Exercise 1: Propagation of uncertainties (multiplication and division) A student

Question

Exercise 1: Propagation of uncertainties (multiplication and division) A student weighed a 26.91 g block to the nearest 0.01 g and measured its volume as 25 ml to the nearest ml. What is the uncertainty in the calculated density? its volume as 25 Density= 26.91g±0.01 g 1.0764 g/ml 25 ml±1 ml The density is 1.0764 g/ml. It should not be rounded off yet! Do you know why? a. Find% uncertainty in mass. Setup: 0.01 alg 0,03 % b. Find % uncertainty in volume. Setup: 1 ml a 5 ml c. Find % uncertainty in density. Setup: d. Find absolute uncertainty in density. Setup e. Now report the density to the correct number of significant figures? f. Report the answer in the correct number of significant figures. g. Why did you round off the density to the hundredth place? Answer: Density-:-03-gml Density= 1, o,g/ml ± 0.04 g/ml r sa tie in tha numerator because its not exaut Ccaunteds. Notice that the answer 1.08 g/nl has three significant figures although the denominator

Explanation / Answer

Many conversion factors that we use in chemistry related one property to another.

Examples are density (mass per volume, g/mL) and molar mass (mass per mole, g/mol).

These conversion factors are based on measurements, and their significant figures must be considered.

The mass 26.91g contains 4 significant figures and thus density should be expressed upto 4 significant figures

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