1. LPChem1415 Mass & Volume: Penny Lab  The purpose of this lab is to graphically determine the mathematical relationship between mass and volume for the pre-1982 pennies that we used.  Your graph needs to have the mass (in grams) of your groups of pennies on the y-axis.  It should have the volume (in milliliters) of your groups of pennies on the x-axis.

2. LPChem1415 Mass & Volume: Penny Lab  The volume of water used does not appear on the graph.  The number of pennies does not appear on the graph.  The graph can be computer-generated or hand-written on graph paper.  Graphs written on notebook paper will not receive credit.

3. LPChem1415 Mass & Volume: Penny Lab  You were encouraged to use groups of pennies (not one at a time) for two reasons.  It is incredibly difficult to measure the volume of one penny accurately by water displacement in the graduated cylinder.  Using a larger number of pennies averages out small imperfections and differences (dirt, distortions, etc) and allows more precise data.

4. LPChem1415 Mass & Volume: Penny Lab  There are several different completely valid ways in which to gather data for this lab. For the sake of simplicity, I will just focus on two. (You may have used some other procedure, and that is fine.)

5. LPChem1415 Mass & Volume: Penny Lab The Start-Again-From-Scratch method goes like this: 1) I weighed 5 pennies and recorded their mass.  2) I filled a graduated cylinder partway with water, then recorded the volume as V i.  3) I added the pennies I’d already weighed to the cylinder, then recorded the new volume as V f.  4) I dumped everything out, dried the pennies, then repeated these steps with 10, 15, 20, 25, and 30 pennies.

6. LPChem1415 Mass & Volume: Penny Lab  My data table might look like this: # penniesmassViVi VfVf (g)(mL) 512.551.252.7 1024.950.353.4 1537.449.954.4 2049.952.058.0 2562.551.159.2 3074.951.761.9

7. LPChem1415 Mass & Volume: Penny Lab  In order to make a graph, I’ll need to find the volume for each number of pennies.  (I need to subtract out the initial volume of water ; V f -V i = V pennies )  Since finding the volume of the pennies requires math, my V pennies values will go in the Evaluation of Data section. V pennies (V f - V i ) (mL) 1.5 3.1 4.5 6.0 8.1 10.2

8. LPChem1415 Mass & Volume: Penny Lab The Addition method works this way:  1) I weighed 5 pennies and recorded their mass.  2) I filled a graduated cylinder partway with water, then recorded the volume.  3) I added the pennies I’d already weighed to the cylinder, then recorded the new volume as V f.  4) I weighed 5 additional pennies (as in step one) and added them to the graduated cylinder that already contained pennies and water. I recorded the new volume as V f for 10 pennies.  5) I repeated step 4 until I had six sets of data.  6) I dumped everything out and dried the pennies.

9. LPChem1415 Mass & Volume: Penny Lab  My data table will need to label the data some other way than in the first method. I can’t list data by “number of pennies” anymore because the masses are each for only five pennies, but the volumes are for all the pennies together.  I decided to just label things as “trials” and leave the number of pennies out. Trial 0 is for zero pennies. (This is where I recorded the volume of water in the graduated cylinder before I started dropping pennies in.)

10. LPChem1415 Mass & Volume: Penny Lab  My data table might look like this: Trial #mass added VfVf (g)(mL) 0051.2 112.552.7 212.454.3 312.555.7 412.557.2 512.659.3 612.461.4

11. LPChem1415 Mass & Volume: Penny Lab  Using this method is definitely more efficient during the lab—I don’t need to stop and dry pennies several times—but it requires more Evaluation of Data.  In order to make a graph, I still need V pennies and m pennies for six data points.  To calculate the volumes, I’ll subtract out the same initial volume every time (V f from trial 0, when only water was in the graduated cylinder).

12. LPChem1415 Mass & Volume: Penny Lab To calculate the volumes, I’ll subtract out the same initial volume every time (V f from trial 0, when only water was in the graduated cylinder). (V f - 51.2)V pennies (mL) 52.7-51.21.5 54.3-51.23.1 55.7-51.24.5 57.2-51.26.0 59.3-51.28.1 61.4-51.210.2

13. LPChem1415 Mass & Volume: Penny Lab  I also need to make a column in “Evaluation of Data” where I calculate the total mass of pennies involved in each trial. mass TOT (g) 12.5 24.9 37.4 49.9 62.5 74.9

14. LPChem1415 Mass & Volume: Penny Lab  Now I have the data I need to generate a graph. Note: I titled the graph, and put both a variable name and a unit on each axis!

15. LPChem1415 Mass & Volume: Penny Lab  Now I need to draw a “best-fit” line through my data points so that I can find the equation of the line.  If I’m using graph paper, I can draw the line with a ruler,then calculate the slope of the line myself.  If I’m using a computer program, I can have the computer do the best fit line and find the equation for me.

16. LPChem1415 Mass & Volume: Penny Lab

17. LPChem1415 Mass & Volume: Penny Lab  When I found an equation for my line, I used mass as the “y variable” because I’m graphing mass on the y- axis. I used Volume as the “x variable” because I’m graphing volume on the x-axis. I included units on both of those variables.  The slope of my graph had a value of 7.7 g/mL. I can only report my slope with two significant figures because most of my V pennies measurements only had two.

18. LPChem1415 Mass & Volume: Penny Lab  The units of my slope are g/mL (grams per milliliter) because of the units of the axes of my graph, and because mass and volume are two different things and cannot cancel out.  My equation shows that for these pennies (pre-1982 pennies, which are made of copper), there is a direct proportion relating mass and volume.  A slope of 7.7 g/mL means that one milliliter of copper has a mass of 7.7 grams.  My intercept is zero because zero milliliters of copper should have a mass of zero. (If I don’t have any copper it doesn’t have any mass.)

19. LPChem1415 Mass & Volume: Penny Lab  I can use this graph (a density graph) to answer questions about other masses and volumes of copper.  Even though I didn’t have a data point at 4.0 mL, I can determine the mass of 4.0 mL of copper from the graph as follows:

20. LPChem1415 Mass & Volume: Penny Lab  I drew a straight line from the 4.0 mL mark up to my best-fit line, then found the mass that corresponded to it. The mass is above 30 g and below 40 g. I’m going to estimate 32 g.  If you are asked to solve GRAPHICALLY, this is what you do. Track the given data to the best-fit line, then see what value it corresponds to on the other axis.

21. LPChem1415 Mass & Volume: Penny Lab  What if I were asked for the mass of 20.0 mL of copper?  That value doesn’t show on my graph. I can extrapolate (extend the graph along its current trajectory) to find the answer.

22. LPChem1415 Mass & Volume: Penny Lab  OR I can solve using the equation of the line!  mass(g) = 7.7 (g/mL) * Volume (mL)  If the volume is 20.0 mL, the equation looks like this:  mass (g) = 7.7 g/mL * 20.0 mL  7.7*20.0 = 154  (g/mL) * mL = g  So 154 g. (150 g, since I only have 2 sig figs.)

23. LPChem1415 Mass & Volume: Penny Lab  Since my y-intercept was zero, I can also use the density from the equation (7.7g/mL) as a conversion factor.  A conversion factor is a fraction that has a value of one, but different numbers in the numerator and denominator (due to different units)  12in/ft means 12inches per 1 foot  It has a VALUE of 1 (which means multiplying by it doesn’t change the value of a measurement)  But 12 and 1 are different numbers… because inches and feet are different units.

24. LPChem1415 Mass & Volume: Penny Lab  Any number with divided units is actually a conversion factor between the units.  7.7 g/mL means  7.7 g (of copper) = 1.0 mL (of copper) 7.7 g/1.0 mL has a value of 1 (for copper) 1.0 mL/7.7g also has a value of 1