Materials Included In Kit

Additional Materials Required

Prelab Preparation

1. Divide the brass shot into four samples, each approximately 35–40 g. Divide the zinc shot into 8 samples, also 35–40 g each.

Safety Precautions

The metal shot pieces used in this experiment are considered nonhazardous. Always wear safety glasses or chemical splash goggles when working with chemicals or glassware in the lab. Zinc and aluminum powders or dust emit flammable gases in contact with water and may ignite spontaneously. Please review current Safety Data Sheets for additional safety, handling and disposal information.

Disposal

The metal shot samples should be thoroughly dried and stored in their original labeled containers for repeat use. Have students decant most of the water from their graduated cylinders and then carefully pour their metal samples onto several layers of paper towels. Allow to air dry.

Lab Hints

• The experimental work for this lab can reasonably be completed in a typical 2-hour lab period. If fewer than three balances are available for classroom use, the instructor may wish to prepackage metal samples to avoid long delays at the balances.
• If more balances are available, students may measure the mass of the graduated cylinder plus water plus metal sample directly on the balance. They can then record a running (cumulative) total of both mass and volume.
• In order to ensure two significant figures in each volume measurement, it is best to work with 8–14 g sample sizes in steps 3–4. Keep the minimum mass above 8 g.
• Aluminum, brass, copper and zinc shot all gave consistently accurate results using this method—percent errors in the density measurements ranged from 4 to 8%. If aluminum shot is used, the sample mass range should be reduced to 3–10 g.
• Metal turnings, metal sheet and so-called “mossy zinc” gave less accurate results (percent errors ranged from 12 to 35%). Mossy zinc pieces, for example, have a large surface area and thus capture many small air bubbles. Air bubbles increase the apparent volume of the metal sample.
• The estimated uncertainty in volume measurements is similar in both 25- and 100-mL graduated cylinders (0.1 versus 0.2 mL, respectively). Thus, 100-mL cylinders may be used in place of the 25-mL cylinders if the latter are not available. Under these conditions, it is important to note the minimum mass of metal shot required to give precise volume measurements—it may be desirable to use samples having a larger mass.
• This lab has been written to compare experimental density results against literature values and to determine the accuracy of the results. The procedure can be adapted to measure the density of common objects (e.g., marbles, dice, hex nuts, bolts). An interesting extension might be to give different student groups different kinds or grades of nuts and bolts and ask students to evaluate their composition. (Are all nuts made of the same material?)
• Brass is an alloy (mixture of metals) and thus may have a variable composition and density. The value of the density for the brass shot included in the sample results was 8.48 g/cm³.
• Students may question the number of groups using “gold” samples compared to “silver.” “Gold” is more rare and valuable.
• It is not necessary to give students the definition and equations for density—let them discover the concept for themselves by collecting the data, recognizing the trend and analyzing the results to find the quantitative relationship between mass and volume.
• Depending on the mathematical background of your students, it may be helpful to review the concept of slope and how it is measured. Students who have learned to use a graphing calculator may be encouraged to use the calculator to find the slope. Slope can also be found using a computer spreadsheet program. Students should include (0,0) as a data point when obtaining the linear regression trendline.
• This experiment can be adapted to a discovery-based or inquiry lab. Start out by telling the story of Archimedes and the king’s gold crown. How did Archimedes prove the crown was gold or not? Give the students metal shot samples, an assortment of graduated cylinders of various sizes, and a challenge—measure the density of the metal. Many variables will influence the reliability of the results. Students who start out with too large a graduated cylinder or too small a sample mass will discover that they need to modify their approach. The advantage of the inquiry approach is that students take it upon themselves to reduce experimental error, especially when they see other groups that “nail” the density. You may be surprised at the number of students who yell a modern version of “Eureka!”
• A common student misconception about density is that “bigger” objects are more dense. Students readily identify the more dense object when two objects are similar in overall size (volume). However, when they have to compare the densities of objects that are very different in size, they may think the bigger object is more dense. Demonstrate this with a large block of wood and a small metal object—the small metal object sinks in water, but the large wood block floats.

Answers to Prelab Questions

1. The volume of a metal cylinder was measured indirectly by water displacement three times. The following volume readings were recorded. Using Equation 1 from the Background section, determine the volume of the metal cylinder for each trial, and then calculate the average volume of the metal cylinder. Note: Since the volume of a solid is being measured, use the units cm³. Recall that 1 mL = 1 cm³.
   {14024_PreLabAnswers_Table_2}
   {14024_PreLabAnswers_Equation_3}
2. The metal cylinder in Question 1 has a radius r = 1.05 cm and a height h = 3.32 cm.
   1. Calculate the volume (V) of the metal cylinder (V = πr²h).

      V = πr²h = (3.14)(1.05 cm)²(3.32 cm) = 11.5 cm³

   2. How does the average measured volume compare to the calculated (accepted) volume?

      The measured volume is greater than the accepted volume. It is not accurate.

   3. Calculate the percent error between the measured and accepted values for the volume of the cylinder. Describe the accuracy of the measurements.
      {14024_PreLabAnswers_Equation_4}
      The accuracy of the volume measurements made by water displacement is 4%.
3. “Bull’s-eye” drawings may be used to illustrate the concepts of accuracy and precision. Which drawing in Figure 2 suggests accurate but imprecise measurements of the quantity x? Which one illustrates precise but inaccurate measurements?
   {14024_PreLabAnswers_Figure_2}
   Drawing B suggests accurate but imprecise measurements of quantity x. The marks are all close to x, but not to each other. Drawing A shows precise measurements (they closely agree) that are inaccurate (they are not close to x). Drawing C is neither accurate nor precise.

Sample Data

Laboratory Report

Graphing the Data*
Plot the mass and sample volume data for samples 1–4 on the following graph. Each sample will be represented by one point on the graph. Use the horizontal (x) axis for the volume and the vertical (y) axis for the mass. Label each axis—do not forget the units—and make sure the scale is clearly marked. Do not “connect-the-dots” with the data points.

*Sample graphs are shown for zinc and brass only.

Answers to Questions

1. Does it make sense that any trend or pattern in the mass and volume data should include (0,0) as a point? Explain your reasoning.

   The point (0,0) should be included in all of the graphs since all matter has mass and occupies space (volume).

2. What kind of trend or pattern is obvious from the plotted graph of the mass and volume data? Is there a consistent relationship between the volume and mass of each sample? Explain.

   As the mass of a sample increases, its volume also increases in a regular or predictable manner. This direct relationship appears to be linear (i.e., a straight line can be drawn through all or most of the data points, including the (0,0) point).

3. Based on your answers to Questions 1 and 2, draw a “best-fit” trendline through the data points. The best way to do this is to place a transparent ruler or straightedge at an angle over the data points—find the “best-fit” line that includes, or comes close to, as many points as possible.

   See sample graphs. Note: Straight lines were drawn using a spreadsheet program to obtain the best-fit straight line through the data. If desired, a graphing calculator can be used. The option of incorporating linear regression analysis should depend on the mathematical background and skill of the students.

4. Calculate the slope (m) of the “best-fit” line. Select two points—(x₁, y₁) and (x₂, y₂)—that are closest to the actual line. Show all of your work! What are the units of the slope? What physical property is represented by the slope?
   {14024_Answers_Equation_5}
   The slope represents the density of the metal. Slope will vary depending on which data points are selected. For the sample data, slope was determined using a spreadsheet program.
5. Compare the calculated slope with that obtained by another student group that used a differently colored metal (i.e., if your samples were silver, compare your data with a group that measured gold samples). Are the values of the slope the same? Why or why not?

   Encourage students to compare slope values with other groups and to brainstorm about what the similarities and differences mean. Students should conclude that different samples are composed of different materials and that the slope corresponds to the density, which is a characteristic physical property of a metal.

6. Use the following information to determine the probable identity of your metal. What type of metal do you have?
   {14024_Answers_Table_4}
   Answers will vary depending on the metals used.
7. Assuming that the identification of your metal is valid, calculate the percent error in your determination of the slope and the physical property it represents. The percent error measures the accuracy of your results. Comment on the accuracy of this procedure and discuss any possible sources of experimental error.
   {14024_Answers_Table_5}
8. Density can be calculated by dividing the mass of an object by its volume. Using the mass and volume measurements recorded in the data table, calculate the density for each sample, the average density, and the difference between each density value and the average value. Comment on the precision of the density determination and express the average density with its uncertainty.
   {14024_Answers_Table_6}

Introduction

When scientific observations and measurements are made, patterns and trends sometimes emerge and relationships among different variables may become evident. One of the best ways to recognize the existence of relationships involving numerical data is to plot the data on a graph.

Concepts

• Scientific measurement
• Mass and volume
• Water displacement
• Precision and accuracy
• Density
• Graphing

Background

Mass is measured directly using a balance. The volume of an irregularly shaped solid, however, cannot be measured directly. Instead, its volume is usually measured by an indirect method called water displacement. The initial volume of a given amount of water is measured using a graduated cylinder. The solid is then carefully added to the water in the graduated cylinder and the new (final) volume is recorded. The volume occupied by the solid must be the same as the volume of water that has been displaced and is therefore equal to the difference between the final and initial volumes (see Figure 1 and Equation 1).

Accuracy and precision are two different ways to describe the error associated with measurement. Accuracy describes how “correct” a measured or calculated value is, that is, how close the measured value is to an actual or accepted value. The only way to determine the accuracy of an experimental measurement is to compare it to a “true” value—if one is known! Precision describes the closeness with which several measurements of the same quantity agree. The precision of a measurement is limited by the uncertainty of the measuring device. Uncertainty is often represented by the symbol ± (“plus or minus”), followed by an amount. Thus, if the measured volume of an object is 10.2 mL and the estimated uncertainty is 0.1 mL, the volume would be reported as 10.2 ±0.1 mL.

Experiment Overview

The purpose of this experiment is to plot mass and volume data for a set of metal objects and to determine the relationship between these measurements. The trend that is revealed will be analyzed and used to identify the substance. The precision and accuracy of the results will also be determined.

Materials

Prelab Questions

1. The volume of a metal cylinder was measured indirectly by water displacement three times. The following volume readings were recorded. Using Equation 1 from the Background section, determine the volume of the metal cylinder for each trial, and then calculate the average volume of the metal cylinder. Note: Since the volume of a solid is being measured, use the units cm³. Recall that 1 mL = 1 cm³.
   {14024_PreLab_Table_1}
2. The metal cylinder in Question 1 has a radius r = 1.05 cm and a height h = 3.32 cm.
   1. Calculate the volume (V) of the metal cylinder (V = πr²h).
   2. How does the average measured volume compare to the calculated (accepted) volume?
   3. Calculate the percent error between the measured and accepted values for the volume of the cylinder. Describe the accuracy of the measurements.
      {14024_PreLab_Equation_2}
3. “Bull’s-eye” drawings may be used to illustrate the concepts of accuracy and precision. Which drawing in Figure 2 suggests accurate but imprecise measurements of the quantity x? Which one illustrates precise but inaccurate measurements?
   {14024_PreLab_Figure_2}

Safety Precautions

The metal shot pieces used in this experiment are considered nonhazardous. Always wear safety glasses or chemical splash goggles when working with chemicals and glassware in the lab. Please follow all normal laboratory safety guidelines.

Procedure

1. Obtain 35–40 g of either silver- or gold-colored metal shot in a 100-mL beaker. In the data table, circle whether the metal is “silver” or “gold.”
2. Use a pen or marker to label four weighing dishes, 1–4.
3. Tare (“zero”) weighing dish 1 on the electronic balance and add about one-fourth of the metal shot to the dish. Measure the precise mass of sample 1 (it should be between 8 and 14 g). Record the mass of sample 1 in the data table.
4. Repeat step 3 to divide the metal shot among the other three weighing dishes. Vary the sample sizes so they are not all the same mass. Thus, if the first sample is 8 g, make the next sample about 10 g, etc. Do not mix up the samples!
5. Obtain a clean, 25-mL graduated cylinder and add approximately 10 mL of water to the cylinder.
6. See Figure 3 for how to measure volume using a graduated cylinder. Always view the meniscus at eye level and read from the bottom of the meniscus.
   {14024_Procedure_Figure_3}
7. Measure the initial volume of water in the cylinder to the nearest 0.1 mL and record the value for sample 1 in the data table. Note: Use the units cm³.
8. Carefully add sample 1 to the water in the graduated cylinder. The best way to do this is to tip the cylinder at a slight angle and gently slide the metal shot into the water so that the water does not splash or splatter (and the glass cylinder does not break). Lightly tap the cylinder to release any trapped air bubbles. Record the final volume of water plus the sample.
9. Subtract the initial volume from the final volume to determine the volume of sample 1 and record the result.
10. Repeat steps 6–8 for each of the remaining samples. Do NOT remove prior samples from the cylinder between measurements! Before adding a new sample to the cylinder, measure the new “initial” volume in the graduated cylinder. This may not always be precisely the same as the previous final volume reading. Record initial and final volume measurements and the volume of each subsequent sample.
11. Decant the water from the graduated cylinder into a sink or container and pour the metal shot onto folded paper towels. Allow to air dry for use by subsequent lab sections if needed.

Student Worksheet PDF

14024_Student1.pdf