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 will follow these steps:

### Step 1: Determine the mass of ethanol and water in the solution.
Given that the spirit contains 85% ethanol by mass, we can assume we have 100 grams of the spirit for simplicity. Therefore:
- Mass of ethanol = 85 grams
- Mass of water = 100 grams - 85 grams = 15 grams

### Step 2: Calculate the molar mass of ethanol and water.
The molecular formula of ethanol (C₂H₅OH) is composed of:
- Carbon (C): 2 atoms × 12 g/mol = 24 g/mol
- Hydrogen (H): 6 atoms × 1 g/mol = 6 g/mol
- Oxygen (O): 1 atom × 16 g/mol = 16 g/mol

Adding these together gives the molar mass of ethanol:
\[ \text{Molar mass of ethanol} = 24 + 6 + 16 = 46 \text{ g/mol} \]

For water (H₂O):
- Hydrogen (H): 2 atoms × 1 g/mol = 2 g/mol
- Oxygen (O): 1 atom × 16 g/mol = 16 g/mol

Thus, the molar mass of water is:
\[ \text{Molar mass of water} = 2 + 16 = 18 \text{ g/mol} \]

### Step 3: Calculate the number of moles of ethanol and water.
Using the formula:
\[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}} \]

**For ethanol:**
\[ \text{Number of moles of ethanol} = \frac{85 \text{ g}}{46 \text{ g/mol}} \approx 1.85 \text{ moles} \]

**For water:**
\[ \text{Number of moles of water} = \frac{15 \text{ g}}{18 \text{ g/mol}} \approx 0.833 \text{ moles} \]

### Step 4: Calculate the mole fraction of ethanol.
The mole fraction (X) of a component in a solution is given by the formula:
\[ X_{\text{ethanol}} = \frac{\text{Moles of ethanol}}{\text{Moles of ethanol} + \text{Moles of water}} \]

Substituting the values we calculated:
\[ X_{\text{ethanol}} = \frac{1.85}{1.85 + 0.833} \]
\[ X_{\text{ethanol}} = \frac{1.85}{2.683} \approx 0.69 \]

### Conclusion:
The mole fraction of ethanol in the spirit is approximately 0.69.

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