LPChem1415 Mass & Volume: Penny Lab The purpose of this lab is to graphically determine the...

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.

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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.

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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.

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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.)

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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 Vi.

3) I added the pennies I’d already weighed to the cylinder, then recorded the new volume as Vf.

4) I dumped everything out, dried the pennies, then repeated these steps with 10, 15, 20, 25, and 30 pennies.

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My data table might look like this:

# pennies mass Vi Vf

(g) (mL) (mL)

5 12.5 51.2 52.7

10 24.9 50.3 53.4

15 37.4 49.9 54.4

20 49.9 52.0 58.0

25 62.5 51.1 59.2

30 74.9 51.7 61.9

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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 ; Vf-Vi = Vpennies)

Since finding the volume of the pennies requires math, my Vpennies values will go in the Evaluation of Data section.

Vpennies

(Vf - Vi)

(mL)1.53.14.56.08.1

10.2

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Mass & Volume: Penny LabThe 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.

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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.)

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My data table might look like this:

Trial # massadded Vf

(g) (mL)

0 0 51.2

1 12.5 52.7

2 12.4 54.3

3 12.5 55.7

4 12.5 57.2

5 12.6 59.3

6 12.4 61.4

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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 Vpennies and mpennies for six data points.

To calculate the volumes, I’ll subtract out the same initial volume every time (Vf from trial 0, when only water was in the graduated cylinder).

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To calculate the volumes, I’ll subtract out the same initial volume every time (Vf from trial 0, when only water was in the graduated cylinder).

(Vf - 51.2) Vpennies

(mL) (mL)

52.7-51.2 1.5

54.3-51.2 3.1

55.7-51.2 4.5

57.2-51.2 6.0

59.3-51.2 8.1

61.4-51.2 10.2

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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.

massTOT

(g)

12.5

24.9

37.4

49.9

62.5

74.9

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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!

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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.

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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 Vpennies

measurements only had two.

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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.)

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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:

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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.

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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.

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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.)

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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.

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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

LPChem1415 Mass & Volume: Penny Lab The purpose of this lab is to graphically determine the...

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