### Derived Units and Density

```Derived Units and
Density
1.
2.
3.
A piece of metal has the mass of 3.45 kg. What is its
mass in g?
A container has 2.3 L of gas in it? What is its volume
in mL?
A container has 750.00 mL of liquid in it. What is its
volume in dL?
Bell Ringer…
• Many SI units are combinations of quantities
• These units are produced by multiplying or dividing
standard units
Derived units…
Quantity
Name of Unit
Abbreviation
Area (A)
square meter
m2
Length x width
Volume (V)
Cubic meter
m3
Length x width x
height
Density (D)
Kilograms per
cubic meter
kg/m3
Mass / volume
Molar mass (M)
Kilograms per
mole
kg/mol
Mass / amt of
substance
Concentration (c)
Moles per liter
M
Amt of
substance/
volume
Molar volume (Vm)
Cubic meters
per mole
m3/mol
Volume / amt of
substance
joule
J
Force x length
Energy (E)
Derived SI units…
Derivation
• The measure of the resistance of an object to a change in
its state of motion OR the amount of “stuff” in an object
• A scale is used to mass an object
Mass
• An important point concerning measurements is
the relationship between mass and weight
• Weight is the force gravity exerts on mass,
therefore weight varies with the strength of the
gravitational field
• Therefore if you went to the moon your weight
would change but not your mass
• Many times the terms mass and weight are
sometimes used interchangeably, although this is
incorrect!
Mass vs. weight…
• The derived SI unit of volume is cubic meters (m3)
• Many times this unit is way too large to be a practical
way of expressing volume in a chemistry lab
• Instead, a smaller unit cubic centimeters (cm3) is used
• When dealing with the volumes of liquids and gases, the
non-SI unit liter (L) is often used
• Again the liter is often too large so the unit milliliter (mL)
is used
• This means 1 cm3 = 1mL
Volume…
1. How many mL are in 14.65 kL?
2. How many L are in 48.6 cm3?
3. How many dm3 are in 29100 mL?
It can be tricky with
volume conversions…
•
•
•
•
•
Ratio of mass to volume
D = m/V
Unit usually: g/mL or g/cm3
Useful for predicting mass
Does not depend on the amount of material in a
compound
Density…
• A characteristic physical property of a substance
• It does not depend on the size of the sample because as
the sample’s mass increases, its volume increases
proportionally
• Density varies with temperature – V ↑ T↑ D↓
Density…
• What is the density of an object that has a mass of 14 g
and a volume of 2 ml?
• What is the mass of an object with a volume of 2 cm3 and
a density of 1.5 g/mL?
• What is the volume of an object with the mass of 20 kg
and a density of 2.5 g/mL?
Try a few…
• An empty container weighs 121.3 g. Filled with
carbon tetrachloride (density 1.53 g/cm3) the
container weighs 283.2 g. What is the volume of
the container?
• A 55.0 gal drum weighs 75 lbs when empty.
What will the total mass be when filled with
ethanol?
density of ethanol = 0.789 g/cm3
1 gal = 3.78 L
1 lb = 454 g
Bell Ringer…
• In the opening scenes of the movie Raiders of the Lost Ark,
Indiana Jones tries to remove a gold idol from a booby-trapped
pedestal. He replaces the idol with a bag of sand of
approximately the same volume. (density of gold = 19.32
g/mL; density or sand = 2 g/mL)
• Did he have a reasonable chance of not activating the mass
sensitive bobby-trap?
• In a later scene he and an unscrupulous guide play catch
with the idol. Assume the volume of the idol is 1.0 L. If it
were solid gold, what mass would the idol have?
• Is playing catch plausible?
```