Calculate mole fraction of ethyl alcohol and water in a solution containing 46 g ethyl and 36g water.

Explanation

To calculate the mole fraction of ethyl alcohol (C2H5OH) and water (H2O) in a solution containing 46 g of ethyl alcohol and 36 g of water, follow these steps:

### Step 1: Calculate the number of moles of ethyl alcohol (C2H5OH)

1. **Find the molecular weight of ethyl alcohol (C2H5OH)**:
- Carbon (C): 2 × 12.01 g/mol = 24.02 g/mol
- Hydrogen (H): 6 × 1.008 g/mol = 6.048 g/mol
- Oxygen (O): 1 × 16.00 g/mol = 16.00 g/mol
- Total molecular weight = 24.02 + 6.048 + 16.00 = 46.068 g/mol (approximately 46 g/mol)

2. **Calculate the number of moles of ethyl alcohol**:
\[ \text{Number of moles of C2H5OH} = \frac{\text{mass}}{\text{molar mass}} = \frac{46 \text{ g}}{46 \text{ g/mol}} = 1 \text{ mol} \]

### Step 2: Calculate the number of moles of water (H2O)

1. **Find the molecular weight of water (H2O)**:
- Hydrogen (H): 2 × 1.008 g/mol = 2.016 g/mol
- Oxygen (O): 1 × 16.00 g/mol = 16.00 g/mol
- Total molecular weight = 2.016 + 16.00 = 18.016 g/mol (approximately 18 g/mol)

2. **Calculate the number of moles of water**:
\[ \text{Number of moles of H2O} = \frac{\text{mass}}{\text{molar mass}} = \frac{36 \text{ g}}{18 \text{ g/mol}} = 2 \text{ mol} \]

### Step 3: Calculate the total number of moles in the solution

\[ \text{Total moles} = \text{moles of C2H5OH} + \text{moles of H2O} = 1 + 2 = 3 \text{ mol} \]

### Step 4: Calculate the mole fraction of ethyl alcohol (C2H5OH)

\[ \text{Mole fraction of C2H5OH} = \frac{\text{moles of C2H5OH}}{\text{total moles}} = \frac{1}{3} \]

### Step 5: Calculate the mole fraction of water (H2O)

\[ \text{Mole fraction of H2O} = \frac{\text{moles of H2O}}{\text{total moles}} = \frac{2}{3} \]

### Final Answer:
- Mole fraction of ethyl alcohol (C2H5OH) = \(\frac{1}{3}\)
- Mole fraction of water (H2O) = \(\frac{2}{3}\)

---