`A` mixture of ethanol and water contains `54%` water by mass. Calculate the mole fraction of alcohol in this solution.

Explanation

To solve the problem of calculating the mole fraction of ethanol in a mixture that contains 54% water by mass, we can follow these steps:

### Step 1: Determine the mass of each component in the solution
Assume we have a total mass of the solution as 100 grams. Given that the solution contains 54% water by mass:
- Mass of water = 54 grams
- Mass of ethanol = Total mass - Mass of water = 100 grams - 54 grams = 46 grams

### Step 2: Calculate the number of moles of each component
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{Mass (g)}}{\text{Molar mass (g/mol)}} \]

**For ethanol (C₂H₅OH):**
- Molar mass of ethanol = 46 g/mol
- Moles of ethanol = \( \frac{46 \text{ g}}{46 \text{ g/mol}} = 1 \text{ mole} \)

**For water (H₂O):**
- Molar mass of water = 18 g/mol
- Moles of water = \( \frac{54 \text{ g}}{18 \text{ g/mol}} = 3 \text{ moles} \)

### Step 3: Calculate the total number of moles in the solution
Total moles = Moles of ethanol + Moles of water
\[ \text{Total moles} = 1 + 3 = 4 \text{ moles} \]

### Step 4: Calculate the mole fraction of ethanol
The mole fraction of a component is given by the formula:
\[ \text{Mole fraction of ethanol} = \frac{\text{Moles of ethanol}}{\text{Total moles}} \]
\[ \text{Mole fraction of ethanol} = \frac{1}{4} = 0.25 \]

### Final Answer
The mole fraction of ethanol in the solution is **0.25**.

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