17
Percent concentration, mass, volume and density of a solution
Textbook: pp. 84–85
GoalApply the relation between the mass, volume and density of a solution (ρ = m/V) in percent-concentration problems.
New words
density · zichlikvolume of solution · eritma hajmig/mL · g/mlmass fraction · massa ulushi
Explanation
The density ρ of a solution is the ratio of its mass m₂ to its volume V: ρ = m₂/V, so m₂ = V·ρ and V = m₂/ρ. Density is expressed in g/mL (or kg/L) and volume in mL or L. In problems where the volume of a solution is given, first find the mass from volume and density, then calculate the mass of solute from C% (m₁ = C%·m₂/100 %) or the reverse. A concentrated solution is denser than water (1 g/mL), so 100 mL of it weighs more than 100 g. Volumes of solutions are in general not additive, so on mixing it is the masses that add, not the volumes.
Worked examples
300 mL of solution has a density of 1.1 g/mL. m₂ = V·ρ = 300·1.1 = 330 g. If it is 10 % there are 33 g of solute.
A 220 g solution of density 1.1 g/mL has volume V = m₂/ρ = 220/1.1 = 200 mL.
Class activity
Measuring: with a measuring cylinder and a balance, find the masses of 50 mL of water and 50 mL of sugar solution, calculate their densities and compare them (under the teacher’s supervision).
Practice
1
500 mL of solution has a density of 1.2 g/mL. What is its mass in grams?
600
2
A 360 g solution has a density of 1.2 g/mL. What is its volume in mL?
300
3
A 250 mL bottle of solution has a density of 1.08 g/mL and contains 13.5 g of solute. Find the percent concentration.
5
4
Why do we add masses, not volumes, when solutions are mixed?
Mass is conserved, whereas volume need not equal the sum because the density changes.