Calculate the mole fraction of ethyl alcohol and water in a solution in which 46 g of ethyl alcohol and 180 g of water are mixed together.

Answer

To calculate the mole fraction of ethyl alcohol (C2H5OH) and water (H2O) in the solution, follow these steps:

### Step 1: Calculate the moles of ethyl alcohol
1. **Given mass of ethyl alcohol**: 46 g
2. **Molar mass of ethyl alcohol (C2H5OH)**:
- Carbon (C): 2 × 12 g/mol = 24 g/mol
- Hydrogen (H): 6 × 1 g/mol = 6 g/mol
- Oxygen (O): 1 × 16 g/mol = 16 g/mol
- Total = 24 + 6 + 16 = 46 g/mol

3. **Moles of ethyl alcohol**:
\[ \text{Moles of ethyl alcohol} = \frac{\text{mass}}{\text{molar mass}} = \frac{46 \text{ g}}{46 \text{ g/mol}} = 1 \text{ mole} \]

### Step 2: Calculate the moles of water
1. **Given mass of water**: 180 g
2. **Molar mass of water (H2O)**:
- Hydrogen (H): 2 × 1 g/mol = 2 g/mol
- Oxygen (O): 1 × 16 g/mol = 16 g/mol
- Total = 2 + 16 = 18 g/mol

3. **Moles of water**:
\[ \text{Moles of water} = \frac{\text{mass}}{\text{molar mass}} = \frac{180 \text{ g}}{18 \text{ g/mol}} = 10 \text{ moles} \]

### Step 3: Calculate the total moles of the solution
\[ \text{Total moles} = \text{Moles of ethyl alcohol} + \text{Moles of water} = 1 \text{ mole} + 10 \text{ moles} = 11 \text{ moles} \]

### Step 4: Calculate the mole fraction of ethyl alcohol
\[ \text{Mole fraction of ethyl alcohol} = \frac{\text{Moles of ethyl alcohol}}{\text{Total moles}} = \frac{1 \text{ mole}}{11 \text{ moles}} \approx 0.0909 \]

### Step 5: Calculate the mole fraction of water
\[ \text{Mole fraction of water} = \frac{\text{Moles of water}}{\text{Total moles}} = \frac{10 \text{ moles}}{11 \text{ moles}} \approx 0.9091 \]

### Final Results
- **Mole fraction of ethyl alcohol**: 0.0909
- **Mole fraction of water**: 0.9091