent (kg)}} \]

We need to convert the mass of water from grams to kilograms:

\[ \text{Mass of water} = 18 \, \text{g} = 0.018 \, \text{kg} \]

Now we can calculate the molality:

\[ m = \frac{0.2 \, \text{mol}}{0.018 \, \text{kg}} \approx 11.11 \, \text{mol/kg} \]

### Final Results
- Mole fraction of NaOH in solution: **0.167**
- Molality of the solution: **11.11 mol/kg**