Mole fraction of ethyl alcohol in aqueous ethyl alcohol (`C_2H_5OH`) solution is 0.33. Hence percentage of ethyl alcohol by weight is:

Options

A. 55.72%
B. 65.72%
C. 25.45%
D. 23%

Explanation

To find the percentage of ethyl alcohol by weight in an aqueous ethyl alcohol solution where the mole fraction of ethyl alcohol is 0.33, we can follow these steps:

### Step 1: Understand the Mole Fraction
The mole fraction of ethyl alcohol (C₂H₅OH) is given as 0.33. This means that in a mixture, 33% of the moles are ethyl alcohol, and the remaining 67% of the moles are water.

### Step 2: Calculate the Mole Fraction of Water
Since the mole fraction of ethyl alcohol is 0.33, the mole fraction of water can be calculated as:
\[ \text{Mole fraction of water} = 1 - \text{Mole fraction of ethyl alcohol} = 1 - 0.33 = 0.67 \]

### Step 3: Assign Molar Masses
- Molar mass of ethyl alcohol (C₂H₅OH) = 46 g/mol
- Molar mass of water (H₂O) = 18 g/mol

### Step 4: Calculate the Weight of Ethyl Alcohol
To find the weight of ethyl alcohol in the solution, we can use the mole fraction and molar mass:
\[ \text{Weight of ethyl alcohol} = \text{Mole fraction of ethyl alcohol} \times \text{Molar mass of ethyl alcohol} \]
\[ \text{Weight of ethyl alcohol} = 0.33 \times 46 \, \text{g/mol} = 15.18 \, \text{g} \]

### Step 5: Calculate the Weight of Water
Similarly, we can calculate the weight of water:
\[ \text{Weight of water} = \text{Mole fraction of water} \times \text{Molar mass of water} \]
\[ \text{Weight of water} = 0.67 \times 18 \, \text{g/mol} = 12.06 \, \text{g} \]

### Step 6: Calculate the Total Weight of the Solution
Now, we can find the total weight of the solution:
\[ \text{Total weight of solution} = \text{Weight of ethyl alcohol} + \text{Weight of water} \]
\[ \text{Total weight of solution} = 15.18 \, \text{g} + 12.06 \, \text{g} = 27.24 \, \text{g} \]

### Step 7: Calculate the Percentage by Weight of Ethyl Alcohol
Finally, we can calculate the percentage by weight of ethyl alcohol in the solution:
\[ \text{Percentage of ethyl alcohol} = \left( \frac{\text{Weight of ethyl alcohol}}{\text{Total weight of solution}} \right) \times 100 \]
\[ \text{Percentage of ethyl alcohol} = \left( \frac{15.18 \, \text{g}}{27.24 \, \text{g}} \right) \times 100 \approx 55.72\% \]

### Conclusion
The percentage of ethyl alcohol by weight in the solution is approximately **55.72%**.

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