The mole fraction of solute in aqueous urea solution is 0.2. Calculate the mass percent of solute ?

Answer

To solve the problem of calculating the mass percent of solute (urea) in an aqueous solution given the mole fraction of solute (urea) as 0.2, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Mole Fraction**:
The mole fraction of urea (solute) is given as 0.2. This means that the mole fraction of water (solvent) can be calculated as:
\[ \text{Mole fraction of water} = 1 - \text{Mole fraction of urea} = 1 - 0.2 = 0.8 \]

2. **Assign Moles**:
Let's assume we have 1 mole of the solution. Therefore, the moles of urea and water can be calculated as:
- Moles of urea = 0.2 moles
- Moles of water = 0.8 moles

3. **Calculate Mass of Urea**:
The molar mass of urea (NH2CONH2) is 60 g/mol. Thus, the mass of urea can be calculated as:
\[ \text{Mass of urea} = \text{Moles of urea} \times \text{Molar mass of urea} = 0.2 \, \text{moles} \times 60 \, \text{g/mol} = 12 \, \text{grams} \]

4. **Calculate Mass of Water**:
The molar mass of water (H2O) is 18 g/mol. Thus, the mass of water can be calculated as:
\[ \text{Mass of water} = \text{Moles of water} \times \text{Molar mass of water} = 0.8 \, \text{moles} \times 18 \, \text{g/mol} = 14.4 \, \text{grams} \]

5. **Calculate Total Mass of Solution**:
The total mass of the solution is the sum of the mass of urea and the mass of water:
\[ \text{Total mass of solution} = \text{Mass of urea} + \text{Mass of water} = 12 \, \text{grams} + 14.4 \, \text{grams} = 26.4 \, \text{grams} \]

6. **Calculate Mass Percent of Solute**:
The mass percent of the solute (urea) can be calculated using the formula:
\[ \text{Mass percent of solute} = \left( \frac{\text{Mass of solute}}{\text{Total mass of solution}} \right) \times 100 \]
Substituting the values:
\[ \text{Mass percent of urea} = \left( \frac{12 \, \text{grams}}{26.4 \, \text{grams}} \right) \times 100 \approx 45.45\% \]

### Final Answer:
The mass percent of solute (urea) in the solution is approximately **45.45%**.