Molality calculation — A solution is prepared by dissolving 1 kilomole of a nonvolatile solute in 2000 kg of solvent. What is the molality (mol/kg) of the solution?

Introduction:Molality is a composition unit commonly used in colligative property calculations because it is independent of temperature (mass-based rather than volume-based). This problem is a direct substitution exercise.

Given Data / Assumptions:

• Moles of solute = 1 kmol = 1000 mol.
• Mass of solvent = 2000 kg.
• Ideal dilute solution; unit consistency required.

Concept / Approach:Molality m is defined as m = moles of solute / kilograms of solvent. No information about solute molar mass is needed since moles are given directly.

Step-by-Step Solution:Convert 1 kmol to mol: 1 kmol = 1000 mol.Apply definition: m = 1000 mol / 2000 kg.Compute: m = 0.5 mol/kg.

Verification / Alternative check:Dimensional check: (mol) / (kg) → mol/kg, correct for molality.

Why Other Options Are Wrong:

• 2.0 and 1.0 assume fewer kilograms of solvent or more moles.
• 0.25 or 0.05 would require greater solvent mass (or fewer moles) than provided.

Common Pitfalls:Confusing molality with molarity; forgetting to convert kmol to mol.

Final Answer:0.5