Units and Calculations
The Metric System
Chemistry is an experimental science. In order for experiments to be quantitative and reproducible we need a standard set of units. The agreed upon system of measurement in the sciences is the International System, otherwise known as
S.I. stands for Le Systéme International. This is the metric system with which you may already be familiar. The metric system is easy to learn and use because subdivisions and multiples of the base units employ only factors of 10. Prefices indicate the size of the unit relative to the base unit.
| Prefix | Symbol | Multiple of Base Unit |
|---|---|---|
| mega- | M | 1,000,000 or 106 |
| kilo- | k | 1,000 or 103 |
| deci- | d | 0.1 or 10-1 |
| centi- | c | 0.01 or 10-2 |
| milli- | m | 0.001 or 10-3 |
| micro- | μ | 0.000001 or 10-6 |
| nano- | n | 10-9 |
| pico- | p | 10-12 |
Length
The Base unit for length in the metric system is the
meter. The abbreviated symbol for meters is m
. A
meter is slighly longer than a yard (i.e., 1 m =
39.37 inches).
Volume
The Base unit for volume in the metric system is the
cubic meter. The abbreviated symbol for meters is
m3
. In practice, the cubic meter is not a
convenient unit for everyday use, so the cubic decimeter
(dm3) is used instead. Because it is so often
used 1 dm3 is given the name liter. The
abbreviated symbol for a liter is L
or l
.
When working with even smaller volumes the cubic centimeter
is more commonly used. Since
we often use 1 mL (mL is the symbol for milliliter) in
place of 1 cm3. You will sometimes see a mL
called a cc
, which stands for cubic centimeter.
Mass
The Base unit for mass in the metric system is the
kilogram. The abbreviated symbol for meters is kg
. 1
kg is approximately 2.2 pounds.
Density
Density is defined as the mass per unit volume.
The S.I. units for density are kg/m3, but again these are not very convenient units for everyday use. The more common units are:
g/cm3 for solids
g/ml for liquids
g/L for gases
If we know the mass and volume of a sample, then we can calculate its density.
A cube of lead 3.00 cm on a side has a mass of 305.0 g. What is the density of lead?
To answer this question we need to put the mass and volume of the sample into the equation above. The mass of lead is given at 305.0 g. Although we are not given the volume directly, we do know that the sample is a cube (i.e., all sides of equal length), and that length of a side is 3.00 cm . The volume of this cube would be
Thus, the density of the cube of lead is density = mass/volume = 305.0 g / 27.0 cm3 = 11.3 g/cm3. Notice that the density is the same no matter the size or shape of the sample.
Temperature
The scale for Temperature in the metric system is the Celsius scale. On the Celsius scale the freezing point of water is set at 0°C, and the boiling point is set at 100°C. The coldest temperature theoretically possible is -273.15°C. You simply cannot go any lower. In fact, it is experimentally impossible to even reach -273.15°C. This temperature is defined as zero on another temperature scale called the Kelvin scale. The Kelvin scale is related to the Celsius scale by
T(in Kelvin) = T(in Celsius) + 273.15
To give you some other reference points:
| System | Temperature |
|---|---|
| Sun's Interior (thermonuclear fusion of hydrogen to helium) | 108 K |
| Sun's Surface | 6000 K |
| Earth's Core | 4600 K |
| Liquid N2 (boiling pt.) | 77 K |
| Liquid He (boiling pt.) | 4.2 K |
Intensive and Extensive Properties
All the units of measure we just discussed (i.e., temperature, volume, mass, etc.,) describe the properties of a substance. Many properties can be classified as extensive or intensive.
- Extensive Properties:
- dependent on the amount of substance. Examples: mass, volume, energy
- Intensive Properties:
- independent of the amount of substance. Examples: temperature, pressure, density
For example, if I took 1.0 liter of water at room temperature (25°C) and added another 1.0 liter of water at the same temperature then I would have 2.0 liters of water at 25°C. From this example we see that Volume and Mass are extensive properties (i.e., volume and mass doubled), while Temperature is an intensive property (i.e., temperature stayed the same). You would also expect the density to remain the same, so it is also an intensive property.
In the language of thermodynamics we say: when two identical systems are brought together extensive properties will double in value, and intensive properties will stay the same.
Can you explain why pressure is an intensive property?
Dimensional Analysis
When doing calculations we always write each number with its associated units. As you do the calculation the units should cancel so that the final number you calculate also has the correct units. Let's look at some examples.
Donuts cost $2.79 a dozen. How much do 3 dozen donuts cost?
Convert 0.34 cm to mm (micrometers).
In these two examples the conversion factors are exact numbers. That is, they have infinite precision. Conversions factors, however, are not always exact numbers. Let's look at an example using density as a conversion factor to convert between volume and mass.
What volume will 50.0g of ether occupy if the density of ether is 0.71g/mL?
A pitcher throws a baseball at 90 miles/hour. What is the speed in feet/second?
If the distance between the pitcher's mound and homeplate is 60.5 feet, how long does it take the ball to travel this distance?
