A solution is prepared by dissolving 46 g of ethyl alcohol in 90 g of water. The mole fraction of ethyl alcohol in this solution is:

Options

A. `46/90`
B. `90/46`
C. `46/(90 + 46)`
D. `1/6`

Explanation

To find the mole fraction of ethyl alcohol in the solution, we can follow these steps:

### Step 1: Calculate the moles of ethyl alcohol
The formula to calculate moles is:
\[ \text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}} \]
For ethyl alcohol (C₂H₅OH):
- Mass = 46 g
- Molar Mass = 46 g/mol

Calculating the moles of ethyl alcohol:
\[ \text{Moles of ethyl alcohol} = \frac{46 \text{ g}}{46 \text{ g/mol}} = 1 \text{ mole} \]

### Step 2: Calculate the moles of water
For water (H₂O):
- Mass = 90 g
- Molar Mass = 18 g/mol

Calculating the moles of water:
\[ \text{Moles of water} = \frac{90 \text{ g}}{18 \text{ g/mol}} = 5 \text{ moles} \]

### Step 3: Calculate the total moles of the solution
Total moles in the solution is the sum of the moles of ethyl alcohol and the moles of water:
\[ \text{Total moles} = \text{Moles of ethyl alcohol} + \text{Moles of water} = 1 \text{ mole} + 5 \text{ moles} = 6 \text{ moles} \]

### Step 4: Calculate the mole fraction of ethyl alcohol
The mole fraction (X) of a component in a solution is given by:
\[ X = \frac{\text{Moles of component}}{\text{Total moles of solution}} \]
Thus, the mole fraction of ethyl alcohol is:
\[ X_{\text{ethyl alcohol}} = \frac{\text{Moles of ethyl alcohol}}{\text{Total moles}} = \frac{1 \text{ mole}}{6 \text{ moles}} = \frac{1}{6} \]

### Final Answer
The mole fraction of ethyl alcohol in the solution is \(\frac{1}{6}\).

---