Density = Mass/Volume
Density is the relationship of mass to volume. The more stuff (matter) you place into a defined space (volume), the denser that object becomes.
For example, New York City is DENSELY populated because there are a lot of people in a small area. 20 people in an elevator is DENSER than 2 people in an elevator.
Take a look at the image below. The cube on the left is more dense than the cube on the right because the left cube has more matter inside it.
Density of Water
The density of water is 1 g/cm3 or 1 g/mL
Sink, Float, or Suspend?
An object will float in water if its density is less than 1g/cm3. An object will sink in water if its density is greater than 1g/cm3.
If an object is more dense than the material it is placed in then it will sink to the bottom.
If an object is less dense than the material it is placed in then it will float to the top.
If an object has equal density as the material it is placed in then it will suspend in the middle.
For example, in the Coca Cola vs. Diet Coke demonstration from class, the Diet Coke floated in the water because its density was less that 1g/cm3, (in other words, Diet Coke is less dense than water). The regular Coca Cola sank to the bottom of the water tank because its density is greater than 1g/cm3, (in other words, regular Coca Cola is more dense than water). The regular Coca Cola is denser than the Diet Coke because because it has more sugar crammed into the same size aluminum can giving it a greater density.
Example 1: If a bar of soap has a density of 1.50 g, then it will sink in water because the soap bar is more dense than the water.
Example 2: If a bar of soap has a density of 0.70 g, then it will float in water because the soap bar is less dense than the water.
To calculate an object’s density, a scientist must identify the volume and mass of the object.
To find volume…
Use the volume formula: Volume of Regular object (rectangular prism) = Length x Width x Height
Use the water displacement method: Volume of Irregular object = Ending volume – Starting volume
To find mass:
Use a triple beam balance.
One you have the volume and mass of an object, substitute the values in the density formula (D=M/V)
Solving Density Problems
Density = Mass/Volume (D=M/V)
Example: A brick has a mass of 100g and a volume of 25 cm3. What is the density of the brick?
D = 100g / 25 cm3
D = 4 g/cm3
Just like in algebra, scientists can use the density formula to solve for other variables. For example, if a scientists knows the density and volume of a sample, he ore she can easily solve for the mass by rearranging the formula:
Mass = Volume x Density (M=VxD)
Example: The density of gold is 19.3 g/cm3. If I have a nugget with a volume of 10 cm3, what is the mass of the cube?
M = 19.3 g/cm3 x 10 cm3
M = 193 g
Or, if the scientists knows the density and mass of a sample, he or she can easily solve for volume:
Volume = Mass/Density (V=M/D)
Example: My paperweight has a mass of 50 g and a density of 2.5 g/cm3. How much space does it take up?
V = 50g / 2.5 g/cm3
V = 20 cm3
Volume: The amount of space an object takes up. We use cm3 or mL to measure volume.
Mass: The amount of matter in an object. The amount of “stuff” is measured in grams.
Density: The amount of matter in a given space or volume. g/mL or g/cm3