E-9 Density – Practice Calculations
Density is a ratio of a substance’s mass to it’s volume and is a derived unit calculated by
dividing an object’s mass by its volume.
Density is a physical property.
Density is an intensive property – meaning it does not change depending on the amount of
the substance present.
Density can be used to identify substances and determine whether they are pure.
Density = Mass / Volume
Units are usually g / mL or g / cm3
Density of pure water is 1.00 g/mL
Calculate the densities of the following:
1. An Ancient Greek tyrant king has a new golden crown made for him self. After a few
months he starts to think that he may have been cheated and that the crown might not
be pure gold, but an mixture of gold and silver. He commands Archimedes, the famous
mathematician, to find out whether the crown is pure gold or not. Archimedes knows the
density of pure gold to be 19.3 g / cm3. He also knows that silver is less dense at
10.49 g / cm3.
Problem: the crown is an odd shape and the volume can’t be calculated by any
mathematical equation.
Problem: Archimedes can’t melt down the crown to find the volume because it would
destroy the crown. How can he solve this problem?????
As Archimedes is taking a bath and thinking about this problem he notices that the water
in the tub rises as he sits down in his bath. He yells out “Eureka!” “I have it!”.
Using the “water displacement method” Archimedes finds the volume of the crown to be
126. 7 mL. The mass of the crown is found to be 2.45 kg (a very heavy crown!)
Is the king’s crown pure gold or a fake? Solve by finding the density.
2. A rock has a mass of 23.25 grams. Water displacement is used to find the volume to be
4. 98 mL. Calculate the density of the rock.
3. A piece of white oak wood has the following dimensions. L = 28.45 cm, W = 12.20 cm, H =
9.80 cm. The mass of the block is 2517.10 g. Calculate the density of the white oak.
4. Would you expect the piece of white oak in question 3 to float? Why?
5. 3 different cubes of metal are found in the storeroom in containers labeled “pure
element”, but the element’s name is rubbed away. The chemistry teachers want to know
what the elements are because depending on the metal, the cubes could be worth a lot of
money.
All three cubes’ sides are 2.50 cm each.
Cube 1’s mass is 329.5 g.
Identity?___________
Cube 2’s mass is 187.8 g.
Identity?___________
Cube 3’s mass is 140.3 g.
Identity?___________
Which cube is most valuable? Least valuable?
Elements
Palladium
Platinum
Nickel
Gold
Tin
Magnesium
Silver
Aluminum
Densities (g/cm3)
12.023
21.09
8.908
19.3
7.31
1.738
10.49
2.7
Cost
$654.55/oz.
$919.25/oz.
$4.46/lb.
$1131.96/oz.
$6.99/lb
$1.75/kg
$14.71/oz.
$0.70/lb.
6. A new synthetic motor oil is being designed by the Mobil Oil Company. It is a known fact
that the density and viscosity of motor oil changes as the temperature of the oil changes.
Because engines become very hot when running the density can change quite a bit. A chemist
wants to figure out the density of the oil at two different temperatures. She decides to
measure the density of the oil at 0C and 100C.
She measures exactly 10.00 mL of the oil in a small graduated cylinder in each test. The
mass of the graduated cylinder when empty is 26.10g.
The mass of the oil and the graduated cylinder at 0C is 35.03 g.
The mass of the oil and the graduated cylinder at 100C is 34.39 g.
Find the densities of the oil at the two temperatures. How much does the density change
over the 100 degree Celsius difference?