Chemistry Measurement Density
They are related by the the density triangle.
d = #m/V#
m = d×V
V = #m/d#
DENSITY
Density is defined as mass per unit volume.
d = #m/V#
Example:
A brick of salt measuring 10.0 cm x 10.0 cm x 2.00 cm has a mass of 433 g. What is its density?
Step 1: Calculate the volume
V = lwh = 10.0 cm × 10.0 cm × 2.00 cm = 200 cm³
Step 2: Calculate the density
d = #m/V# = #(433 g)/(200 cm³)# = 2.16 g/cm³
MASS
d = #m/V#
We can rearrange this to get the expression for the mass.
m = d×V
Example:
If 500 mL of a liquid has a density of 1.11 g/mL, what is its mass?
m = d×V = 500 mL × #(1.11 g)/(1 mL)# = 555 g
VOLUME
d = #m/V#
We can rearrange this to get the expression for the volume.
V = #m/d#
Example:
What is the volume of a bar of gold that has a mass of 14.83 kg. The density of gold is 19.32 g/cm³.
Step 1: Convert kilograms to grams.
14.83 kg × #(1000 g)/(1 kg)# = 14 830 g
Step 2: Calculate the volume.
V = #m/d# = 14 830 g × #(1 cm³)/(19.32 g)# = 767.6 cm³
You can identify an unknown substance by measuring its density and comparing your result to a list of known densities.
Density = mass/volume. Assume that you have to identify an unknown metal. You can determine the mass of the metal on a scale. You can determine the volume by dropping the object into a graduated cylinder containing a known volume of water and measuring the new volume. You divide the mass by the volume and compare the density to a list of known densities.
EXAMPLE
A metal bolt with a mass of 99.7 g is dropped into a graduated cylinder containing 50.0 cm³ of water. The new volume reads
72.1 cm³. Identify the metal.
Solution
V = 72.1 cm³ - 50.0 cm³ = 22.1 cm³
D = #m/V = (99.7 g)/(22.1 cm³)# = 4.51 g/cm³
Now you compare your density with a list obtained from your instructor or from an on-line source such as
//sites.google.com/site/chempendix/densities-of-pure-metals
What metal was your bolt made of?
Density measures the compactness in molecular arrangement in any substance which determines how heavy or light any substance is.
The density formula is #"density"# = #"mass"/"volume"#. Mass units are most commonly grams or kilograms. Volume units are most commonly cubic centimeters (#"cm"^3#), cubic meters (#"m"^3#), or millileters (mL).
Examples of density include the following:
The density of water at #"4"^"o""C"# can be written as #"1.000g/cm"^3#, #"1.000g/mL"#, #"1000Kg/m"^3#, and #"1.000kg/L"#.
The density of iron at #"0"^"o""C"# is #"7.874g/cm"^3# and #"7874kg/m"^3#.
The density of sodium metal at #"0"^"o""C"# is #"0.968g/cm"^3#, and #"968kg/m"^3#.
In order to determine the density of a substance, you need to know its mass and its volume. Then divide its mass by its volume, remembering to divide the units as well.
Example
A #"1.26cm"^3# sample of the element mercury has a mass of #"17.05g"#. What is it's density?
Solution
#"density"# = #"mass"/"volume"# = #"17.05g"/"1.26cm"^3# =
#"13.5g/cm"^3"#
Here is a video example of how to solve a density problem.