Calculate the mass of urea (`NH_2CONH_2`) required in making 2.5kg of 0.35 molal aqueous solution.

Options

A. 51.4g
B. 23g
C. 54g
D. 19g

Explanation

To calculate the mass of urea required to make a 2.5 kg of a 0.35 molal aqueous solution, we can follow these steps:

### Step 1: Understand the definition of molality
Molality (m) is defined as the number of moles of solute (in this case, urea) per kilogram of solvent (water).

### Step 2: Calculate the number of moles of urea in 2.5 kg of solution
Given that the solution is 0.35 molal, this means there are 0.35 moles of urea per 1 kg of water.

Since we have 2.5 kg of solution, we need to find out how much of that is solvent (water).

Assuming the mass of solute (urea) is negligible compared to the mass of solvent, we can approximate that:
- Mass of solvent (water) ≈ 2.5 kg (since urea's mass will be small).

### Step 3: Calculate the moles of urea in 2.5 kg of solution
Using the molality definition:
- For 1 kg of water, we have 0.35 moles of urea.
- For 2.5 kg of water, the moles of urea can be calculated as:

\[ \text{Moles of urea} = 0.35 \, \text{moles/kg} \times 2.5 \, \text{kg} = 0.875 \, \text{moles} \]

### Step 4: Calculate the mass of urea
Next, we need to find the mass of urea using its molar mass. The molar mass of urea (NH₂CONH₂) is approximately 60 g/mol.

Using the formula:

\[ \text{Mass of urea} = \text{Moles of urea} \times \text{Molar mass of urea} \]

Substituting the values:

\[ \text{Mass of urea} = 0.875 \, \text{moles} \times 60 \, \text{g/mol} = 52.5 \, \text{g} \]

### Step 5: Conclusion
Therefore, the mass of urea required to make a 2.5 kg of 0.35 molal aqueous solution is **52.5 grams**.

---