2: Concentration Metrics

Correct answer: B. 0.10 mol

Explanation: Molarity is the number of moles of solute present in one litre of solution. Use n = M × V, but first convert the volume: 200 mL = 0.200 L. Therefore, n = 0.5 mol L⁻¹ × 0.200 L = 0.100 mol. Hence, option B is correct. The other values result from using an incorrect volume conversion or confusing the given molarity with the required amount of solute.

Correct answer: C. 1.5 mol

Explanation: Molality is defined as moles of solute per kilogram of solvent, not per kilogram of solution. Convert the solvent mass first: 500 g = 0.500 kg. Rearranging m = n_solute/mass_solvent gives n_solute = m × mass_solvent = 3 mol kg⁻¹ × 0.500 kg = 1.5 mol. Thus option C is correct. The value 3.0 mol would require 1 kg of solvent, while the smaller values do not satisfy the stated molality.

Correct answer: B. 25 g

Explanation: Mass percentage is calculated as (mass of solute ÷ mass of solution) × 100. Here the sugar mass is 5% of the total 500 g solution: mass of sugar = (5/100) × 500 g = 25 g. Therefore, option B is correct. The value 50 g represents 10% of 500 g, 100 g represents 20%, and 20 g is less than the required 5% amount.

Correct answer: A. 30 g and 270 g

Explanation: A 10% by-mass solution contains salt equal to 10/100 of the total solution mass. Salt required = (10/100) × 300 g = 30 g. Since the total mass must be 300 g, water required = 300 − 30 = 270 g. Thus option A is correct. Option D reverses salt and water, option B gives only about 3.33% salt, and option C is not exactly 10% of 300 g.

Correct answer: B. 2%

Explanation: Mass by volume percentage tells how many grams of solute are present in 100 mL of solution. The formula is % (m/v) = (mass of solute in g ÷ volume of solution in mL) × 100. Substituting the data gives (5 ÷ 250) × 100 = 2%. Therefore, option B is correct. The final solution volume, not the initial water volume, must be used in the denominator.

Correct answer: D. 0.8

Explanation: For a binary solution, the two mole fractions must add to unity: x_solute + x_solvent = 1. With x_solute = 0.2, x_solvent = 1 − 0.2 = 0.8. Hence option D is correct. Option A is simply the given solute fraction, while 0.4 and 0.6 would make the total mole fraction 0.6 and 0.8 respectively, not 1. The result also lies within the valid range from 0 to 1.

Correct answer: B. 0.50 mol L⁻¹

Explanation: First calculate the amount of NaOH using its molar mass, 40 g mol⁻¹: n = 40 g ÷ 40 g mol⁻¹ = 1 mol. Molarity is moles of solute divided by the final solution volume in litres. Thus M = 1 mol ÷ 2 L = 0.50 mol L⁻¹. Option B is correct. The stated 2 L is the final solution volume; using the water volume before dissolving would be inappropriate.

Correct answer: B. 0.2 mol L⁻¹

Explanation: The molar mass of NaCl is 58.5 g mol⁻¹, so the number of moles is n = 5.85 ÷ 58.5 = 0.10 mol. Convert the final volume: 500 mL = 0.500 L. Molarity is n/V, so M = 0.10 ÷ 0.500 = 0.20 mol L⁻¹. Therefore, option B is correct. Ignoring the volume conversion would produce an incorrect concentration.

Correct answer: B. 0.050 mol

Explanation: Molarity relates the amount of solute to the volume of solution in litres. Use n = M × V and convert 200 mL to 0.200 L. Thus n = 0.25 mol L⁻¹ × 0.200 L = 0.050 mol. Therefore, option B is correct. The answer 0.250 mol would require 1 L of solution, while 0.025 mol and 0.125 mol do not follow the stated product of molarity and volume.

Correct answer: B. 0.125 mol L⁻¹

Explanation: The governing principle of dilution is conservation of solute: adding solvent changes the volume but not the amount of solute. Therefore, M₁V₁ = M₂V₂. Substituting the values, M₂ = (0.5 mol L⁻¹ × 0.250 L) ÷ 1.00 L = 0.125 mol L⁻¹. Thus option B is correct. Options C and D do not account for the fourfold increase in volume, while option A is too small.

Correct answer: B. 0.50 mol kg⁻¹

Explanation: Molality is defined as the number of moles of solute per kilogram of solvent, not per kilogram of solution. Sodium chloride has molar mass 58.5 g mol⁻¹, so 58.5 g NaCl equals 1 mol. The solvent mass is 2 kg; hence molality = 1 mol ÷ 2 kg = 0.50 mol kg⁻¹. Option B is correct. The other values arise from using an incorrect denominator or arithmetic.

Correct answer: A. 0.25 mol

Explanation: Molarity is the number of moles of solute per litre of solution, so the amount of solute is found from n = M × V. Convert the volume first: 250 mL = 0.250 L. Thus n = 1 mol L⁻¹ × 0.250 L = 0.25 mol. Option A is correct. A value of 1.00 mol would require 1 L of this solution, while 0.50 mol and 2.50 mol result from incorrect scaling.

Correct answer: C. 2.0 mol L⁻¹

Explanation: Molarity is moles of solute per litre of the final solution. H₂SO₄ has molar mass 98 g mol⁻¹, so 98 g corresponds to 1 mol. The final volume is 500 mL = 0.500 L. Therefore, M = 1 mol ÷ 0.500 L = 2.0 mol L⁻¹, so option C is correct. The value 1.0 mol L⁻¹ would incorrectly treat 500 mL as 1 L.

Correct answer: B. 0.50 mol kg⁻¹

Explanation: Molality uses moles of solute divided by the mass of solvent in kilograms. For NaCl, n = 11.7 g ÷ 58.5 g mol⁻¹ = 0.2 mol. The water mass is 400 g = 0.4 kg. Thus molality = 0.2 mol ÷ 0.4 kg = 0.50 mol kg⁻¹, making option B correct. Using grams directly or the total solution mass would give an incorrect result.

Correct answer: A. 0.20

Explanation: Mole fraction is the amount of the selected component divided by the total amount of all components. From the ratio, take solute = 1 mol and solvent = 4 mol, so total moles = 1 + 4 = 5 mol. Hence x_solute = 1/5 = 0.20, making option A correct. Option D is the solvent mole fraction, and option B incorrectly uses only the solvent amount as a denominator.

Correct answer: C. 0.30 mol

Explanation: Molarity is defined as moles of solute per litre of solution, so use n = M × V with volume in litres. Convert 750 mL to 0.750 L. Thus n = 0.4 mol L−1 × 0.750 L = 0.300 mol. Therefore, option C is correct. Options A, B, and D result from using an incorrect volume or an incorrect multiplication.

Correct answer: C. 0.50 M

Explanation: Molarity is the number of moles of solute divided by the volume of the final solution in litres. Convert 600 mL to 0.600 L, then calculate M = n/V = 0.30 mol ÷ 0.600 L = 0.50 mol L−1. Therefore, option C is correct. Using 600 without conversion or using the solvent volume instead of final solution volume would be incorrect.

Correct answer: B. 0.50 mol

Explanation: Molality is defined as moles of solute per kilogram of solvent. Convert the solvent mass: 250 g = 0.250 kg. Therefore, moles of solute = molality × solvent mass in kilograms = 2 mol kg−1 × 0.250 kg = 0.50 mol. Option B is correct. Failing to convert grams to kilograms would produce an answer that is 1000 times too large.

Correct answer: B. 10%

Explanation: Mass percentage is calculated from the mass of solute and the total mass of solution: mass percent = (mass of solute/mass of solution) × 100. Substitution gives (120 g/1200 g) × 100 = 10%. Therefore, option B is correct. The one-litre volume is not needed because this concentration unit is based entirely on mass; 12% would incorrectly use the solute-to-volume figures.

Correct answer: C. 120 g

Explanation: A 20 mass percent solution contains 20 g solute in every 100 g of solution. For 150 g solution, solute mass = (20/100) × 150 = 30 g. Since total solution mass = solute mass + solvent mass, solvent mass = 150 − 30 = 120 g. Therefore, option C is correct. Option A gives the solute mass, not the requested solvent mass.

Correct answer: A. 40 ppm

Explanation: For a dilute aqueous solution, the density is taken as approximately 1 kg L−1. Consequently, 1 mg of solute in 1 L of water is approximately 1 mg kg−1, and mg kg−1 is equivalent to ppm. Therefore, 40 mg L−1 is approximately 40 ppm. Option A is correct. The other choices result from multiplying or dividing by an extra factor of ten or one hundred.

Correct answer: A. 12:88

Explanation: Mass percentage is calculated as (mass of solute ÷ mass of solution) × 100. Assume 100 g of solution, so it contains 12 g solute and 100 − 12 = 88 g solvent. Therefore, the solute-to-solvent mass ratio is 12:88, which can also be simplified to 3:22. Option A gives the direct masses corresponding to 100 g solution; 12:100 incorrectly uses solution mass as solvent mass.

Correct answer: A. 20%

Explanation: The governing idea is that mass percentage uses the total solution mass as the denominator, not the solvent mass alone. Let the solute mass be 1 part and the solvent mass be 4 parts; the total solution mass is therefore 5 parts. Solute percentage = (1 ÷ 5) × 100 = 20%. Option B would divide by 4, while 80% is the solvent percentage.

Correct answer: A. 60 g

Explanation: A 4% mass-by-volume solution contains 4 g of solute in every 100 mL of solution. Convert 1.5 L to 1500 mL. Since 1500 mL contains 15 groups of 100 mL, the solute mass is 15 × 4 = 60 g. The percentage is based on final solution volume, not solvent volume. Options C and D reflect incorrect scaling, while B does not apply the stated concentration.

Correct answer: A. 300 mL

Explanation: Volume-by-volume percentage is defined as (volume of solute ÷ volume of solution) × 100. Therefore, solute volume = 15/100 × 2 L = 0.30 L. Converting 0.30 L to millilitres gives 300 mL. Option B uses only 1 L as a reference, and option C loses a factor of ten; the percentage must be applied to the full 2 L solution volume.