Measuring Density
Per.:
Name:
Date:
Predictions and Pre-lab: For all explanations, write in complete sentences.
For questions 1-2, you are to predict, without looking up actual values, densities, etc.
1. Make an educated guess which of the following substances do you think modern pennies
are primarily made out of: zinc, copper, aluminum, lead, or water:
prediction (not
H2O); Why do you think that? Your reasoning
2. Make an educated guess and rank what you think the densities of zinc, copper, aluminum,
lead, and water will be the starting at the lowest density (1) and going to the highest density (7).
sub 5
3
What is/are the metric unit(s) of density we’ll use in this class? g/mL or g/cm
1 (least):
3.
sub 1
; 2:
sub 2
; 3:
sub 3
; 4:
sub 4
; 5 (most):
4. What is the conceptual definition of density (the definition you can use to conceptually
understand density)?
How much “stuff” (or matter) there is in a given amount
of space.
5. If an object’s volume stays about the same, but its mass increases (like loading a car full of
supplies), what will happen to the object’s density? Explain using the conceptual definition.
You’ll have more stuff packed into the same space, so
the density will increase (it’s more densely packed).
6. Most materials expand in volume while heated, and contract in volume while cooled (but they
keep the same mass). Thus, when heated, the density of most materials
and when cooled, the density of most materials
conceptual definition.
increase
decrease
;
Explain using the
When heated the space increases, so there’s the same amount of
stuff packed into a larger space, so it’s less densely packed.
When cooled, the space decreases so the same amount of stuff is
packed into less space, and hence more densely packed.
7. What is the density of an object with a mass of 20. g and a volume of 15 mL? Show your work,
let your units be your key to solving!
20.𝑔
15 𝑚𝐿
= 1.333333 g/mL = 1.3 g/mL (2 sig figs)
8. An object has a mass of 650.2g and a density of 1.45g/mL, what is the object’s volume? Show
your work using unit canceling method.
650.2 𝑔
1
·
1 𝑚𝐿
1.45 𝑔
= 448.4138 mL = 448 mL (3 sig figs)
9. An object has a volume of 20.2mL and a density of 2.4g/mL, what is the object’s mass? Show
your work using the unit canceling method.
20.2 𝑚𝐿
10.
1
·
2.4 𝑔
1 𝑚𝐿
= 48.48 g = 48 g (2 sig figs)
A way of describing where people live is using “population density” or number of people
living in a certain area. How is this similar to density in the science?
It’s very similar, density in science in how much stuff there is
in a certain space, so instead of stuff per space the pop. density
is people per area (hard to do volume without stacking people).
Data:
Find the mass (to the precision of 1/100th of a gram), volume (to the nearest 1/10th of a mL: so, if
it’s exactly 13 mL, write it as 13.0mL), and density of each of the following substances:
Density (show work and express to correct
Sample
Mass (with units) Volume (show work and units!)
significant figures!)
3
3
Zinc
61.07 g
Aluminum 39.72 g
Copper
60.32 g
Lead
116.33 g
(show work for water
mass here):
66.15 g – 24.19g
Water
= 41.96 g
37.3ml-28.6ml=8.7ml
40.2ml-25.7ml=14.5ml
30.8ml-24.0ml=6.8ml
83.3ml-72.9ml=10.4ml
no work to show here for water volume
42.4 ml
61.07 g/8.7 cm =7.0 g/cm
39.72 g/14.5 cm3=2.74 g/cm3
60.32 g/6.8 cm3=8.9 g/cm3
116.33 g/10.4 cm3=11.2 g/cm3
41.96 g/42.4 ml = 0.990g/ml
Find the mass, volume and density of (again measure to the correct level of precision, use the
50mL graduated cylinder and start with about 20 mL):
Pennies
Mass
Volume (show work!)
Density (show work and express to correct
significant figures!)
3
3
5 pennies
10 pennies
20 pennies
12.54g
25.08g
50.21g
19.4ml–17.5m=1.9ml
21.0ml–17.5m=3.5ml
24.7ml–17.5m=7.2ml
12.54 g/1.9 cm = 6.6 g/cm
25.08 g/3.5 cm3= 7.2 g/cm3
50.21 g/7.2 cm3= 7.0 g/cm3
Conclusions:
1. Which measurement likely has more error to it, the mass measurement or the volume
measurement?
Volume
Why is that? (Hint, think about where we have to
estimate and in which case and in which case(s) do we have more significant figures?)
For volume, we had to estimate between mL marks (could easily be ±
0.3mL) and vol. only had 2-3 sig. fig., the mass had 4-5 sig figs and was
estimated by the scale to the nearest 0.01g
2.
Which density calculation is likely the most accurate (5, 10, 20 pennies)? Why is that (think
about how being off by the same amount in each case would affect the results)?
The 20 penny data, because a small error in volume measurement
leads to a lower error (0.1 ml out of 7.2mL isn’t as big of a deal as
0.1ml out of 1.9ml)
3.
Look at the masses of the pennies each time you doubled the number of pennies (from 5 to 10
and 10 to 20), divide the mass of the larger amount of pennies by the smaller amount of
pennies to see a relationship (show work):
5 to 10
10 to 20
25.08 𝑔
12.54 𝑔
50.21 𝑔
= 2.000
25.08 𝑔
= 2.002
Approximately what happened to the masses each time? (Did the masses half, double, quadruple,
doubled Why does that make sense?
Since there are twice as many pennies, assuming all
pennies have the same mass, the mass should be about
twice as much
stay about the same, or was there no relationship?)
4.
Look at the volumes of the pennies each time you doubled the number of pennies (from 5 to 10
and 10 to 20), divide the volume of the larger amount of pennies by the smaller amount of
pennies to see a relationship (show work):
5 to 10
10 to 20
3.5 𝑚𝐿
1.9 𝑚𝐿
= 1.8
7.2 𝑚𝐿
3.5 𝑚𝐿
= 2.1
Approximately what happened to the volume each time? (Did the volume half, double, quadruple,
doubled Why does that make sense?
Each penny has about the same volume, so when the
number of pennies is doubled, the volume doubles
stay about the same, or was there no relationship?)
5.
Look at the densities of the pennies each time you doubled the number of pennies (from 5 to 10
and 10 to 20), divide the density of the larger amount of pennies by the smaller amount of
pennies to see a relationship (show work):
5 to 10
10 to 20
𝑔
𝑚𝑙
𝑔
6.6
𝑚𝑙
7.2
= 1.1
𝑔
𝑚𝑙
𝑔
7.2
𝑚𝑙
7.0
= 1.0
Approximately what happened to the density each time? (Did the density half, double, quadruple,
stay about the same, or was there no relationship?)
sense?
stayed same Why does that make
Both the mass and volume doubled, so we have twice as
much stuff, packed into twice as much space, so there is
no change in how packed they are. Each penny has the
same composition, so it should have the same density.
6.
Look at the density values from the data and results section. Compare those densities with the
density of the pennies you said would be most accurate. Based on these observations, which of
Zinc
these materials are pennies primarily made out of?
Why are you able to make
this conclusion, and how does this compare to your prediction in number 1? (write in complete
sentences)
The density of a modern penny is closest to that of zinc (7.0 g/cm3
is closer to 7.0 g/cm3 than to Al: 2.74 g/cm3, Cu: 8.9 g/cm3, or to
Pb: 11.2 g/cm3). Compare to pre-lab #1.
7.
Several of another coin from a different country have a total mass of 13.24g and a total volume
of 4.9mL. What is this coin likely made of? Explain.
13.24 𝑔
= 2.7 g/mL = 2.7 g/cm3, so the coin is likely made
4.9 𝑚𝐿
from Aluminum because, according to our data, Al has a
density of 2.74 g/cm3.
11. Rank the zinc, aluminum, copper, lead, and water starting at the lowest density (1) and going to
the highest density (5).
1 (least):
Water; 2: Aluminum; 3: Zinc ; 4: Copper; 5 (most): Lead
How does this compare to your prediction in pre-lab question 2?
Compare to pre-lab #2.
12. Based on your density values, why are airplanes often constructed out of aluminum instead of
another metal like steel or copper, make sure to include ideas of density in your explanation?
Aluminum is far less dense than many other metals. This
means the aircraft can be constructed with less mass for the
same volume of metal used.
13. Based on your density values, why is lead often used as “sinkers” in fishing, make sure to
include ideas of density in your explanation?
Lead is used as a sinker because it is very dense, so a
smaller object can be used to weigh down the line (less
distracting to fish) but still be fairly massive.
14. Any constant ratio can be written as a conversion factor (if an object is constantly moving at
10m/s, we can say 10m = 1s for that object, because there is 10m travelled for every 1s of
time). Given this, write what you determined to be the most accurate density value as three
conversion factors (#pennies = mass of pennies, #pennies = vol of pennies; and mass of pennies
= vol of pennies):
20 pennies = 50.21 g pennies; 20 pennies = 7.2 cm3 pennies;
50.21 g pennies = 7.2 cm3 pennies
15.
Using your most accurate density value, calculate the volume of 155g of pennies (show
work using the unit canceling method and the conversion factor from concl. #14):
155 𝑔 𝑝𝑒𝑛. 1 𝑐𝑚3 𝑝𝑒𝑛.
·
1
16.
7.0 𝑔 𝑝𝑒𝑛.
= 22.1429 cm3 pen. = 22 cm3 pen. (2 sig fig)
Using your most accurate density value, calculate the mass of 15.0 mL of pennies (show
work using the unit canceling method and the conversion factor from concl. #14):
15.0 𝑚𝐿 𝑝𝑒𝑛. 7.0 𝑔 𝑝𝑒𝑛.
·
1
17.
1 𝑚𝐿 𝑝𝑒𝑛.
Using the data you found in what you determined to be the most accurate density data:
a. Find the vol. and mass of a single penny. Show your work using the unit canceling
method, and conversion factors from concl. #14 (start with 1 penny and go to g or mL).
i. Volume:
1 𝑝𝑒𝑛. 7.2 𝑚𝐿 𝑝𝑒𝑛.
·
1
= 105 g pen. = 110 g pen. (2 sig fig)
20 𝑝𝑒𝑛.
= 0.36 mL pen. (2 sig fig)
ii. Mass:
1 𝑝𝑒𝑛. 50.21 𝑔 𝑝𝑒𝑛.
·
1
20 𝑝𝑒𝑛.
= 2.5105 g pen. = 2.511 g pen. (4 sig fig)
b. Calculate how many pennies could fill a 120.0 m3 room (1m3 = 1,000,000cm3; 1 mL = 1
cm3), assuming there was no space between the pennies. Show your work using the
unit canceling method, and using conversion factors from concl. #14. Express in
scientific notation with correct significant figures.
3
120.0 𝑚 1,000,000 𝑐𝑚3 1 𝑚𝐿 20 𝑝𝑒𝑛.
·
·
·
= 333,333,333.3 pennies =
1 𝑚3
1 𝑐𝑚3 7.2 𝑚𝐿
3.3x108 pennies (2 sig fig)
1
c. How much mass would the number of pennies in part b have? Show your work using
the unit canceling factor method, using conversion factors from concl. #14. Express in
scientific notation with correct significant figures.
Keeping all digits in calculator until the very end:
3.333x108 𝑝𝑒𝑛. 50.21 𝑔 𝑝𝑒𝑛.
1
·
20 𝑝𝑒𝑛.
= 8.368x108 g = 8.4x108 g (2 sig fig)
Starting with the rounded number (not advised, mult rounding errors possible)
3.3x108 𝑝𝑒𝑛𝑛𝑖𝑒𝑠 50.21 𝑔 𝑝𝑒𝑛.
1
18.
·
20 𝑝𝑒𝑛𝑛𝑖𝑒𝑠
= 8.285x108 g= 8.3x108 g (2 sig fig)
What are some sources of error in this experiment? (write in complete sentences)
At least 2 sources of error
Hard to estimate to the nearest 1/10th of a ml.
Mass not zeroed properly
Water splashed out of cylinder when adding materials