A chemist prepares 0.50 mol NaCl by two methods: Method A dissolves the salt in 1.00 L of water; Method B dissolves the salt and then adds water until the total solution volume reaches 1.00 L. Which method produces a 0.50 M solution?
AMethod A, because 0.50 mol divided by 1.00 L of water equals 0.50 M
BMethod B, because molarity requires liters of solution, not liters of solvent
CBoth methods produce 0.50 M because the same amount of solute is used
DNeither method, because molarity also depends on the density of the solvent
Molarity is moles of solute per liter of *solution* (solute + solvent combined). Method A uses 1.00 L of water as the solvent, but the final solution volume will exceed 1.00 L once solute is added — giving a molarity slightly below 0.50 M. Method B correctly measures the final solution volume as 1.00 L, yielding exactly 0.50 M. This is the most common practical error when preparing solutions: confusing the volume of solvent with the final volume of solution.
Question 2 Multiple Choice
A 1.0 m aqueous glucose solution is prepared at 25°C. The solution is then heated to 75°C, causing the solution to expand slightly in volume. Which of the following best describes what happens to the concentration?
ABoth molarity and molality decrease because the solution expands
BMolarity decreases but molality remains unchanged
CMolality decreases but molarity remains unchanged
DBoth molarity and molality remain unchanged because the amount of solute is constant
Molarity is moles per liter of solution, and liquid volume changes with temperature — so heating expands the solution, increasing its volume, and the molarity decreases. Molality is moles per kilogram of *solvent*, and mass is unaffected by temperature. The same grams of solvent remain, so molality is invariant. This is exactly why molality — not molarity — is used in colligative property calculations, which are often performed across temperature ranges.
Question 3 True / False
Adding water to a solution decreases its molarity while the number of moles of solute remains constant.
TTrue
FFalse
Answer: True
This is the principle behind the dilution equation M₁V₁ = M₂V₂. Moles of solute = M × V. When only solvent is added, the moles of solute do not change, but the total volume increases, so molarity (moles/volume) decreases. The equation works precisely because moles are conserved: M₁V₁ = moles = M₂V₂.
Question 4 True / False
For any aqueous solution, molarity and molality typically have the same numerical value because water has a density of 1 kg/L.
TTrue
FFalse
Answer: False
Molarity and molality are only approximately equal for *dilute* aqueous solutions. Molarity uses total solution volume (solute + solvent); molality uses solvent mass only. For dilute solutions where the solute contributes little to the total volume or mass, the values are numerically close. But for concentrated solutions — like 18 M sulfuric acid — they diverge dramatically. And for non-aqueous solvents, the approximation breaks down even at low concentrations.
Question 5 Short Answer
Why is molality preferred over molarity for calculating colligative properties such as boiling point elevation and freezing point depression?
Think about your answer, then reveal below.
Model answer: Molality is preferred because it is temperature-independent. Colligative property calculations require a concentration unit that reflects the ratio of solute particles to solvent, and this ratio must not change as temperature changes. Molarity uses solution volume, which expands or contracts with temperature, so the same solution has different molarities at different temperatures. Molality uses solvent mass, which is invariant with temperature, ensuring the concentration value stays constant across the conditions of the calculation.
The physical laws underlying colligative properties (boiling point elevation = Kbm, etc.) are formulated in terms of molality for exactly this reason. Using molarity would require knowing the exact temperature at the time of measurement, and the calculated values would shift if the temperature changed. Molality neatly sidesteps this problem by anchoring concentration to a temperature-independent quantity.