Mole fraction of a solute in an aqueous solution is 0.2. The molality of the solution will be

Options

A. 13.88
B. 1.388
C. 0.138
D. 0.0138

Explanation

To find the molality of a solution given the mole fraction of the solute, we can follow these steps:

### Step 1: Understand the Definitions
- **Mole Fraction (X)**: The mole fraction of a component in a solution is the ratio of the number of moles of that component to the total number of moles of all components in the solution.
- **Molality (m)**: Molality is defined as the number of moles of solute per kilogram of solvent.

### Step 2: Identify Given Values
- The mole fraction of the solute (XB) is given as 0.2.

### Step 3: Calculate the Mole Fraction of the Solvent (XA)
Using the relationship:
\[ XA + XB = 1 \]
We can find the mole fraction of the solvent (XA):
\[ XA = 1 - XB = 1 - 0.2 = 0.8 \]

### Step 4: Determine the Molar Mass of the Solvent
Since the solvent is water (H2O), we calculate its molar mass:
- Molar mass of H2O = 2 (Hydrogen) + 16 (Oxygen) = 18 g/mol.

### Step 5: Use the Formula for Molality
The formula for molality (m) in terms of mole fraction is:
\[ m = \frac{XB \times 1000}{XA \times M_A} \]
Where:
- \( XB \) = mole fraction of solute = 0.2
- \( XA \) = mole fraction of solvent = 0.8
- \( M_A \) = molar mass of solvent = 18 g/mol

### Step 6: Substitute the Values into the Formula
Now, substitute the known values into the formula:
\[ m = \frac{0.2 \times 1000}{0.8 \times 18} \]

### Step 7: Calculate the Molality
Calculating the numerator and denominator:
- Numerator: \( 0.2 \times 1000 = 200 \)
- Denominator: \( 0.8 \times 18 = 14.4 \)

Now, divide:
\[ m = \frac{200}{14.4} \approx 13.88 \, \text{mol/kg} \]

### Final Answer
The molality of the solution is approximately **13.88 mol/kg**.

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