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, C2H5OH) in a mixture that contains 46% ethyl alcohol by weight, we can follow these steps:

### Step 1: Determine the mass of ethanol and water in the mixture
Given that the mixture is 100 grams and contains 46% ethanol by weight:
- Mass of ethanol = 46 grams
- Mass of water = 100 grams - 46 grams = 54 grams

### Step 2: Calculate the number of moles of ethanol
To find the number of moles of ethanol, we need its molar mass. The molar mass of ethanol (C2H5OH) can be calculated as follows:
- Molar mass of C2H5OH = (2 × 12) + (6 × 1) + (16) = 24 + 6 + 16 = 46 g/mol

Now, we can calculate the moles of ethanol:
- Moles of ethanol = Mass of ethanol / Molar mass of ethanol
- Moles of ethanol = 46 g / 46 g/mol = 1 mole

### Step 3: Calculate the number of moles of water
Next, we calculate the moles of water (H2O). The molar mass of water is:
- Molar mass of H2O = (2 × 1) + (16) = 2 + 16 = 18 g/mol

Now, we can calculate the moles of water:
- Moles of water = Mass of water / Molar mass of water
- Moles of water = 54 g / 18 g/mol = 3 moles

### Step 4: Calculate the total number of moles in the mixture
Now we can find the total number of moles in the mixture:
- Total moles = Moles of ethanol + Moles of water
- Total moles = 1 mole + 3 moles = 4 moles

### Step 5: Calculate the mole fraction of ethanol
The mole fraction of ethanol (C2H5OH) is given by the formula:
- Mole fraction of ethanol = Moles of ethanol / Total moles
- Mole fraction of ethanol = 1 mole / 4 moles = 0.25

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

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