Name_______________
Period ________
DETERMINATION OF DENSITY AND THE USE OF THE TI-83
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
32 post-1982 pennies
50 mL graduated cylinder
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
_______
Volume of water
______
Mass of beaker + 12 pennies
_______
Volume of water + 12 pennies
______
Mass of beaker + 16 pennies
_______
Volume of water + 16 pennies
______
Mass of beaker + 20 pennies
_______
Volume of water + 20 pennies
______
Mass of beaker + 24 pennies
_______
Volume of water + 24 pennies
______
Mass of beaker + 28 pennies
_______
Volume of water + 28 pennies
______
Mass of beaker + 32 pennies
_______
Volume of water + 32 pennies
______
# of Pennies
Volume of
pennies
Mass of
pennies
Density of
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. 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 post1982 penny. Show work.
4. Using your theoretical density (#3) and your average density (#2), calculate the
experimental error. Show work.
| theoretica l value - experiment al value |
Percent error 
x 100
theoretica l value
5. The “a” value that you determined with the regression analysis 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.
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