Mole fraction of ethyl alcohol in aqueous ethyl alcohol (`C_2H_5OH`) solution is 0.75. Hence percentage of ethyl alcohol by weight is:

Options

A. 81.42%
B. 88.46%
C. 32.45%
D. 74.45%

Explanation

To find the percentage of ethyl alcohol (ethanol, C₂H₅OH) by weight in an aqueous solution where the mole fraction of ethyl alcohol is 0.75, we can follow these steps:

### Step 1: Understand the mole fraction
The mole fraction (X) of ethyl alcohol is given as 0.75. This means that in a mixture of ethyl alcohol and water, 75% of the moles are ethyl alcohol and 25% are water.

### Step 2: Define the moles of components
Let’s assume we have 1 mole of the solution.
- Moles of ethyl alcohol (C₂H₅OH) = 0.75 moles
- Moles of water (H₂O) = 1 - 0.75 = 0.25 moles

### Step 3: Calculate the mass of ethyl alcohol
The molar mass of ethyl alcohol (C₂H₅OH) is 46 g/mol. Therefore, the mass of ethyl alcohol in the solution is:
\[ \text{Mass of ethyl alcohol} = \text{Moles} \times \text{Molar mass} = 0.75 \, \text{moles} \times 46 \, \text{g/mol} = 34.5 \, \text{g} \]

### Step 4: Calculate the mass of water
The molar mass of water (H₂O) is 18 g/mol. Therefore, the mass of water in the solution is:
\[ \text{Mass of water} = \text{Moles} \times \text{Molar mass} = 0.25 \, \text{moles} \times 18 \, \text{g/mol} = 4.5 \, \text{g} \]

### Step 5: Calculate the total mass of the solution
The total mass of the solution is the sum of the masses of ethyl alcohol and water:
\[ \text{Total mass of solution} = \text{Mass of ethyl alcohol} + \text{Mass of water} = 34.5 \, \text{g} + 4.5 \, \text{g} = 39 \, \text{g} \]

### Step 6: Calculate the percentage by weight of ethyl alcohol
The percentage by weight of ethyl alcohol in the solution is given by:
\[ \text{Percentage of ethyl alcohol} = \left( \frac{\text{Mass of ethyl alcohol}}{\text{Total mass of solution}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage of ethyl alcohol} = \left( \frac{34.5 \, \text{g}}{39 \, \text{g}} \right) \times 100 \approx 88.46\% \]

### Final Answer
The percentage of ethyl alcohol by weight in the solution is approximately **88.46%**.

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