3.2. Unit Conversions http://www.ck12.org
With gases, a balloon filled with helium floats because helium is less dense than air. However, a balloon filled with
carbon dioxide sinks because carbon dioxide is denser than air.
Sample Problem 3.5: Density Calculations
An 18.2 g sample of zinc metal has a volume of 2.55 cm^3. Calculate the density of zinc.
Step 1: List the known quantities and plan the problem.
Known
- mass = 18.2 g
- volume = 2.55 cm^3
Unknown
- density =? g/cm^3
Use the equation for density, D = m/V, to solve the problem.
Step 2: Calculate.
D=
m
V=
18 .2 g
2 .55 cm^3= 7 .14 g/cm^3Step 3: Think about your result.
If 1 cm^3 of zinc has a mass of about 7 grams, then a sample that is approximately 2.5 cm^3 will have a mass between
2 and 3 times its density, which is consistent with the values given in this problem. Additionally, metals are expected
to have a density that is greater than that of water, and zinc’s density falls within the range of the other metals listed
above (Table3.4).
Since density values are known for many substances, density can be used to determine an unknown mass or an
unknown volume. Dimensional analysis will be used to ensure that units cancel appropriately.
Sample Problem 3.6: Using Density to Determine Mass and Volume
- What is the mass of 2.49 cm^3 of aluminum?
- What is the volume of 50.0 g of aluminum?
Step 1: List the known quantities and plan the problem.
Known
- density = 2.70 g/cm^3
- volume = 2.49 cm^3
- mass = 50.0 g
Unknown
- mass =? g
- volume =? cm^3
Use the equation for density, D = m/V, and dimensional analysis to solve each problem.
Step 2: Calculate.
- 2.49 cm^3 ×
2 .70 g
1 cm^3
= 6 .72 g