2: Concentration Metrics

Correct answer: B. 0.25 m

Explanation: Molality is the governing concentration measure defined as moles of solute divided by kilograms of solvent, not kilograms of solution. Thus, m = nsolute/mass of solvent = 0.5 mol/2 kg = 0.25 mol kg−1, written as 0.25 m. Option A results from an incorrect division, while 0.50 m ignores the 2 kg denominator and 1.00 m doubles the correct value. Therefore, option B is correct.

Correct answer: B. 0.02 mol

Explanation: Molarity is defined as the number of moles of solute present in one litre of solution: M = n/V. Rearranging gives n = M × V. Substituting the given values, n = 0.02 mol L⁻¹ × 1 L = 0.02 mol. The litre units cancel, leaving moles. Therefore, option B is correct. Always ensure that volume is expressed in litres when using molarity.

Correct answer: B. 0.01 mol

Explanation: Molality is defined as moles of solute divided by the mass of solvent in kilograms: m = n/mass of solvent. Rearranging gives n = m × mass of solvent. The solvent mass is already 0.100 kg, so n = 0.1 mol kg⁻¹ × 0.100 kg = 0.010 mol. The mass of the solution is not used in the molality formula. Therefore, option B is correct.

Correct answer: B. 0.10 mol

Explanation: Molality is the amount of solute in moles divided by the mass of solvent in kilograms: m = n/mass of solvent. Rearranging gives n = m × mass of solvent. Substitution gives n = 0.5 mol kg⁻¹ × 0.2 kg = 0.10 mol. The solvent mass, rather than the total solution mass, must be used. Thus, option B is correct. The result also has the proper unit, mol.

Correct answer: B. 0.050 mol

Explanation: Molality is defined as the moles of solute divided by the mass of solvent in kilograms: m = nsolute ÷ mass of solvent. Rearranging gives nsolute = m × mass of solvent. Therefore, nsolute = 0.2 mol kg⁻¹ × 0.25 kg = 0.050 mol. The kilogram units cancel, leaving mol. Thus, option B is correct.

Correct answer: B. 0.1 m

Explanation: Molality is defined as the number of moles of solute present in one kilogram of solvent. Therefore, m = moles of solute ÷ mass of solvent in kg = 0.1 ÷ 1 = 0.1 mol kg⁻¹, written as 0.1 m. Hence, option B is correct. The mass used must be that of the solvent, not the total solution.

Correct answer: B. 0.04 M

Explanation: First calculate the amount of solute: moles = mass ÷ molar mass = 2 g ÷ 100 g mol⁻¹ = 0.02 mol. The solution volume is 500 mL, which equals 0.500 L. Therefore, molarity = moles of solute ÷ volume of solution in litres = 0.02 ÷ 0.500 = 0.04 mol L⁻¹, or 0.04 M. Hence option B is correct.

Correct answer: C. 0.10 M

Explanation: Molarity is defined as the number of moles of solute per litre of solution. First convert the volume: 100 mL = 0.100 L. Therefore, M = moles ÷ volume in litres = 0.01 mol ÷ 0.100 L = 0.10 mol L⁻¹, or 0.10 M. Hence, option C is correct. The volume of the complete solution, not merely the solvent, must be used.

Correct answer: B. 0.2 m

Explanation: Molality is defined as moles of solute per kilogram of solvent, not per kilogram of solution. The solute amount is n = mass/molar mass = 2/100 = 0.02 mol. The solvent mass is 100 g = 0.100 kg. Thus, molality = 0.02/0.100 = 0.20 mol kg⁻¹, or 0.2 m. Therefore, option B is correct.