A solution contains one mole of alcohol and four moles of water. What are the mole fractions of water and alcohol-

Options

A. 1/4,4/1
B. 4/1,1/4
C. 4/5,1/5
D. 1/5,4/5

Answer

To find the mole fractions of alcohol and water in the solution, we can follow these steps:

### Step 1: Identify the number of moles of each component.
- Given:
- Moles of alcohol (n_alcohol) = 1 mole
- Moles of water (n_water) = 4 moles

### Step 2: Calculate the total number of moles in the solution.
- Total moles (n_total) = n_alcohol + n_water
- n_total = 1 mole (alcohol) + 4 moles (water) = 5 moles

### Step 3: Calculate the mole fraction of alcohol.
- The formula for mole fraction (X) is:
\[ X_{component} = \frac{n_{component}}{n_{total}} \]
- For alcohol:
\[ X_{alcohol} = \frac{n_{alcohol}}{n_{total}} = \frac{1}{5} = 0.2 \]

### Step 4: Calculate the mole fraction of water.
- For water:
\[ X_{water} = \frac{n_{water}}{n_{total}} = \frac{4}{5} = 0.8 \]

### Step 5: Summarize the mole fractions.
- Mole fraction of alcohol (X_alcohol) = 0.2
- Mole fraction of water (X_water) = 0.8

### Final Answer:
- The mole fractions are:
- Mole fraction of alcohol = \( \frac{1}{5} \) or 0.2
- Mole fraction of water = \( \frac{4}{5} \) or 0.8

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