2: Concentration Metrics

Molarity is the number of moles of solute per litre of the final solution, whereas molality is the number of moles of solute per kilogram of solvent. Their numerical values can sometimes be similar, but their definitions and reference quantities differ. Molarity depends on solution volume, while molality uses solvent mass and is less affected by temperature-related volume changes. Therefore, A is correct.

Molality is defined as moles of solute per kilogram of solvent, so its basis is the mass of the solvent. Molarity instead uses litres of the final solution. Mole fraction is based on the ratio of moles of one component to total moles, while volume percentage uses component volumes. Therefore, only option A correctly pairs a concentration term with its basis.

Mole fraction is defined as the number of moles of a selected component divided by the total number of moles of all components present in the solution. For component i, the expression is Xi = ni ÷ ntotal, where ntotal = n1 + n2 + n3 and so on. The quantity is dimensionless because both numerator and denominator are measured in moles. Therefore option A gives the correct general formula. Option B is not the standard definition of a concentration term. Option C represents molality when the numerator is the solute amount and the denominator is kilograms of solvent. Option D represents molarity because it uses litres of solution.

Mass percentage is the mass of solute divided by the total mass of solution, multiplied by 100: mass % = (m_solute / m_solution) × 100. Substitution gives (5 g / 250 g) × 100 = 2%. Therefore option A is correct. Option B uses the solute mass as though it were a percentage, while C and D result from incorrect denominators or factors.

Volume percentage is calculated from the volume of solute relative to the total volume of solution: volume % = (V_solute / V_solution) × 100. Here, volume % = (20 mL / 80 mL) × 100 = 25%. Thus A is correct. The value 20 is only the measured solute volume, 80 is the denominator, and 100% would incorrectly imply that the whole solution is solute.

Parts per million compares the amount of solute with a fixed reference amount of mixture or solvent. Since every option uses the same basis, 1 kg of water, the option containing the greatest solute mass has the greatest ppm concentration. Ten milligrams per kilogram is larger than 5, 2, or 1 mg per kilogram, so A is correct.

The governing relation is mass percentage = (mass of solute / total mass of solution) × 100. Rearranging gives mass of solute = (mass percentage / 100) × total solution mass. Therefore, m = (8/100) × 125 g = 10 g, so A is correct. B confuses percentage with mass, C uses an incorrect factor, and D represents most of the solution mass.

Molality is the number of moles of solute divided by the mass of solvent in kilograms. It is written as m = nsolute/mass of solvent in kg. The denominator is specifically the solvent mass, not the volume of the complete solution. Therefore option A is correct; option B is molarity, while C is a percentage concentration.

Molarity is defined as moles of solute per litre of solution, so its usual unit is mol L−1, also written as mol/L or M. The litre refers to the volume of the complete solution. Option B, mol kg−1, is the unit of molality. Options C and D do not express the defining ratio for molarity, so option A is correct.

Molality is calculated by dividing the moles of solute by the mass of solvent expressed in kilograms: m = nsolute/kg solvent. Hence its usual unit is mol kg−1, often represented by m. Moles per litre, or mol L−1, belongs to molarity because molarity uses solution volume. The other options do not match the defining formula, so A is correct.

Molarity equals moles of solute divided by the volume of the solution. Temperature can cause the solution to expand or contract, changing its volume and therefore changing the numerical molarity even when the amount of solute is unchanged. Molality, mass percentage, and mole fraction depend on masses or mole amounts, which are generally unaffected by ordinary temperature changes. Thus A is correct.

Molality is the ratio of moles of solute to kilograms of solvent. Since it uses mass rather than the volume of the solution, ordinary thermal expansion or contraction does not significantly alter the denominator. Molarity, volume percentage, and mass–volume percentage involve volume and can therefore change with temperature. Consequently, option A is the correct choice.

The mole fraction of component i is defined as Xi = ni/ntotal, where ni is the number of moles of that component and ntotal is the sum of the moles of every component present in the solution. It is therefore a mole-to-mole ratio. Neither solution volume nor solute or solvent mass appears directly in the definition, making option A correct.

For a binary solution containing components 1 and 2, X1 = n1/(n1+n2) and X2 = n2/(n1+n2). Adding them gives X1 + X2 = (n1+n2)/(n1+n2) = 1. Mole fraction is dimensionless, so the answer is unity rather than 100. The value 100 applies only when the fractions are separately expressed as percentages, not as mole fractions.

In a binary solution, the mole fractions of solute and solvent always add to one: Xsolute + Xsolvent = 1. Substituting Xsolute = 0.2 gives Xsolvent = 1 − 0.2 = 0.8. Thus option A is correct. A mole fraction cannot exceed one, so 1.2 and 2.0 are impossible; choosing 0.2 would ignore the complementary relationship between the two components.

Mole fraction is the ratio of the moles of one component to the total moles of all components: Xi = ni/ntotal. Both numerator and denominator are measured in moles, so their units cancel and the result is dimensionless. Molarity has units such as mol L−1, molality has mol kg−1, and mass–volume percentage is reported as a percentage concentration. Therefore A is correct.

The concentration unit ppm means parts per million. Consequently, 5 ppm means that there are 5 parts of impurity for every 1,000,000 parts of the sample, using a consistent mass or volume basis. Thus option A is correct. Five parts per 100 would be 5%, and five parts per 1,000 would be 5,000 ppm, so the other choices misstate the scale.

Dilution adds solvent, so the final solution volume increases while the amount of dissolved solute remains essentially constant. From M = n/V, constant n and larger V produce a smaller molarity. Therefore option A is correct. Molarity does not become zero after a finite dilution, and it remains a meaningful concentration term; it simply decreases as water is added.

Molarity is the number of moles of solute divided by the volume of the final solution in litres: M = nsolute/Vsolution. Therefore option A is correct. Molality instead uses kilograms of solvent, mass percentage uses mass of solution, and mole fraction uses total moles. The phrase ‘volume of solution in the denominator’ uniquely identifies molarity.

Mass-by-mass percentage, written as % (w/w), is calculated as (mass of solute ÷ mass of the complete solution) × 100. Therefore, a 10% w/w sugar solution contains 10 g of sugar in every 100 g of solution; the remaining 90 g is mainly solvent. Option B incorrectly uses the mass of water instead of the total solution mass.

The governing concept is volume-by-volume percentage, written as % (v/v). It is calculated using % (v/v) = [volume of liquid solute ÷ final volume of solution] × 100. For a 20% (v/v) alcohol solution, 20 mL of alcohol is taken and solvent is added until the total, final solution volume becomes exactly 100 mL. This is not the same as adding 20 mL alcohol to 100 mL water, because the final volume may then exceed 100 mL. Option A states the correct meaning. Option B uses mass rather than volume, while C reverses the scale and uses incompatible units. Option D describes an amount in moles per solvent volume, not volume percentage.

The mole fraction of component i is defined as xᵢ = nᵢ ÷ n_total, where n_total is the sum of the moles of every component in the solution. Hence it directly uses total moles. Molarity uses solution volume, mass–volume percentage uses mass and volume, and ppm uses a specified parts-based ratio rather than this total-mole definition.

Molarity is the number of moles of solute present per litre of the final solution: M = n/V. Substituting the given values gives M = 0.25 mol ÷ 1 L = 0.25 mol L⁻¹, or 0.25 M. Therefore option A is correct. The reciprocal, 4 M, would result from dividing 1 by 0.25 and is not the molarity formula.

Molality is defined as the moles of solute divided by the mass of solvent in kilograms: m = n_solute / mass_solvent. Here, m = 0.5 mol ÷ 1 kg = 0.5 mol kg⁻¹, written as 0.5 m. Thus option A is correct. Molality uses solvent mass, not the total solution mass, concentration volume, or a reciprocal ratio.

The mole fraction of a component is calculated as the moles of that component divided by the total moles of all components. Here, total moles are 3 + 7 = 10. Therefore, the mole fraction of the solvent is 7/10 = 0.7. It must be a dimensionless number between 0 and 1, so option A is correct.