Mole fraction of ethanol is ethanol water mixture is 0.25. Hence, the percentage concentration of ethanol by weight of mixture is

Options

A. 0.25
B. 0.75
C. 0.46
D. 0.54

Explanation

To find the percentage concentration of ethanol by weight in an ethanol-water mixture where the mole fraction of ethanol is given as 0.25, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Mole Fraction**:
- The mole fraction of ethanol (X_ethanol) is given as 0.25. Therefore, the mole fraction of water (X_water) can be calculated as:
\[ X_{\text{water}} = 1 - X_{\text{ethanol}} = 1 - 0.25 = 0.75 \]

2. **Assuming a Total Amount**:
- Assume we have 1 mole of the mixture. This means:
- Moles of ethanol = 0.25 moles
- Moles of water = 0.75 moles

3. **Calculating Masses**:
- The molar mass of ethanol (C₂H₅OH) is approximately 46 g/mol.
- The molar mass of water (H₂O) is approximately 18 g/mol.
- Now, calculate the mass of ethanol:
\[ \text{Mass of ethanol} = \text{moles of ethanol} \times \text{molar mass of ethanol} = 0.25 \, \text{moles} \times 46 \, \text{g/mol} = 11.5 \, \text{grams} \]
- Calculate the mass of water:
\[ \text{Mass of water} = \text{moles of water} \times \text{molar mass of water} = 0.75 \, \text{moles} \times 18 \, \text{g/mol} = 13.5 \, \text{grams} \]

4. **Calculating Total Mass of the Mixture**:
- The total mass of the mixture is the sum of the mass of ethanol and the mass of water:
\[ \text{Total mass} = \text{Mass of ethanol} + \text{Mass of water} = 11.5 \, \text{grams} + 13.5 \, \text{grams} = 25 \, \text{grams} \]

5. **Calculating Percentage Concentration**:
- The percentage concentration of ethanol by weight in the mixture is given by:
\[ \text{Percentage concentration of ethanol} = \left( \frac{\text{Mass of ethanol}}{\text{Total mass}} \right) \times 100 \]
- Substituting the values:
\[ \text{Percentage concentration of ethanol} = \left( \frac{11.5 \, \text{grams}}{25 \, \text{grams}} \right) \times 100 = 46\% \]

### Final Answer:
The percentage concentration of ethanol by weight of the mixture is **46%**.