September 8, 2008
Density of an Unknown Metal
G. Bergskaug*, J. Boucher
The goal of this investigation was to determine experimentally the identity of a piece of metal by finding its density. Mass and volume measurements were recorded for six different samples of the substance. The experimental value for the density was comparable to the published value for copper. Therefore, the identity of the metal was determined within reasonable error.
Introduction
Pure substances have intensive properties, or characteristic properties that can be used to identify them. These properties include but are not limited to index of refraction, chemical reactivity, and electronegativity. Unfortunately, these stated properties are difficult to measure in a high school laboratory. A property that is easier to measure is density.
The density of a substance is the ratio of its mass to its volume. Equal volumes of different substances may have different masses. For example, Styrofoam has a much lower density than lead. This means that a sample of Styrofoam will have a lower mass than the same volume of lead.
The formula for density is density = mass/volume. Typically, mass is measured in grams and volume is measured in milliliters. The density, therefore, is often expressed in g/mL. The ratio of mass to volume of a given element will not change as long as the temperature and pressure are held constant. Thus, the density of an element is a characteristic property of the element and can be used to identify the element.
Density can be determined theoretically or experimentally. Periodic trends in the densities of the elements show that, in general, density increases as the atomic number increases. The densities of the various elements are well-established and are published in most science textbooks. One way density can be determined experimentally is by measuring the mass and volume of a given substance and applying the above density formula.
Methods
Samples of the unknown substance—indicated as samples A through F—were tested. The mass and volume of each were measured. To measure the mass, the sample was placed on an electronic balance with a precision of ± 0.01 g. The water displacement method was used to measure the volume. A graduated cylinder with a precision of ± 0.1 mL was filled with a known volume of water. The initial volume was recorded. Then, the sample was placed in the water. The final volume (the volume of the water and the sample) was recorded. The experimental density (i.e. the slope of the graph) was compared to published density values to determine the substance’s identity. Percent error was calculated.
Results
Table 1: Raw Data
Sample / Mass, g / Volinitial water, mL / Volfinal water, mLA / 44.77 / 25.0 / 30.1
B / 89.20 / 25.0 / 34.8
C / 233.05 / 25.0 / 50.0
D / 448.90 / 25.0 / 76.0
E / 161.28 / 25.0 / 42.8
F / 321.94 / 25.0 / 61.0
Table 2: Manipulated Data
Sample / Mass, g / Volume, mLA / 44.77 / 5.1
B / 89.20 / 9.8
C / 233.05 / 25.0
D / 448.90 / 51.0
E / 161.28 / 17.8
F / 321.94 / 36.0
Figure 1: The mass as a function of volume was plotted for six samples of an unknown substance. The slope of the graph, which is the density of the substance, is 8.8 g/mL.
Sample Calculation(s):
For Sample A:Volume = Volfinalwater – Volinitialwater
= 30.1 mL - 25.0 mL
= 5.1 mL
Percent Error:% Error = (Experimental Value – Theoretical Value) X 100
Theoretical Value
= (8.8 g/mL – 8.96 g/mL) X 100
8.96 g/mL
= -1.79 %
Discussion/Conclusions
The linear graph has a slope of 8.8 g/mL, representing the substance’s density. This density value is consistent with the published value of 8.96 g/mL for the density of copper (University Physics, Wilson and Buffa, p. 78).
The calculated percent error is -1.79%, which suggests that the experimental results are slightly low. Several factors could have contributed to the negative percent error. First, the samples may not have been sufficiently dried after other groups used them. The final volume would have been artificially high, making the calculated volume of the sample too high. Extending this argument, the calculated density would then be too low. Impurity of the substance could also have affected the results. For example, if the substance contained other material with a lower density, then the measured mass would be lower than if the substance was pure. In this case, the calculated density would also be lower. Other errors could include the precision of the instruments, error in determining the meniscus location for the volume reading, and the low number of trials performed. Finally, the samples were physically small.
To minimize the effects of these errors in the future, several steps could be followed. The sample sizes could be dried with an electric hair dryer or placed in the chemistry oven between groups to avoid contamination from water. Substances used should be as pure as possible. In addition, multiple trials for each sample should be performed and additional samples should be used. Finally, larger samples should be used to minimize errors.
In conclusion, the density of an unknown substance was experimentally determined to be comparable to the published value for copper within a small margin of error.
Questions
Usually there are questions to answer on the lab handout. Place your complete answers here. Be sure to show all work when applicable (for calculations).
References
Dingrando, Lauren, Kathleen V. Gregg, Nicholas Hainen, and Cheryl Wistrom. Chemistry:
Matter and Change. New York: Glencoe McGraw-Hill, 2002.
Wilson, J., and G. Buffa. University Physics. New York: University Press, 1999.
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