A student conducts a series of experiments to determine the density of an unknown liquid. They measure the mass of a graduated cylinder, then add 25.0 mL of the liquid and measure the combined mass. This procedure is repeated three times. The results are: Trial 1: Mass of cylinder = 50.2 g, Mass of cylinder + liquid = 75.7 g Trial 2: Mass of cylinder = 50.1 g, Mass of cylinder + liquid = 75.6 g Trial 3: Mass of cylinder = 50.3 g, Mass of cylinder + liquid = 75.8 g What is the average density of the liquid, expressed with the correct number of significant figures?
- A1.0 g/mL
- B1.02 g/mL
- C1.0200 g/mL
- D1.020 g/mL
Show answer & explanationAnswer & explanation
Correct answer: B. 1.02 g/mL
First, calculate the mass of the liquid for each trial: Trial 1: 75.7 - 50.2 = 25.5 g. Trial 2: 75.6 - 50.1 = 25.5 g. Trial 3: 75.8 - 50.3 = 25.5 g. The volume is 25.0 mL. Density = mass/volume. For each trial, 25.5 g / 25.0 mL = 1.02 g/mL. The average density is also 1.02 g/mL. When subtracting, the result is limited by the least number of decimal places (one decimal place here). When dividing, the result is limited by the least number of significant figures (three for 25.5 and 25.0). Thus, the answer should have three significant figures.
Why the other options are wrong
- A. This has only two significant figures, which is too few.
- C. This has five significant figures, which is incorrect based on the input measurements.
- D. This has four significant figures, which is incorrect based on the input measurements.
Significant Figures (Calculations)
Rules for determining the number of digits that are considered reliable in a calculated result, based on the precision of the input measurements.
- Addition/Subtraction: Result limited by fewest decimal places.
- Multiplication/Division: Result limited by fewest significant figures.
- Helps avoid misrepresenting precision.
Memory trick: ADD-SUB: Decimal Places are your guide. MULT-DIV: Sig Figs you must abide.