15 gm urea `(NH_(2)CONH_(2))` is dissolved in 18 gm water to form an
aq. Solution. Find `x_("urea") and x_(H_(2)O)`

Answer

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

### Step 1: Calculate the number of moles of urea
The formula to calculate the number of moles is:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
For urea (NH₂CONH₂), the molar mass is 60 g/mol. Given that we have 15 g of urea:
\[ \text{Moles of urea} = \frac{15 \, \text{g}}{60 \, \text{g/mol}} = \frac{1}{4} \, \text{moles} \]

### Step 2: Calculate the number of moles of water
The molar mass of water (H₂O) is 18 g/mol. Given that we have 18 g of water:
\[ \text{Moles of water} = \frac{18 \, \text{g}}{18 \, \text{g/mol}} = 1 \, \text{mole} \]

### Step 3: Calculate the total number of moles
Now, we can calculate the total number of moles in the solution:
\[ \text{Total moles} = \text{Moles of urea} + \text{Moles of water} = \frac{1}{4} + 1 = \frac{1}{4} + \frac{4}{4} = \frac{5}{4} \, \text{moles} \]

### Step 4: Calculate the mole fraction of urea
The mole fraction (x) of a component is given by the formula:
\[ x = \frac{\text{Number of moles of the component}}{\text{Total number of moles}} \]
For urea:
\[ x_{\text{urea}} = \frac{\text{Moles of urea}}{\text{Total moles}} = \frac{\frac{1}{4}}{\frac{5}{4}} = \frac{1}{5} = 0.2 \]

### Step 5: Calculate the mole fraction of water
Using the same formula for water:
\[ x_{\text{H}_2\text{O}} = \frac{\text{Moles of water}}{\text{Total moles}} = \frac{1}{\frac{5}{4}} = \frac{4}{5} = 0.8 \]

### Final Answer
- Mole fraction of urea, \( x_{\text{urea}} = 0.2 \)
- Mole fraction of water, \( x_{\text{H}_2\text{O}} = 0.8 \)