36g water and 828g ethyl alcohol form an ideal solution. The mole fraction of water in it, is

Options

A. `1.0`
B. `0.7`
C. `0.4`
D. `0.1`

Explanation

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

### Step 1: Calculate the number of moles of water (H2O)
- Given mass of water = 36 g
- Molar mass of water (H2O) = 18 g/mol

Using the formula for moles:
\[ \text{Moles of water} = \frac{\text{mass}}{\text{molar mass}} = \frac{36 \text{ g}}{18 \text{ g/mol}} = 2 \text{ moles} \]

### Step 2: Calculate the number of moles of ethyl alcohol (C2H5OH)
- Given mass of ethyl alcohol = 828 g
- Molar mass of ethyl alcohol (C2H5OH) = 46 g/mol

Using the formula for moles:
\[ \text{Moles of ethyl alcohol} = \frac{\text{mass}}{\text{molar mass}} = \frac{828 \text{ g}}{46 \text{ g/mol}} \approx 18 \text{ moles} \]

### Step 3: Calculate the total number of moles in the solution
\[ \text{Total moles} = \text{Moles of water} + \text{Moles of ethyl alcohol} = 2 + 18 = 20 \text{ moles} \]

### Step 4: Calculate the mole fraction of water
The mole fraction of water (X_H2O) is given by the formula:
\[ X_{H2O} = \frac{\text{Moles of water}}{\text{Total moles}} = \frac{2}{20} = 0.1 \]

### Final Answer
The mole fraction of water in the solution is **0.1**.

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