Calculate the mole fraction of rectified spirit (95% ethyl alcohol by mass).

Explanation

To calculate the mole fraction of rectified spirit (95% ethyl alcohol by mass), we will follow these steps:

### Step 1: Determine the mass of ethyl alcohol and water
Given that rectified spirit is 95% ethyl alcohol by mass, we can assume we have 100 grams of the solution for simplicity. This means:
- Mass of ethyl alcohol = 95 grams
- Mass of water = 100 grams - 95 grams = 5 grams

### Step 2: Calculate the number of moles of ethyl alcohol
The molar mass of ethyl alcohol (C₂H₅OH) is calculated as follows:
- Carbon (C): 2 × 12 g/mol = 24 g/mol
- Hydrogen (H): 6 × 1 g/mol = 6 g/mol
- Oxygen (O): 1 × 16 g/mol = 16 g/mol
- Total molar mass of ethyl alcohol = 24 + 6 + 16 = 46 g/mol

Now, we can calculate the number of moles of ethyl alcohol:
\[ \text{Number of moles of ethyl alcohol} = \frac{\text{mass of ethyl alcohol}}{\text{molar mass of ethyl alcohol}} = \frac{95 \text{ g}}{46 \text{ g/mol}} \approx 2.07 \text{ moles} \]

### Step 3: Calculate the number of moles of water
The molar mass of water (H₂O) is:
- Hydrogen (H): 2 × 1 g/mol = 2 g/mol
- Oxygen (O): 1 × 16 g/mol = 16 g/mol
- Total molar mass of water = 2 + 16 = 18 g/mol

Now, we can calculate the number of moles of water:
\[ \text{Number of moles of water} = \frac{\text{mass of water}}{\text{molar mass of water}} = \frac{5 \text{ g}}{18 \text{ g/mol}} \approx 0.277 \text{ moles} \]

### Step 4: Calculate the total number of moles
Total number of moles in the solution:
\[ \text{Total moles} = \text{moles of ethyl alcohol} + \text{moles of water} = 2.07 + 0.277 \approx 2.347 \text{ moles} \]

### Step 5: Calculate the mole fraction of ethyl alcohol
The mole fraction (X) of ethyl alcohol is given by the formula:
\[ X_{\text{ethyl alcohol}} = \frac{\text{moles of ethyl alcohol}}{\text{total moles}} = \frac{2.07}{2.347} \approx 0.88 \]

### Final Result
The mole fraction of rectified spirit (ethyl alcohol) is approximately **0.88**.

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