Mole fraction of ethyl alcohol in aqueous ethyl alcohol (`C_2H_5OH`) solution is 0.20. Hence percentage of ethyl alcohol by weight is:

Options

A. 38.98%
B. 41%
C. 35.48%
D. 15%

Answer

To find the percentage of ethyl alcohol by weight in an aqueous ethyl alcohol solution where the mole fraction of ethyl alcohol is 0.20, we can follow these steps:

### Step 1: Understand the mole fraction
The mole fraction of ethyl alcohol (C₂H₅OH) is given as 0.20. This means that in a mixture, 20% of the moles are ethyl alcohol and the remaining 80% are water (H₂O).

### Step 2: Calculate the mole fraction of water
If the mole fraction of ethyl alcohol is 0.20, then the mole fraction of water can be calculated as:
\[ \text{Mole fraction of water} = 1 - \text{Mole fraction of ethyl alcohol} = 1 - 0.20 = 0.80 \]

### Step 3: Assume a number of moles for calculation
Assume we have 1 mole of the solution. This assumption simplifies our calculations. Therefore:
- Moles of ethyl alcohol = 0.20 moles
- Moles of water = 0.80 moles

### Step 4: Calculate the mass of ethyl alcohol
The molar mass of ethyl alcohol (C₂H₅OH) is 46 g/mol. Therefore, the mass of ethyl alcohol can be calculated as:
\[ \text{Mass of ethyl alcohol} = \text{Moles} \times \text{Molar mass} = 0.20 \, \text{moles} \times 46 \, \text{g/mol} = 9.2 \, \text{grams} \]

### Step 5: Calculate the mass of water
The molar mass of water (H₂O) is 18 g/mol. Therefore, the mass of water can be calculated as:
\[ \text{Mass of water} = \text{Moles} \times \text{Molar mass} = 0.80 \, \text{moles} \times 18 \, \text{g/mol} = 14.4 \, \text{grams} \]

### Step 6: Calculate the total mass of the solution
The total mass of the solution is the sum of the mass of ethyl alcohol and the mass of water:
\[ \text{Total mass of solution} = \text{Mass of ethyl alcohol} + \text{Mass of water} = 9.2 \, \text{grams} + 14.4 \, \text{grams} = 23.6 \, \text{grams} \]

### Step 7: Calculate the percentage of ethyl alcohol by weight
The percentage by weight of ethyl alcohol in the solution can be calculated using the formula:
\[ \text{Percentage of ethyl alcohol} = \left( \frac{\text{Mass of ethyl alcohol}}{\text{Total mass of solution}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage of ethyl alcohol} = \left( \frac{9.2 \, \text{grams}}{23.6 \, \text{grams}} \right) \times 100 \approx 38.98\% \]

### Final Answer
The percentage of ethyl alcohol by weight in the solution is approximately **38.98%**.

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