Equal moles of water and user are taken in a flask. What is mass percentage of urea in the solution ?

Options

A. `C_(2)H_(6)`
B. `C_(3)H_(4)`
C. `C_(6)H_(6)`
D. `CH_(4)`

Answer

To find the mass percentage of urea in a solution where equal moles of water and urea are taken, follow these steps:

### Step-by-Step Solution:

1. **Identify the Chemical Formulas:**
- Urea: \( \text{NH}_2\text{CONH}_2 \)
- Water: \( \text{H}_2\text{O} \)

2. **Calculate the Molar Masses:**
- **Molar mass of Urea:**
- Nitrogen (N): \( 14 \, \text{g/mol} \times 2 = 28 \, \text{g/mol} \)
- Hydrogen (H): \( 1 \, \text{g/mol} \times 4 = 4 \, \text{g/mol} \)
- Carbon (C): \( 12 \, \text{g/mol} \)
- Oxygen (O): \( 16 \, \text{g/mol} \)
- Total: \( 28 + 4 + 12 + 16 = 60 \, \text{g/mol} \)

- **Molar mass of Water:**
- Hydrogen (H): \( 1 \, \text{g/mol} \times 2 = 2 \, \text{g/mol} \)
- Oxygen (O): \( 16 \, \text{g/mol} \)
- Total: \( 2 + 16 = 18 \, \text{g/mol} \)

3. **Let the number of moles of urea and water be \( A \).**

4. **Calculate the Mass of Urea and Water:**
- **Mass of Urea:**
\[ \text{Mass of Urea} = \text{Number of moles} \times \text{Molar mass} = A \times 60 = 60A \, \text{g} \]
- **Mass of Water:**
\[ \text{Mass of Water} = \text{Number of moles} \times \text{Molar mass} = A \times 18 = 18A \, \text{g} \]

5. **Calculate the Total Mass of the Solution:**
\[ \text{Total Mass of Solution} = \text{Mass of Urea} + \text{Mass of Water} = 60A + 18A = 78A \, \text{g} \]

6. **Calculate the Mass Percentage of Urea:**
\[ \text{Mass Percentage of Urea} = \left( \frac{\text{Mass of Urea}}{\text{Total Mass of Solution}} \right) \times 100 = \left( \frac{60A}{78A} \right) \times 100 \]
- Simplifying this gives:
\[ \text{Mass Percentage of Urea} = \frac{60}{78} \times 100 \approx 76.92\% \]

### Final Answer:
The mass percentage of urea in the solution is approximately **76.92%**.