Mole fraction of ethyl alcohol in aqueous ethyl alcohol (`C_2H_5OH`) solution is 0.35. Hence percentage of ethyl alcohol by weight is:

Explanation

To find the percentage of ethyl alcohol (ethanol) by weight in an aqueous solution where the mole fraction of ethyl alcohol is 0.35, follow these steps:

### Step 1: Identify the mole fractions
Given:
- Mole fraction of ethyl alcohol (C₂H₅OH) = 0.35
- Mole fraction of water (H₂O) = 1 - 0.35 = 0.65

### Step 2: Use the mole fractions to find the number of moles
Assume we have 1 mole of the solution:
- Moles of ethyl alcohol = 0.35 moles
- Moles of water = 0.65 moles

### Step 3: Calculate the mass of ethyl alcohol
The molecular weight of ethyl alcohol (C₂H₅OH) is 46 g/mol.
- Mass of ethyl alcohol = moles × molecular weight
- Mass of ethyl alcohol = 0.35 moles × 46 g/mol = 16.1 g

### Step 4: Calculate the mass of water
The molecular weight of water (H₂O) is 18 g/mol.
- Mass of water = moles × molecular weight
- Mass of water = 0.65 moles × 18 g/mol = 11.7 g

### Step 5: Calculate the total mass of the solution
- Total mass of the solution = mass of ethyl alcohol + mass of water
- Total mass of the solution = 16.1 g + 11.7 g = 27.8 g

### Step 6: Calculate the percentage of ethyl alcohol by weight
- Percentage of ethyl alcohol = (mass of ethyl alcohol / total mass of solution) × 100
- Percentage of ethyl alcohol = (16.1 g / 27.8 g) × 100 ≈ 57.9%

### Final Answer:
The percentage of ethyl alcohol by weight in the solution is approximately **57.9%**.

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