Density Practice Problems
Use the GRASS method to solve each of the following questions on a separate page.
Part 1 – Basic
1) Wood has a density of 5.53g/cm3. What must the volume of 33.3 g of wood?
2) Copper has a density of 4.44 g/cm3. What is the volume of 2.78mg of copper?
3) Sodium has a density of 1.95 g/cm3. What is the volume of 56.2kg of sodium?
4) What is the density of a piece of iron that has a mass of 59.8g and a volume of 2.08 cm 3?
5) What is the density of mercury that has a mass of 39.6 mg and a volume of 0.00900 cm3?
6) Granite has a density of 4.67 g/cm3. What is the mass of 46.8 cm3 of granite?
7) Corn oil has density of 6.89 g/cm3. What is the mass of 34.0 cm3 of corn oil?
8) A pencil has a density of 0.875 g/mL. It has a mass of 3.5 g. What is the volume?
Part 2 – More Thinking
1) A bar of soap is 12 cm tall, 6 cm wide, and 10 cm long. It has a mass of 0.415 kg. What is the density
of the bar of soap.
2) A flask that weighs 345.8 g is filled with 225 mL of carbon tetrachloride. The weight of the flask and
carbon tetrachloride is found to be 703.55 g. From this information, calculate the density of carbon
tetrachloride.
3) 28.5 g of iron shot is added to a graduated cylinder containing 45.50 mL of water. The water level
rises to the 49.10 mL mark, From this information, calculate the density of iron.
4) A piece of PVC plumbing pipe displaces 60 mL when placed into a container of water. If the pipe has
a mass of 78 g, what is the density of PVC?
5) A machine shop worker records the mass of an aluminum cube as 176 g. If one side of the cube
measures 4 cm, what is the density of the aluminum?
Part 3 - Lab Scenario Problem Set
Imagine you are conducting an experiment as described below. On a separate page, use the GRASS
method to perform each calculation along the way as described.
The graduated cylinder used in this experiment has mass of 143.5g.
1) 12mL of isopropyl alcohol is added to the cylinder. The combined mass becomes 152.6g. What is
the density of isopropyl alcohol?
2) 15mL of n-Butyl alcohol is added to the cylinder. The combined mass becomes 155.4g. What is the
denisty of n-Butyl alcohol?
3) 8 mL of ethylene glycol is added to the cylinder. The combined mass becomes 152.1g. What is the
density of ethylene glycol?
4) All three samples are placed in the cylinder at the same time. From top to bottom, assuming that
each of these three substances would not mix, what will be the order of the chemicals? Sketch a
labeled diagram of the cylinder with each substance.
(in reality these three substance would mix, for practice and learning, let us assume they do not)
5) A plastic bead with a known volume of 0.5cm3 and a mass of 0.45g is placed into the cylinder with
the three samples. What do you expect to observe?
Challenge Question
6) A second plastic bead with a mass of 0.4g and a diameter of 0.6cm is placed into the cylinder with
the three samples. What do you expect to observe?
Hint: you can calculate the volume of a sphere using V=(4/3)πr3
Part 4 – Generating and Solving Practice Problems
Use Appendix A (pg. 568) of your textbook to generate 3 questions about density. Each question should
be about real substances with accurate densities. Each question must ask to solve for a different variable
(either mass, volume or density).
SOLUTION SET
Part 1 – Basic
1) Wood has a density of 5.53g/cm3. What must the volume of 33.3 g of wood?
D = 5.53g/cm3
m = 33.3 g
V = m/D = 33.3 g / 5.53 g/cm3 = 6.02 cm3
2) Copper has a density of 4.44 g/cm3. What is the volume of 2.78mg of copper?
D = 4.44 g/cm3
m = 2.78 mg = 0.00278 g
V = m/D = 0.00278 g / 4.44 g/cm3 = 6.26 x 10-4 cm3
3) Sodium has a density of 1.95 g/cm3. What is the volume of 56.2kg of sodium?
D = 1.95 g/cm3
m = 56.2 kg = 56200 g
V = m/D = 56200 g / 1.95 g/cm3 = 2.88 x 104 cm3
4) What is the density of a piece of iron that has a mass of 59.8g and a volume of 2.08 cm 3?
m = 59.8 g
V = 2.08 cm3
D= m/V = 59.8 g / 2.08 cm3 = 28.8 g/cm3
5) What is the density of mercury that has a mass of 39.6 mg and a volume of 0.00900 cm3?
m = 39.6 mg = 0.0396 g
V = 0.0900 cm3
D= m/V = 0.0396 g / 0.00900 cm3 = 4.40 g/cm3
6) Granite has a density of 4.67 g/cm3. What is the mass of 46.8 cm3 of granite?
D = 4.67 g/ cm3
V = 46.8 cm3
m= DV = (4.67 g / cm3) (46.8 cm3) = 219 g
7) Corn oil has density of 6.89 g/cm3. What is the mass of 34.0 cm3 of corn oil?
D = 6.89 g/ cm3
V = 34.0 cm3
m= DV = (6.89g / cm3) (34.0 cm3) = 234 g
8) A pencil has a density of 0.875 g/mL. It has a mass of 3.5 g. What is the volume?
D = 0.875 g/ mL
m = 3.5 g
V= m/D = 3.5 g / 0.875 g / cm3 = 4.0 mL
Part 2 – More Thinking
1) A bar of soap is 12 cm tall, 6 cm wide, and 10 cm long. It has a mass of 0.415 kg. What is the density
of the bar of soap.
V = 12cm x 6cm x 10cm = 720cm3 D = m/V = (415g)/(720cm3) = 0.576g/cm3
2) A flask that weighs 345.8 g is filled with 225 mL of carbon tetrachloride. The weight of the flask and
carbon tetrachloride is found to be 703.55 g. From this information, calculate the density of carbon
tetrachloride.
m = 703.55g - 345.8g = 357.75g D = m/V = (357.75g/225mL) = 1.59 g/mL
3) 28.5 g of iron shot is added to a graduated cylinder containing 45.50 mL of water. The water level
rises to the 49.10 mL mark, from this information, calculate the density of iron.
V = 49.10 mL – 45.50 mL = 3.60mL D = m/V = 28.5g/3.60mL = 7.92 g/mL
4) A piece of PVC plumbing pipe displaces 60 mL when placed into a container of water. If the pipe has
a mass of 78 g, what is the density of PVC?
D = m/V = 78g /60mL = 1.3g/mL
5) A machine shop worker records the mass of an aluminum cube as 176 g. If one side of the cube
measures 4 cm, what is the density of the aluminum?
V = (4cm)3 = 64cm3 D = m/V = 176g / 64cm3 = 2.75g/cm3
Part 3 - Lab Scenario Problem Set
Imagine you are conducting an experiment as described below. On a separate page, use the GRASS
method to perform each calculation along the way as described.
1) 12mL of isopropyl alcohol is added to the cylinder. The combined mass becomes 152.6g. What is
the density of isopropyl alcohol?
Mass of liquid = 152.6g-143.5g = 9.1g
Volume of liquid= 12mL
D=m/v = 9.1g/12mL = 0.758g/mL
2) 15mL of n-Butyl alcohol is added to the cylinder. The combined mass becomes 155.4g. What is the
denisty of n-Butyl alcohol?
Mass of liquid = 155.4g-143.5g = 11.9g
Volume of liquid= 15mL
D=m/v = 11.9g/15mL = 0.793g/mL
3) 8 mL of ethylene glycol is added to the cylinder. The combined mass becomes 152.1g. What is the
density of ethylene glycol?
Mass of liquid = 152.1g-143.5g = 8.6g
Volume of liquid= 8mL
D=m/v = 8.6g/8mL = 1.08g/mL
4) All three samples are placed in the cylinder at the same time. From top to bottom, assuming that
each of these three substances would not mix, what will be the order of the chemicals? Sketch a
labeled diagram of the cylinder with each substance.
(in reality these three substance would mix, for practice and learning, let us assume they do not)
Isopropyl alcohol, n-butyl alcohol, ethylene glycol
5) A plastic bead with a known volume of 0.5cm3 and a mass of 0.45g is placed into the cylinder with
the three samples. What do you expect to observe?
Mass = 0.45g
Volume= 0.5cm3
Density=m/v= 0.45g/0.5cm3 = 0.9g/cm3
The plastic bead would lie above the layer of ethylene glycol, but below the layer of n-butyl
alcohol
Challenge Question
6) A second plastic bead with a mass of 0.4g and a diameter of 0.6cm is placed into the cylinder with
the three samples. What do you expect to observe? (Hint: you can calculate the volume of a sphere
using V=(4/3)πr3)
Mass bead = 0.4g
Volume bead = 4/3*3.14*(0.6cm3)3 = 0.904cm3
D=m/v= 0.4g/0.904cm3= 0.442g/cm3
This bead would float on top because it is the least dense of all the substances in the cylinder.