Download density formula and problems

DENSITY
Density is a physical property that compares the amount of matter of
material in a given amount of space. Every substance has a specific
density. Therefore, density is often used to identify an unknown
substance.
To calculate the density of an object, you need to know the mass and
the volume of the object. Once these are known, density is a simple
mathematical calculation using the following formula:
mass
density 
volume
m  DV
D
m
V
V 
m
D
The SI (System International) units often used for density of solids are
kg/m3 or g/cm3. For fluids, the units used for density are kg/L or g/mL.
Note: that 1mL = 1 cm3.
Mass is the amount of matter present.
Volume is the amount of space an object takes up.
Sample Question 1
A student measures the mass of a piece of metal as 29.8g, and finds
its volume to be 2.64 mL. What is the density of this metal?
Solution
Given:
Required:
m = 29.8 g
V = 2.64 mL
D=?
m
V
Analysis:
D=
Solution:
29.8 g
D = 2.64mL
D = 11.28787878
D = 11.29 g/mL
Sentence:
(Note: always round your
answer to 2 digits after the
decimal point)
Therefore, the density of the metal is 11.29g/mL.
Sample Question 2
The density of nickel is 8.9 g/cm3. What is the volume of 500 g of
nickel?
Solution
Given:
D = 8.9 g/cm3
m = 500 g
Required:
V =?
Analysis:
V 
m
D
Solution:
V
500 g
8.9 g / cm 3
V = 56.18 cm3
Sentence:
Therefore, the volume of 500g of nickel is 56.18 cm3.
Sample Question 3
What is the mass, in kilograms, of a 5.6 m3 block of iron? Iron has a
density of 7900 kg/m3.
Solution
Given:
V = 5.6 m3
D = 7900 kg/m3
Required:
m=?
Analysis:
m = DV
Solution:
m = (7900 kg/m3) (5.6 m3)
m = 44 240 kg
Sentence:
Therefore, a 5.6 m3 block of iron has a mass of
44,240kg.
Density Practice Problems
Solve the density problems below showing all your steps.
1. A 4.0 kg object occupies 2.0 m3. What is the density of the object?
2. A graduated cylinder of mass 128 g had 25 mL of a liquid poured into it. The mass of the
graduated cylinder and its contents is 153 g. What is the density of the liquid? Use the
table of known densities to determine the liquid’s identity.
3. A) Use the table to determine the density of birch wood.
b) If a block of wood measuring 5 cm x 10 cm x 3 cm has a mass of 100 g, could it be birch
wood? Explain your reasoning.
4. A magnificent metal piece in the shape of a crown is unearthed at the excavation of an
ancient tomb. The mass of the crown is measured to be 17 800 kg and its volume is 2 m3.
What is the density of the crown? Use the density table to predict what is might be made
of.
5. An empty graduated cylinder has a mass of 82.14 g. When 25.0 mL of an unknown liquid
are poured into the cylinder and the liquid is 104.52 g. What is the density of the liquid?
6. A graduated cylinder containing 40 mL of water has a total mass of 60 g. A solid object is
carefully lowered into the graduated cylinder. The level of the water rises to 70 mL. The
total mass of the cylinder, water and object is now 95 g.
a. What is the mass of the object?
b. What is the volume of the object?
c. What is the density of the object?
7. Calculate the mass of nickel found in a block that has a volume of 50 cm3.
8. If a ring of gold has a volume of 0.84 cm3, what is the mass of the ring?
9. A room that is 5.0 m by 4.0 m by 2.5 m contains 65 kg of air. Calculate the air’s volume
and its density.
10. An object has a mass of 4500 g and its density is 8.95 g/cm3. What is its volume?
11. What volume would nitrogen gas take up if you had a mass of 5.67 g?