What will be the mole fraction of ethanol in a sample of spirit containing 85% ethanol by mass ?

Options

A. `0.69`
B. `0.82`
C. `0.85`
D. `0.60`

Explanation

To find the mole fraction of ethanol in a sample of spirit containing 85% ethanol by mass, we can follow these steps:

### Step 1: Determine the mass of ethanol and water in the solution.
Since the solution is 85% ethanol by mass, in a 100 g sample of the solution:
- Mass of ethanol = 85 g
- Mass of water = 100 g - 85 g = 15 g

### Step 2: Calculate the number of moles of ethanol.
The molar mass of ethanol (C₂H₅OH) is 46 g/mol. To find the number of moles of ethanol:
\[ \text{Number of moles of ethanol} = \frac{\text{Mass of ethanol}}{\text{Molar mass of ethanol}} = \frac{85 \text{ g}}{46 \text{ g/mol}} \approx 1.85 \text{ moles} \]

### Step 3: Calculate the number of moles of water.
The molar mass of water (H₂O) is 18 g/mol. To find the number of moles of water:
\[ \text{Number of moles of water} = \frac{\text{Mass of water}}{\text{Molar mass of water}} = \frac{15 \text{ g}}{18 \text{ g/mol}} \approx 0.833 \text{ moles} \]

### Step 4: Calculate the total number of moles in the solution.
\[ \text{Total moles} = \text{Number of moles of ethanol} + \text{Number of moles of water} = 1.85 + 0.833 \approx 2.683 \text{ moles} \]

### Step 5: Calculate the mole fraction of ethanol.
The mole fraction of ethanol (Xₑ) is given by the formula:
\[ X_{\text{ethanol}} = \frac{\text{Number of moles of ethanol}}{\text{Total moles}} = \frac{1.85}{2.683} \approx 0.689 \]

### Final Answer:
The mole fraction of ethanol in the spirit sample is approximately **0.689**.

---