Calculate the mass of urea (`NH_2CONH_2`) required in making 1.5kg of 0.25 molal aqueous solution.

Options

A. 22g
B. 16g
C. 18g
D. 20g

Explanation

To calculate the mass of urea (NH₂CONH₂) required to make 1.5 kg of a 0.25 molal aqueous solution, follow these steps:

### Step 1: Understand the definition of molality
Molality (m) is defined as the number of moles of solute per kilogram of solvent. In this case, we have a 0.25 molal solution, which means there are 0.25 moles of urea in 1 kg of water.

### Step 2: Calculate the number of moles of urea needed for 1.5 kg of solution
Since we know that 0.25 moles of urea are needed for 1 kg of water, we can set up a proportion to find out how many moles are needed for 1.5 kg of solution.

Let \( m \) be the mass of urea needed for 1.5 kg of solution.

1. The total mass of the solution is the mass of the solvent (water) plus the mass of the solute (urea).
2. We can assume that the mass of the solvent (water) is approximately 1.5 kg for simplicity in calculations, as the mass of urea will be small compared to the mass of water.

### Step 3: Calculate the moles of urea for 1.5 kg of solution
Using the molality formula:

\[ \text{Moles of urea} = \text{molality} \times \text{mass of solvent (in kg)} \]

Since we are making a solution that is 0.25 molal and we have approximately 1 kg of water in the solution:

\[ \text{Moles of urea} = 0.25 \, \text{mol/kg} \times 1 \, \text{kg} = 0.25 \, \text{moles} \]

### Step 4: Calculate the molar mass of urea
The molar mass of urea (NH₂CONH₂) is calculated as follows:

- Nitrogen (N): 14 g/mol × 2 = 28 g/mol
- Carbon (C): 12 g/mol × 1 = 12 g/mol
- Oxygen (O): 16 g/mol × 1 = 16 g/mol
- Hydrogen (H): 1 g/mol × 4 = 4 g/mol

Total molar mass of urea = 28 + 12 + 16 + 4 = 60 g/mol

### Step 5: Calculate the mass of urea required
Now, we can calculate the mass of urea needed using the number of moles and the molar mass:

\[ \text{Mass of urea} = \text{moles of urea} \times \text{molar mass of urea} \]

Substituting the values:

\[ \text{Mass of urea} = 0.25 \, \text{moles} \times 60 \, \text{g/mol} = 15 \, \text{grams} \]

### Step 6: Adjust for the total mass of the solution
Since we need to make 1.5 kg of solution, we need to find out how much urea is required in this total mass.

1. The total mass of the solution (1.5 kg) includes both water and urea.
2. We can find the proportion of urea in the total mass:

\[ \text{Mass of urea in 1.5 kg solution} = \left(\frac{15 \, \text{g}}{1015 \, \text{g}}\right) \times 1500 \, \text{g} = 22.15 \, \text{g} \]

Thus, the mass of urea required to make 1.5 kg of a 0.25 molal aqueous solution is approximately **22 grams**.

### Final Answer:
**The mass of urea required is approximately 22 grams.**