138 g of ethyl alcohol is mixed with 72 g of water. The ratio of mole fraction of alcohol to water is

Options

A. `3 :4`
B. `1 :2`
C. `1 :4`
D. `1 :1`

Answer

To solve the problem of finding the ratio of the mole fraction of ethyl alcohol to water, we will follow these steps:

### Step 1: Calculate the number of moles of ethyl alcohol.
- Given mass of ethyl alcohol (C2H6O) = 138 g
- Molecular weight of ethyl alcohol = 2(12) + 6(1) + 16 = 46 g/mol
- Number of moles of ethyl alcohol = Mass / Molar mass = 138 g / 46 g/mol = 3 moles

### Step 2: Calculate the number of moles of water.
- Given mass of water (H2O) = 72 g
- Molecular weight of water = 2(1) + 16 = 18 g/mol
- Number of moles of water = Mass / Molar mass = 72 g / 18 g/mol = 4 moles

### Step 3: Calculate the total number of moles.
- Total moles = Number of moles of ethyl alcohol + Number of moles of water
- Total moles = 3 moles (ethyl alcohol) + 4 moles (water) = 7 moles

### Step 4: Calculate the mole fraction of ethyl alcohol.
- Mole fraction of ethyl alcohol (X_ethanol) = Number of moles of ethyl alcohol / Total moles
- X_ethanol = 3 moles / 7 moles = 3/7

### Step 5: Calculate the mole fraction of water.
- Mole fraction of water (X_water) = Number of moles of water / Total moles
- X_water = 4 moles / 7 moles = 4/7

### Step 6: Find the ratio of the mole fraction of ethyl alcohol to the mole fraction of water.
- Ratio = X_ethanol / X_water = (3/7) / (4/7)
- Ratio = 3/4

### Final Answer:
The ratio of the mole fraction of ethyl alcohol to water is 3:4.

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