ACT Preparation / Unit 22 ACT 2115 worked example, 60 to 90 seconds
Density and Concentration Problems
The idea
Density and concentration problems are solved in three steps. First, write the defining ratio: density is mass over volume, and concentration is the amount of solute over the amount of solution. Second, substitute the two known quantities with their units. Third, solve for the unknown, rearranging if needed, and check that the units of the answer match the question.
In practice
Worked example: a liquid has a density of 1.2 grams per milliliter. What is the mass of 250 milliliters? Mass = density × volume = 1.2 × 250 = 300 grams. Second: a solution holds 15 grams of sugar in 300 milliliters, so its concentration is 15/300 = 0.05 grams per milliliter. Diluted to 600 milliliters, the same 15 grams give 0.025 grams per milliliter, half as concentrated.
Where people slip
Rearrange the ratio rather than guessing: volume is mass divided by density, not mass times density. A check of the units catches the slip.
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