Determination of Density and Use of Graphical Analysis

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Objective

To determine the density of a solid (pennies) and use graphical analysis to analyze the results.

Discussion

Density is a physical property of a substance. It is defined as mass per unit volume. Density can be used to distinguish one substance from another. The units for solids and liquids are g/cm³ or g/mL. The units for gases are g/L.

Equipment

• triple beam balance
• 50 mL graduated cylinder
• 32 pennies
• 50 mL beaker

Procedure

1. Mass a clean, dry 50 mL beaker to the nearest 0.01 gram. Record the results on the data page.
2. Place 12 pennies into the beaker and remass the beaker and contents. Record. Repeat the process using 16, 20, 24, 28, and 32 pennies.
3. Half-fill a 50-mL graduated cylinder with water. Carefully read the volume to the nearest 0.1 mL and record.
4. Very carefully lower 12 pennies into the cylinder and read and record the new volume. Repeat the process using 16, 20, 24, 28, and 32 pennies.
5. Using a computer, load Graphical Analysis.
6. To include labels for the horizontal and vertical axes, double-click on the top cell of either column and enter the new label and unit in the pop-up menu that appears. Change the labels and units to be "volume" in "mL" on the x-axis and "Mass" in "grams" on the y-axis. Click OK to accept the changes.
7. Input the "x and "y" values from the Data Table for the various trials.
8. Click anywhere on the graph in order to make it the active window. To change the title of the graph, click the Title of the graph and enter a new title in the pop-up box that appears. Change the title to be "Density-(Your names)."
9. Now from the Graph menu, make sure Point Protectors is turned on. Selecting a menu item "toggles" it on or off. If the item is preceded by a check mark, the item is on. We want Point Protectors turned on. We also want to make sure Connecting Lines is turned off.
10. Make sure to move the mouse to each axis label & click. In the dialog box, choose AutoScale at 0. This insures your graph will go through the origin.
11. The Regression Line button on the Tool Bar will be used to calculate the best-fit line for the curve. Before you determine the best-fit line, you must select the region of the graph you want to include. Starting at the origin, Click & Drag the mouse across the entire graph. Then Click the Regression Line button (7th one). A best-fit line will be drawn on the graph and a floating box will display the numeric results. Copy the data from this box into the corresponding data table.
12. Print one copy of your graph for each group member. To do this, choose Print from the File menu. Print the "whole screen."

Data

Mass of beaker: __________

Mass of beaker plus 12 pennies: __________

Mass of beaker plus 16 pennies: __________

Mass of beaker plus 20 pennies: __________

Mass of beaker plus 24 pennies: __________

Mass of beaker plus 28 pennies: __________

Mass of beaker plus 32 pennies: __________

Volume of water: __________

Volume of water plus 12 pennies: __________

Volume of water plus 16 pennies: __________

Volume of water plus 20 pennies: __________

Volume of water plus 24 pennies: __________

Volume of water plus 28 pennies: __________

Volume of water plus 32 pennies: __________

Number of Pennies	Mass	Volume	Density

Graphical Analysis information

Correlation Coefficient: __________

M = ___________

B = _________________

Calculations

1. Using the equation D = M / V, determine the density for the pennies. Show ONE sample calculation here.

2. Using all of your calculated densities, determine the average value for density. Show work here.

3. Post-1982 pennies are 97.5% zinc and 2.5% copper. The density of zinc is 7.13 g/mL and the density of copper is 8.92 g/mL. Calculate the theoretical density of a post-1982 penny. Show work.

4. Using your theoretical density and your average density, calculate the experimental error. Show work.

5. The M value that you determined with the graphical analysis program is the slope of the best-fit line. Since we graphed mass vs volume, the slope represents our density. Use the M value as your experimental value and calculate the experimental error again.

6. Did the average density or the slope of the best-fit line give you the lowest percent error?

7. Why should the slope give you better results?

8. Give some sources for your error.