Mole fraction of ethyl alcohol in aqueous ethyl alcohol (`C_2H_5OH`) solution is 0.25. Hence percentage of ethyl alcohol by weight is:

Options

A. 54%
B. 25%
C. 46%
D. 44%

Explanation

To find the percentage of ethyl alcohol by weight in an aqueous ethyl alcohol solution where the mole fraction of ethyl alcohol is 0.25, we can follow these steps:

### Step 1: Understand the mole fraction
The mole fraction of ethyl alcohol (C₂H₅OH) is given as 0.25. This means that in a mixture, for every 1 mole of ethyl alcohol, there are 3 moles of water (since the total mole fraction must equal 1).

- Mole fraction of water = 1 - Mole fraction of ethyl alcohol = 1 - 0.25 = 0.75

### Step 2: Calculate the number of moles
Assuming we have 1 mole of the solution:
- Moles of ethyl alcohol = 0.25
- Moles of water = 0.75

### Step 3: Calculate the mass of ethyl alcohol
The molecular weight of ethyl alcohol (C₂H₅OH) is 46 g/mol. Therefore, the mass of ethyl alcohol can be calculated as:
- Mass of ethyl alcohol = Moles of ethyl alcohol × Molecular weight of ethyl alcohol
- Mass of ethyl alcohol = 0.25 moles × 46 g/mol = 11.5 grams

### Step 4: Calculate the mass of water
The molecular weight of water (H₂O) is 18 g/mol. Therefore, the mass of water can be calculated as:
- Mass of water = Moles of water × Molecular weight of water
- Mass of water = 0.75 moles × 18 g/mol = 13.5 grams

### Step 5: Calculate the total mass of the solution
Total mass of the solution = Mass of ethyl alcohol + Mass of water
- Total mass = 11.5 grams + 13.5 grams = 25 grams

### Step 6: Calculate the percentage of ethyl alcohol by weight
The percentage of ethyl alcohol by weight can be calculated using the formula:
- Percentage of ethyl alcohol = (Mass of ethyl alcohol / Total mass of solution) × 100
- Percentage of ethyl alcohol = (11.5 grams / 25 grams) × 100 = 46%

### Final Answer
The percentage of ethyl alcohol by weight in the solution is **46%**.

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