Calculate mole fractions of urea and water if `2.0g` of urea is dissolved in `31.4g` of aqueous solution.

Answer

To calculate the mole fractions of urea and water in the solution, we can follow these steps:

### Step 1: Calculate the number of moles of urea.
The formula for calculating moles is:

\[ \text{Moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

Given:
- Mass of urea = 2.0 g
- Molar mass of urea (NH₂CO) = 60 g/mol

Calculating moles of urea:

\[ \text{Moles of urea} = \frac{2.0 \, \text{g}}{60 \, \text{g/mol}} = 0.0333 \, \text{moles} \]

### Step 2: Calculate the mass of water in the solution.
The mass of the aqueous solution is given as 31.4 g. To find the mass of water, we subtract the mass of urea from the total mass of the solution:

\[ \text{Mass of water} = \text{Total mass of solution} - \text{Mass of urea} = 31.4 \, \text{g} - 2.0 \, \text{g} = 29.4 \, \text{g} \]

### Step 3: Calculate the number of moles of water.
Using the same formula for moles:

Given:
- Molar mass of water (H₂O) = 18 g/mol

Calculating moles of water:

\[ \text{Moles of water} = \frac{29.4 \, \text{g}}{18 \, \text{g/mol}} = 1.6333 \, \text{moles} \]

### Step 4: Calculate the mole fractions of urea and water.
The mole fraction (X) is calculated using the formula:

\[ X = \frac{\text{moles of component}}{\text{total moles of solution}} \]

Total moles of solution = moles of urea + moles of water:

\[ \text{Total moles} = 0.0333 \, \text{moles (urea)} + 1.6333 \, \text{moles (water)} = 1.6666 \, \text{moles} \]

Now, calculating the mole fraction of urea (X₁):

\[ X_{\text{urea}} = \frac{0.0333}{1.6666} \approx 0.020 \]

Calculating the mole fraction of water (X₂):

\[ X_{\text{water}} = \frac{1.6333}{1.6666} \approx 0.980 \]

### Final Results:
- Mole fraction of urea (X₁) ≈ 0.020
- Mole fraction of water (X₂) ≈ 0.980