Determination of Density and the Use of the TI-83

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Objective

To determine the density of a solid (pennies) and use the TI-83 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 post-1982 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. Subtract the mass of the beaker from each mass measurement and the volume of water from each volume measurement. Record these values in the chart.
6. On a TI-83 or 83+ calculator, press 2nd CATALOG and scroll down to Diagnostics On. Press ENTER twice.
7. Press STAT and choose EDIT to view the lists. If there is any data in the lists, clear them by arrowing up to highlight the list name and press CLEAR and ENTER. Do this until all lists are empty. Press the Y= button to check to see if there are any active equations. Clear any equations showing.
8. Go back to STAT, choose EDIT, and enter the volume values from the Data Table into L1 and the mass values into L2. Make sure that you are entering the values from the table (after subtracting empty beaker and water!)for the various trials. We put volume into L1 because it is the default x value (independent variable). The mass is the dependant variable (y value).
9. You can calculate the density of each sample in one step by using a "batch transformation." While you are still in STAT EDIT, arrow over and up to highlight L3. You should see L3 = showing up on the bottom of the screen. Type in L2, L1 and press ENTER. (L1 and L2 are the 2nd functions of the 1 and 2 keys). You should see density values show up in L3. Copy them into your data table.
10. Press 2nd, Y= (which is the STAT PLOT). Make sure all plots are turned off (other than plot 1). If plot 1 is turned off, turn it on by highlighting Plot 1, pressing ENTER, arrowing to highlight the ON selection and pressing ENTER. Plot one should also have the first graph type selected (scatter plot). If not, select it. The X list should be L1 and the Y list should be L2. Choose the first mark type.
11. To view the graph of your data, press ZOOM and select 9:Zoom Stat. Your graph should look close to being linear.
12. To determine how linear your data is and also to calculate the slope of your line, you want to run a linear regression analysis on your data. Press STAT, choose CALC, and then choose 4: LinReg. It will automatically choose L1, L2 as your x and y values unless you tell it otherwise. Press Enter. The information is in the form of the equation for a line. The "a" value is the slope (your density in this case), the "b" value is the y-intercept and the "r" value is the correlation coefficient. The closer the value of "r" is to 1.0000, the closer your data is to being a straight line. Record these values.
13. To view the regression line on top of your graph, press Y=, press VARS, choose 5: Statistics, Choose EQ, Choose 1:RegEQ. The equation should show up on the Y= screen. Press ZOOM and choose 9:Zoom Stat. The graph should show up with the regression line. Observe how closely the line follows the points.

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: __________

Correlation Coefficient (r): __________

Slope (a) = ___________

Y-intercept (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. You can do this using the lists on your calculator.

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 (#3) and your average density (#2), calculate the experimental error. Show work.

5. The "a" 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 "a" 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. What do the values of "r" and "b" tell us about our results? What are the "ideal" values for "r" and "b" in this experiment?

9. Give some sources for your error.