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 when the mole fraction of the solute is given, we can follow these steps:

### Step 1: Understand the given information
We are given the mole fraction of the solute (let's denote it as \(X_{solute}\)) which is 0.2. In an aqueous solution, the solvent is water.

### Step 2: Calculate the mole fraction of the solvent
The mole fraction of the solvent (let's denote it as \(X_{solvent}\)) can be calculated using the relationship:
\[ X_{solvent} = 1 - X_{solute} \]
Substituting the given value:
\[ X_{solvent} = 1 - 0.2 = 0.8 \]

### Step 3: Relate mole fractions to moles
Let’s assume we have 1 mole of the solution. The moles of solute (\(n_{solute}\)) and moles of solvent (\(n_{solvent}\)) can be expressed as:
\[ n_{solute} = X_{solute} \times \text{Total moles} = 0.2 \times 1 = 0.2 \text{ moles} \]
\[ n_{solvent} = X_{solvent} \times \text{Total moles} = 0.8 \times 1 = 0.8 \text{ moles} \]

### Step 4: Calculate the mass of the solvent
To find the mass of the solvent (water), we use the number of moles of the solvent and the molar mass of water (approximately 18 g/mol):
\[ \text{Mass of solvent} = n_{solvent} \times \text{Molar mass of water} = 0.8 \text{ moles} \times 18 \text{ g/mol} = 14.4 \text{ grams} \]

### Step 5: Convert mass of solvent to kilograms
Since molality is defined as moles of solute per kilogram of solvent, we convert the mass of the solvent from grams to kilograms:
\[ \text{Mass of solvent in kg} = \frac{14.4 \text{ grams}}{1000} = 0.0144 \text{ kg} \]

### Step 6: Calculate molality
Molality (\(m\)) is defined as:
\[ m = \frac{n_{solute}}{\text{Mass of solvent in kg}} = \frac{0.2 \text{ moles}}{0.0144 \text{ kg}} \approx 13.89 \text{ mol/kg} \]

### Final Answer
The molality of the solution is approximately **13.89 mol/kg**.

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