Calculate the mass of urea `("NH"_(2)"CONH"_(2))` required in making 2.5 kg of 0.25 molar aqueous solution.
We know that molarity (m) `=("Moles of solute")/("Mass of solvent in kg")`
and moles of soute `=("Mass of solute")/("Molar mass of solute")`
So, find the molar mass of solute by adding atomic masses of different element present in it and mass by using the formula,
Molality `=("Mass of solute/molar mass of solute")/("Mass of solvent in kg")`

Answer

To calculate the mass of urea required to make a 2.5 kg of a 0.25 molar aqueous solution, we can follow these steps:

### Step 1: Identify the given values
- Molarity (M) = 0.25 mol/L
- Mass of solvent (water) = 2.5 kg
- Molar mass of urea (NH₂CONH₂) = 60 g/mol (calculated from atomic masses: N=14, H=1, C=12, O=16)

### Step 2: Use the molarity formula
The formula for molarity is given by:
\[ M = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \]

Rearranging this formula to find the moles of solute:
\[ \text{moles of solute} = M \times \text{mass of solvent in kg} \]

Substituting the known values:
\[ \text{moles of solute} = 0.25 \, \text{mol/L} \times 2.5 \, \text{kg} \]
\[ \text{moles of solute} = 0.625 \, \text{mol} \]

### Step 3: Calculate the mass of solute (urea)
Using the relationship between moles of solute, mass of solute, and molar mass:
\[ \text{mass of solute} = \text{moles of solute} \times \text{molar mass of solute} \]

Substituting the values:
\[ \text{mass of solute} = 0.625 \, \text{mol} \times 60 \, \text{g/mol} \]
\[ \text{mass of solute} = 37.5 \, \text{g} \]

### Final Answer
The mass of urea required to make 2.5 kg of a 0.25 molar aqueous solution is **37.5 g**.

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