The percentage of ethyl alchol by weight is 46% in a mixture of ethanol and water. The mole fraction of alcohol in this solution is

Options

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

Answer

To find the mole fraction of ethyl alcohol (ethanol) in a mixture that is 46% by weight, we can follow these steps:

### Step 1: Determine the mass of ethyl alcohol and water in the solution
Given that the mixture is 46% ethyl alcohol by weight, in a 100 g solution:
- Mass of ethyl alcohol = 46 g
- Mass of water = 100 g - 46 g = 54 g

### Step 2: Calculate the number of moles of ethyl alcohol
The molar mass of ethyl alcohol (C₂H₅OH) can be calculated as follows:
- Carbon (C) = 12 g/mol × 2 = 24 g/mol
- Hydrogen (H) = 1 g/mol × 6 = 6 g/mol
- Oxygen (O) = 16 g/mol × 1 = 16 g/mol
- Total molar mass of C₂H₅OH = 24 + 6 + 16 = 46 g/mol

Now, we can find the number of moles of ethyl alcohol:
\[ \text{Number of moles of ethyl alcohol} = \frac{\text{mass}}{\text{molar mass}} = \frac{46 \text{ g}}{46 \text{ g/mol}} = 1 \text{ mole} \]

### Step 3: Calculate the number of moles of water
The molar mass of water (H₂O) is:
- Hydrogen (H) = 1 g/mol × 2 = 2 g/mol
- Oxygen (O) = 16 g/mol × 1 = 16 g/mol
- Total molar mass of H₂O = 2 + 16 = 18 g/mol

Now, we can find the number of moles of water:
\[ \text{Number of moles of water} = \frac{\text{mass}}{\text{molar mass}} = \frac{54 \text{ g}}{18 \text{ g/mol}} = 3 \text{ moles} \]

### Step 4: Calculate the total number of moles in the solution
\[ \text{Total moles} = \text{moles of ethyl alcohol} + \text{moles of water} = 1 + 3 = 4 \text{ moles} \]

### Step 5: Calculate the mole fraction of ethyl alcohol
The mole fraction of ethyl alcohol (C₂H₅OH) is given by the formula:
\[ \text{Mole fraction of ethyl alcohol} = \frac{\text{moles of ethyl alcohol}}{\text{total moles}} = \frac{1}{4} = 0.25 \]

### Final Answer
The mole fraction of ethyl alcohol in the solution is **0.25**.

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