Mole fraction fo solvent in an aqueous solution is 0.8. What is the molality of this solution in mol/kg?

Options

A. `13.88xx10^(-2)`
B. `13.88xx10^(-1)`
C. `13.88`
D. `13.88xx10^(-3)`

Answer

To find the molality of the solution given that the mole fraction of the solvent is 0.8, we can follow these steps:

### Step 1: Understand the relationship between mole fractions
The mole fraction of the solute (X_solute) and the mole fraction of the solvent (X_solvent) must add up to 1:
\[ X_{solute} + X_{solvent} = 1 \]
Given that \( X_{solvent} = 0.8 \), we can find \( X_{solute} \):
\[ X_{solute} = 1 - X_{solvent} = 1 - 0.8 = 0.2 \]

### Step 2: Use the formula for molality
The formula for molality (m) is given as:
\[ m = \frac{X_{solute}}{X_{solvent}} \times \frac{1000}{M_{solvent}} \]
where \( M_{solvent} \) is the molar mass of the solvent.

### Step 3: Substitute the known values
We know:
- \( X_{solute} = 0.2 \)
- \( X_{solvent} = 0.8 \)
- The molar mass of water (the solvent) is approximately \( 18 \, \text{g/mol} \).

Now substituting these values into the formula:
\[ m = \frac{0.2}{0.8} \times \frac{1000}{18} \]

### Step 4: Calculate the molality
First, simplify \( \frac{0.2}{0.8} \):
\[ \frac{0.2}{0.8} = 0.25 \]
Now substitute this back into the equation:
\[ m = 0.25 \times \frac{1000}{18} \]
Calculating \( \frac{1000}{18} \):
\[ \frac{1000}{18} \approx 55.56 \]
Now multiply:
\[ m \approx 0.25 \times 55.56 \approx 13.89 \, \text{mol/kg} \]

### Final Answer
The molality of the solution is approximately \( 13.89 \, \text{mol/kg} \).

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