Calculate the mass of urea (NH2CONH2) required in making 2.5 kg of 0.25 molal aqueous solution.

To determine the mass of urea (NH2CONH2) needed to prepare a 2.5 kg solution with a molality of 0.25 mol/kg, we can follow a systematic approach that connects the concepts of molality, moles, and the molar mass of the solute.

Understanding Molality

Molality (m) is defined as the number of moles of solute per kilogram of solvent. In this case, we want a 0.25 molal solution, which means we need 0.25 moles of urea for every kilogram of water (solvent) used.

Calculating the Required Moles

Since we are preparing 2.5 kg of solution, we first need to find out how much of that weight is the solvent. The total weight of the solution includes both the solute and the solvent. However, for a molal solution, we focus on the mass of the solvent, which is usually water.

Assuming that the mass of the urea is negligible compared to the mass of the water, we can estimate the mass of the solvent as approximately 2.5 kg. To calculate the moles of urea needed:

• We need 0.25 moles of urea per kg of water.
• For 2.5 kg of water, we need: 0.25 moles/kg × 2.5 kg = 0.625 moles of urea.

Finding the Molar Mass of Urea

Next, we calculate the molar mass of urea (NH2CONH2). The molar mass can be calculated by summing the atomic masses of each element in the compound:

• Nitrogen (N): 14.01 g/mol (2 atoms) = 28.02 g/mol
• Hydrogen (H): 1.01 g/mol (4 atoms) = 4.04 g/mol
• Carbon (C): 12.01 g/mol (1 atom) = 12.01 g/mol
• Oxygen (O): 16.00 g/mol (1 atom) = 16.00 g/mol

The total molar mass of urea is thus:

28.02 + 4.04 + 12.01 + 16.00 = 60.07 g/mol

Calculating the Mass of Urea Required

With the number of moles required and the molar mass, we can now find the mass of urea needed:

• Mass = Moles × Molar Mass
• Mass of urea = 0.625 moles × 60.07 g/mol = 37.5 g

Thus, to prepare a 2.5 kg of 0.25 molal aqueous solution of urea, you would need approximately 37.5 grams of urea.