𝑚𝑎𝑠𝑠
Density Problems
Memory aid: “I heart density!” means D = 𝑣𝑜𝑙𝑢𝑚𝑒
Show work: formula; substitutions; solve–– Round appropriately.
Include units during the substitution step as well as within your final answer!
1. What is the density of a piece of foam with a mass of 3.57 g and a volume of 10.89 mL?
𝑚𝑎𝑠𝑠
3.57 𝑔
𝐷=
𝐷
=
= 0.328 𝑔/𝑚𝐿
𝑣𝑜𝑙𝑢𝑚𝑒
10.89 𝑚𝐿
2. A solid substance has a mass of 23.36 g and takes up a volume of 74.5 cm3. Calculate its density.
𝐷=
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
𝐷=
23.36 𝑔
= 0.314 𝑔/𝑐𝑚3
74.5 𝑐𝑚3
3. A piece of cement measures 3.0 cm long, 8.20 cm high, and 10.0 cm deep. It has a mass of 153 g. What is
the density of the cement?
V = L x W x H = 3.0 cm x 8.20 cm x 10.0 cm = 246 = 250 cm3
𝐷=
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
153 𝑔
= 250 𝑐𝑚3 = 0.612 = 0.61 𝑔/𝑐𝑚3=
4. A rectangular eraser has a mass of 50.0 g and a volume of 200. mL. What is its density?
𝑚𝑎𝑠𝑠
50.0 𝑔
𝐷=
𝐷
=
= 0.250 𝑔/𝑚𝐿
𝑣𝑜𝑙𝑢𝑚𝑒
200. 𝑚𝐿
5. The eraser in question #4 is cut exactly in half. What is its density now?
𝑚𝑎𝑠𝑠
25.0 𝑔
𝐷=
𝐷=
= 0.250 𝑔/𝑚𝐿
𝑣𝑜𝑙𝑢𝑚𝑒
100. 𝑚𝐿
6. It is cut exactly in half once more. What is its density now?
𝑚𝑎𝑠𝑠
12.5 𝑔
𝐷=
𝐷=
= 0.250 𝑔/𝑚𝐿
𝑣𝑜𝑙𝑢𝑚𝑒
50.0 𝑚𝐿
7. From your answers to questions #4, 5, and 6: Is it true that density depends on the the amount of a
substance? Or, is it true that density is independent of the amount of substance? Explain why you chose this
answer.
Density is independent of the amount. When the amount changes….Density does not change.
8. A property that depends on the amount of a substance is called an “extensive property”. [Memory aid – An
extensive property depends on the “extent” (or how much) there is of something. Is density an extensive
property? Explain. Answer in a complete sentence please.
No, density is NOT and extensive property – because density does NOT depend on the amount of material.
9. A property that does not depend on amount, but instead depends on the composition of a material, is called
an “intensive” property. Is density an intensive property? Explain your answer.
Density is an intensive property – because density depends on the composition (what the material is made of).
10. In order to answer questions # 4, 5, and 6 correctly, you needed to understand that as you cut
something in half, both the mass and the volume would go down by ½. When two properties both decrease (or
both increase) linearly, you could graph the data and see a straight line. Would it make sense to call the straight
line relationship between mass and a “direct proportion” or an “indirect (inverse) proportion”? (pick one)
Explain your answer.
It would make sense to call a straight line relationship a “direct proportion” rather than an “indirect (inverse)
proportion” because I know from math class that an inverse relationship means that as one variable goes down,
the other goes up.
11. The density of liquid “Substance A” is 1.97 g / cm3. The density of liquid “Substance B” is 1.89 g / cm3.
Which substance will sink below the other? (A or B)
Why? Substance A will sink below Substance B because Substance A’s density is greater.
Show work: formula; substitutions; solve–– Round appropriately.
Include units during the substitution step as well as within your final answer!
12. The density of silver is 10.5 g / mL. What is the mass of a 3.50 mL bracelet made of silver?
𝐷=
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
so Mass = Density x Volume Mass = (10.5 g / mL) x 3.50 mL = 36.75 = 36.8 g
13. 450. grams of gasoline is spilled into a puddle of water, and the gasoline floats on top of the water. If the
density of gasoline is 0.665 g / mL, what volume of gasoline is spilled?
𝐷=
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
𝑚𝑎𝑠𝑠
so Volume =𝑑𝑒𝑛𝑠𝑖𝑡𝑦
450.𝑔
Volume = 0.665 𝑔/𝑚𝐿 = 676.69 = 677 mL
14. Calculate the mass of 250.0 mL of a chemical whose density is 0.8765 g / mL.
𝐷=
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
so
Mass = Density x Volume
0.8765 𝑔
=
𝑚𝐿
x 250.0 mL = 219.125 = 219.1 g
OR: cross multiply after substituting:
𝐷𝑒𝑛𝑠𝑖𝑡𝑦
𝑚𝑎𝑠𝑠
=
0.8765
becomes
𝑣𝑜𝑙𝑢𝑚𝑒
1
𝑥
= 250.0
𝑡ℎ𝑒𝑛: 𝑥 = (0.8765)(250.0) = 219.1 𝑔
15. What is the mass in milligrams of an ice cube measuring 5.80 cm by 5.80 cm by 5.80 cm, if its density is
0.917 g / mL?
Complicated question (but, you are supposed to know to use the internet to find “metric unit conversions”).
Hint: 1 mL = 1 cm3.
Step 1:
V=LxWxH=
5.80 cm x 5.80 cm x 5.80 cm =
195.112 = 195 cm3 = 195 mL
Step 2:
cross multiply after substituting:
𝐷 =
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
becomes
0.917
1
𝑥
= 195
𝑡ℎ𝑒𝑛: 𝑥 = (0.917)(195) = 178.815 𝑔 = 179 𝑔
𝑆𝑡𝑒𝑝 3:
1,000 𝑚𝑔
179 𝑔 𝑥 (
1𝑔
) = 179,000 𝑚𝑔
16. What volume would be occupied by 0.01781 kg of Lucky Charms it their density of 0.004510 kg / mL?
Let’s try using dimensional analysis for this one. (otherwise, solve similar to Q # 13).
Step #1: Start with the “one measurement given:
Start with
Hint: density is a CALCULATION!
0.01781 kg
Step #2: multiply by a factor (a fraction with two different units, one in the numerator and one in the
denominator) SO THAT the original measurement’s unit cancels.
Hint: density is a FACTOR:
0.01781 𝑘𝑔
𝑥
1 𝑚𝐿
0.004510 𝑘𝑔
=
“1 volume unit” = the given density
1 mL = 0.004510 kg
3.949 mL
Simple method!
17. The density of air at room temperature is 0.001200 g / cc.
What would be the volume of 1.000 grams of air?
Dimensional analysis method:
1. Start with the measurement.
2. Multiple by a factor where the measurement unit cancels out.
3. Make a factor with 1 “volume unit” = the density given
1.000 𝑔
𝑥
1 𝑐𝑐
=
0.001200 𝑔
833.3 cc
Simple method!
18. Using the density of air given above, what would be the mass of 1,000. cc of air at room temperature?
Dimensional analysis method:
1. Start with the measurement.
2. Multiple by a factor where the measurement unit cancels out.
3. Make a factor with 1 “volume unit” = the density given
1,000. 𝑐𝑐
𝑥
0.001200 𝑔
1 𝑐𝑐
=
1.200 g
Simple method!
19. What is the density of aluminum, if 27.03 grams of aluminum displaces a volume of water equivalent to
10.00 mL?
𝐷=
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
=
27.03 𝑔𝑟𝑎𝑚𝑠
10.00 𝑚𝐿
= 2.703 g / mL
20. Several different amounts of aluminum are used to construct a density graph with the mass in grams plotted
along the y–axis and the volume in milliliters plotted along the x–axis. Using your answer to question # 19,
what should the slope of this graph be?
2.703 g / mL
21. Should the slope of a density graph (with mass plotted on the y-axis and volume plotted on the x-axis) be
positive or negative?
positive
22. What should the y-intercept of a density graph equal?
Well, at zero volume, there should be zero mass!
So, y-intercept = 0
23. When a lava lamp is turned on, the “lava” is exposed to heat from a light bulb at the base of the lamp. The
lava then rises up through the surrounding matrix. We know that mass is always conserved; but, volume is not
necessarily conserved. What must be happening to the volume of the lava in order for it to float upward?
Pick one –– “volume must increase”, “volume must decrease”, or “volume must be conserved (stay the same)”.
Anything that “floats up” (rises up) does so because it has a LESSER DENSITY than its surroundings. If mass
can not change (which it doesn’t), the question is actually asking you what does the “V” part of the formula
does when the “D” part decreases?
The volume, being in the denominator, needs to increase in order for the density to decrease!
If it doesn’t make sense, plug in “easy” numbers and check it out:
𝐷=
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
10 =
40
4
Now, decrease the “D”, keep the mass at 40, and figure out what the “V” has to do.
5=
40
?
? must equal 8. The V used to be 4; now it is 8. Therefore the V has increased when the D decreased.
24. What must happen to the volume of the blob of lava as its sink back down again? Full sentence please.
Since the lava is sinking, its density is increasing. From a similar type of calculation, you can verify that the
volume of the lava must decrease when the density of the lava increases.
10 =
40
4
40 =
40
1
The V used to be 4; now it is 1. Therefore the V has increased when the D increased.
25. There is a “density column” at the front of the classroom. Vegetable oil was poured on top of water
(colored with food dye for better visibility). When an ice cube is placed on top of the vegetable oil it floats; but
as the ice cube melts, droplets of water can be observed to sink down through the oil, and merge in with the
colored water. Do ice cubes have a higher density or a lower density than liquid water? Explain.
Ice cubes have a lower density than liquid water because ice floats above oil, while water stays below oil.