2: Concentration Metrics

A mole fraction is the ratio of the moles of one component to the total moles of the solution, so it is a fraction between zero and one. Multiplying it by 100 expresses the same composition as mole percentage: mole percentage = mole fraction × 100. Molarity and molality have units involving volume or mass, while ppm requires a different conversion. Hence A is correct.

Molarity is defined as the number of moles of solute present in one litre of solution: M = moles of solute / volume of solution in litres. Because solution volume can change with temperature, molarity can also change with temperature. It is measured in mol L⁻¹, so it has a unit. Therefore, option A is the only correct statement.

Molality is defined as the number of moles of solute dissolved in one kilogram of solvent: m = moles of solute / mass of solvent in kilograms. It is therefore based on the solvent’s mass, not the total solution volume. Because mass is largely unaffected by temperature, molality is useful when temperature changes are involved. Thus, option A is correct.

Mass percentage is calculated as (mass of solute ÷ mass of solution) × 100. The total mass of the solution is 5 g + 95 g = 100 g. Therefore, mass percentage = (5 ÷ 100) × 100 = 5%. The denominator must be the total solution mass, not only the solvent mass. Hence, option A is correct.

Volume percentage is defined as (volume of solute ÷ volume of solution) × 100. In this question, the solute volume is 25 mL and the final solution volume is 100 mL. Thus, volume percentage = (25 ÷ 100) × 100 = 25%. The final solution volume, rather than the solvent volume, must be used. Therefore, option A is correct.

Mass-volume percentage expresses the mass of solute in grams present in 100 mL of solution. Option A has exactly this combination: 2 g of solute in 100 mL of solution, corresponding to 2% (mass/volume). Option B is mass percentage, option C is volume percentage, and option D describes molarity. Therefore, option A is correct.

Molarity is defined as the amount of solute in moles divided by the volume of solution in litres: M = n/V. If the original values are n and V, the new molarity is 2n/2V, which simplifies to n/V. Therefore, both changes cancel each other, and the molarity remains unchanged, assuming the volume is measured in litres and the solution is considered under the stated conditions.

Molarity is calculated using M = n/V, where n is the moles of solute and V is the volume of solution in litres. Here, n remains constant, while the new volume is V/2. Thus, the new molarity is n/(V/2) = 2n/V = 2M. Hence, halving the volume while retaining the same amount of solute doubles the molarity.

Molarity is the number of moles of solute present per litre of solution, so its unit is mol L⁻¹. Molality is moles per kilogram of solvent, not per litre. Mole fraction is a dimensionless ratio, while ppm is a parts-per-million measure and is not defined as moles per kilogram. Hence, only option A gives a correct pair.

The total mass of the solution is the mass of solute plus the mass of solvent: 20 g + 180 g = 200 g. Mass percentage is calculated as (mass of solute ÷ mass of solution) × 100. Therefore, (20 ÷ 200) × 100 = 10%. The denominator must be the total solution mass, not only the solvent mass.

Volume percentage is calculated using the volume of solute and the final volume of the solution: volume percentage = (volume of solute ÷ volume of solution) × 100. Here, the value is (40 mL ÷ 200 mL) × 100 = 20%. The final solution volume, rather than the volume of solvent alone, is used in the denominator.

Mass-volume percentage expresses the grams of solute present in 100 mL of solution. Its formula is (mass of solute in grams ÷ volume of solution in mL) × 100. Thus, mass-volume percentage = (12 ÷ 300) × 100 = 4%. The given volume is already in millilitres, so no litre conversion is needed for this percentage calculation.

Molarity is defined as the number of moles of solute per litre of solution. First convert the volume: 400 mL = 0.400 L. Then use M = moles ÷ volume in litres = 0.2 ÷ 0.400 = 0.5 mol L⁻¹, or 0.5 M. Conversion from millilitres to litres is essential because molarity uses litres of solution.

Molality is defined as the number of moles of solute per kilogram of solvent, not per kilogram of solution. Therefore, molality = moles of solute ÷ mass of solvent in kilograms = 0.75 ÷ 1.5 = 0.5 mol kg⁻¹. Hence, the molality is 0.5 m. The solvent mass is the required denominator.

The mole fraction of a component is calculated by dividing the number of moles of that component by the total number of moles of all components. Here, total moles = 4 + 6 = 10. Therefore, the mole fraction of the solute is 4/10 = 0.4. Mole fraction has no unit and lies between 0 and 1.

In a binary solution, only two components are present: solute and solvent. The sum of their mole fractions is always equal to 1. Thus, mole fraction of solute = 1 − mole fraction of solvent = 1 − 0.65 = 0.35. Therefore, option A is correct; the result is also within the permissible range of 0 to 1.

Dilution increases the volume of the solution while the amount of solute remains unchanged. Molarity is defined as moles of solute per litre of solution, so increasing the denominator causes molarity to decrease. Molality uses the mass of solvent, and mole fraction and mass percentage are not the direct volume-based concentration term identified here.

Molarity is defined as the number of moles of solute divided by the final volume of the solution in litres. Consequently, the calculation cannot be completed accurately without knowing that final volume. Molality requires the mass of solvent, mole fraction requires the moles of components, and mass percentage requires masses rather than the final solution volume.

Molality is defined as the number of moles of solute present per kilogram of solvent. Therefore, the mass of the solvent is an essential part of its calculation, and it must be expressed in kilograms. Molarity uses the volume of solution, volume percentage uses volumes, and mole fraction uses the moles of all components.

Molarity is defined as the number of moles of solute present in one litre of solution. First convert the volume: 500 mL = 0.500 L. Therefore, M = moles of solute ÷ volume of solution in litres = 2 ÷ 0.500 = 4 mol L⁻¹. Hence, option A is correct. The volume must be that of the complete solution, not merely the solvent.

Molality is the number of moles of solute divided by the mass of solvent in kilograms. Here, the amount of solute is 1.2 mol and the solvent mass is 0.6 kg. Thus, molality = 1.2 mol ÷ 0.6 kg = 2 mol kg⁻¹, written as 2 m. Therefore, option A is correct. Unlike molarity, molality uses solvent mass rather than solution volume.

Molarity is defined using the volume of the solution: moles of solute per litre of solution. Liquids generally expand or contract when temperature changes, so the solution volume can change and the calculated molarity can therefore change. Molality is based on solvent mass, which is essentially temperature-independent, and mole fraction is a ratio of mole amounts. Thus, option A is correct.

The abbreviation ppm means parts per million. Therefore, a concentration of 2 ppm represents 2 parts of the stated substance for every 1,000,000 parts of the sample, using a consistent basis such as mass for dilute environmental samples. It does not mean 2 parts per 100 or 1000 parts. Hence, option A gives the correct interpretation.

One ppm means one part in one million parts, so its fractional value is 1/1,000,000. To convert a fraction into a percentage, multiply by 100: (1/1,000,000) × 100 = 1/10,000 = 0.0001%. Therefore, 1 ppm is equal to 0.0001 percent, and option A is correct. This very small percentage is appropriate for trace concentrations.

For the same mass basis, 1% means 1 part per 100 parts, which is equal to 10,000 parts per million because one million divided by 100 is 10,000. Therefore, 0.1% = 0.1 × 10,000 ppm = 1000 ppm. Option A is correct. This conversion is useful for expressing dilute concentrations in a more convenient unit.