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

Options

A. `25%`
B. `75%`
C. `46%`
D. `54%`

Explanation

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

### Step 1: Understand Mole Fractions
The mole fraction of ethanol (C2H5OH) is given as 0.25. This means that in a mixture of 1 mole, there are:
- Moles of ethanol = 0.25
- Moles of water (H2O) = 1 - 0.25 = 0.75

### Step 2: Calculate the Molar Masses
The molar masses are:
- Molar mass of ethanol (C2H5OH) = 46 g/mol
- Molar mass of water (H2O) = 18 g/mol

### Step 3: Calculate the Masses of Ethanol and Water
Using the number of moles and molar masses, we can calculate the masses:
- Mass of ethanol = Moles of ethanol × Molar mass of ethanol
\[ \text{Mass of ethanol} = 0.25 \, \text{moles} \times 46 \, \text{g/mol} = 11.5 \, \text{g} \]

- Mass of water = Moles of water × Molar mass of water
\[ \text{Mass of water} = 0.75 \, \text{moles} \times 18 \, \text{g/mol} = 13.5 \, \text{g} \]

### Step 4: Calculate the Total Mass of the Mixture
Now, we find the total mass of the mixture:
\[ \text{Total mass} = \text{Mass of ethanol} + \text{Mass of water} = 11.5 \, \text{g} + 13.5 \, \text{g} = 25 \, \text{g} \]

### Step 5: Calculate the Percentage Concentration of Ethanol by Weight
The percentage concentration of ethanol by weight is given by:
\[ \text{Percentage concentration} = \left( \frac{\text{Mass of ethanol}}{\text{Total mass}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage concentration} = \left( \frac{11.5 \, \text{g}}{25 \, \text{g}} \right) \times 100 = 46\% \]

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

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