Calculate the mole fraction of water in a mixture of 12 g of water, 108 g of acetic acid and 92 g of ethyl alcohol.

Answer

To calculate the mole fraction of water in a mixture of 12 g of water, 108 g of acetic acid, and 92 g of ethyl alcohol, we will follow these steps:

### Step 1: Calculate the moles of water (H2O)
The formula to calculate moles is:
\[ \text{Moles} = \frac{\text{Given mass (g)}}{\text{Molar mass (g/mol)}} \]
The molar mass of water (H2O) is 18 g/mol.

\[ \text{Moles of water} = \frac{12 \, \text{g}}{18 \, \text{g/mol}} = 0.66 \, \text{moles} \]

### Step 2: Calculate the moles of acetic acid (CH3COOH)
The molar mass of acetic acid is 60 g/mol.

\[ \text{Moles of acetic acid} = \frac{108 \, \text{g}}{60 \, \text{g/mol}} = 1.8 \, \text{moles} \]

### Step 3: Calculate the moles of ethyl alcohol (C2H5OH)
The molar mass of ethyl alcohol is 46 g/mol.

\[ \text{Moles of ethyl alcohol} = \frac{92 \, \text{g}}{46 \, \text{g/mol}} = 2 \, \text{moles} \]

### Step 4: Calculate the total moles of the solution
Now, we sum up the moles of all components:

\[ \text{Total moles} = \text{Moles of water} + \text{Moles of acetic acid} + \text{Moles of ethyl alcohol} \]
\[ \text{Total moles} = 0.66 + 1.8 + 2 = 4.46 \, \text{moles} \]

### Step 5: Calculate the mole fraction of water
The mole fraction of a component is calculated using the formula:

\[ \text{Mole fraction of water} = \frac{\text{Moles of water}}{\text{Total moles of solution}} \]
\[ \text{Mole fraction of water} = \frac{0.66}{4.46} \approx 0.148 \]

### Final Answer
The mole fraction of water in the mixture is approximately **0.148**.

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