Question

As chief chemist at Superior Analytical Products (SAP) you must design an experiment to determine the density of an unknown liquid to three (3) significant figures. The density is of the order of 1 g/cm3. You have approximately 7 mL of the liquid and only graduated cylinders and balances are available for your use. Which of the following combinations of equipment will allow you to meet but not exceed your goal?

1) Graduated cylinder with ±0.1 mL uncertainty; balance with ±0.1 g uncertainty
2) Graduated cylinder with ±0.01 mL uncertainty; balance with ±0.1 g uncertainty
3) Graduated cylinder with ±0.01 mL uncertainty; balance with ±0.01 g uncertainty
4) Graduated cylinder with ±0.001 mL uncertainty; balance with ±0.001 g uncertainty
5) Graduated cylinder with ±0.1 mL uncertainty; balance with ±0.001 g uncertainty

Answer 1

The best equipment combination for determining the density of an unknown liquid to three significant figures is a graduated cylinder with ±0.01 mL uncertainty and a balance with ±0.1 g uncertainty, as it matches the significant figures required.Hence, option 2 is the correct answer.

Step-by-step explanation:

To determine the density of an unknown liquid to three significant figures using only a graduated cylinder and a balance, the combination of equipment must provide measurements accurate enough to allow for three significant figures in the final density value. Since density is mass per unit volume, both mass and volume measurements affect the number of significant figures in the calculated density.

The appropriate equipment combination is Option 2: a graduated cylinder with ±0.01 mL uncertainty and a balance with ±0.1 g uncertainty. This ensures the volume measured has three significant figures, meeting the requirements without exceeding them. Using a graduated cylinder with less uncertainty could lead to unnecessary precision beyond the required three significant figures. It would also cause the final density value to be rounded to the significant figures of the balance, which has the least precision.

Correct usage of the equipment will allow for a precise density calculation. Considering the mass measurement has more significant figures than the volume, the final density calculation will be rounded to the least number of decimal places based on the volume measurement, ensuring three significant figures for the density.