1. Yes, zero volume would also have zero mass. (You can also argue for the answer no, since the graph should include only measured data. Using the intercept as a data point biases the measured data.)
2. There are two straight lines indicating two kinds of metals were used. Each line has a slope that is dependent upon the mass/volume ratio. This same ratio is a physical constant for a particular metal.
3. b = 0, therefore y = mx
5. Density
6. Answers will vary. The density of aluminum is 2.70 g/cm 3 and the density of iron is 7.86 g/cm 3. Student answers from reading the graph will vary within a range near the accepted values.
7. Density values determined from the data table should vary in a range more closely to the accepted values than from using the slope to determine the density values.
8. The density value read from the graph is probably less accurate inasmuch as the line is a Òbest fitÓ line. Using all of the data points and a statistical procedure, like the method of least squares, to calculate the slope would lead to a better result from the slope as compared with the tabular data. Measuring volumes from calibrated cylinders presents the largest errors. Steel is an alloy, and measuring the density of steel gives a result different from that expected for iron.
10. Mass in air mass in water = mass of water displaced; 29.03 g 27.43 g = 1.60 g = mass of water displaced. Since the density of water is 1.00 g/mL, the mass of water displaced is equal to the volume of water displaced.
This in turn is equivalent to the volume of the object displacing water.
The amulet is not pure gold. See the October 1989 issue of ChemMatters (page 16) ÒIndianaÕs ErrorÓ for an interesting story dealing with the density of gold.
11. When the masses are measured to this level of accuracy, the minimum mass is 28.9 g in air and the maximum mass is 27.5 g in water. This density is 21 g/cm 3 . So, unless the masses are measured with sufficient accuracy that the difference will have more than two significant figures, answering the question is impossible (see General Resource module for discussion of uncertainty in measurement and significant figures).
Post-Laboratory Discussion
1. Discuss the student results. Compare densities obtained by the volume displacement method to densities obtained by the ArchimedesÕ weight displacement method. Have students locate the accepted values for the densities of these metals in The Handbook of Chemistry and Physics or in a chemistry or physics text.
2. Reemphasize the significance of the slope of a mass versus volume curve in determining the density of a substance. Ask the class to compare the degree of slope of the aluminum line and the iron line to the calculated densities of these metals.
3. For an extension activity, ask students to determine a way to find the density of a material less dense than water (will float on water). Cork stoppers found in your chemistry laboratory would be good candidates for this exercise.
1. The figure below shows a graph of mass vs. volume for two immiscible liquids. Predict from the graph what will happen if Liquid A and Liquid B are poured together. [The liquids are immiscible and thus will not mix but will separate with Liquid A settling below Liquid B in the container. The reason for this occurrence is that Liquid A has a greater density than Liquid B. The density is indicated by the slope of the line plotted on a mass vs. volume graph.)
Figure 8. Plot of mass vs. volume for two immiscible liquids.
2. Ask students to explain the principles of the conventional battery tester or antifreeze tester. [Both battery testers and antifreeze checkers use large bulb pipets (similar to kitchen meat basters) to withdraw a sample of fluid from the battery or radiator. The stem of the pipet contains color-coded beads of known density. By observing which beads float and which sink in the liquid withdrawn, the gas station attendant can estimate the concentration of the acid or antifreeze in the liquid. This rapid, semiquantitative procedure is more than adequate for the purposes of deciding what course of action to take in automobile maintenance.]
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