The essence of science is the measurement and characterization of the world around us. In order to make sense out of our measurements, there must be a concise and standard language in which we can communicate our measurements. One such language is the International System (SI) of units.
In SI, there are units which are defined (suvh as those for mass, distance, and time) and others which are derived from the defined units. The basic set of derived units base on meters, kilograms, and seconds (mks) are the units of choice in SI. Here are some examples.
| Property | Unit | Symbol | mks Units |
|---|---|---|---|
| Length | meter | m | m |
| Mass | kilogram | kg | kg |
| Time | second | s | s |
| Temperature | Kelvin | K | K |
| Volume | cubic meter | m3 | m3 |
| Force | Newton | N | kg m s-2 |
| Energy | joule | J | kg m2 s-2 |
| Pressure | Pascal | Pa | kg m-1 s-2 |
Many units are not strictly part of the SI, but are okay to use. Often this is because of simply a matter of convenience. Units which are not SI units but are acceptable to be used along side of SI units include:
| Property | Unit | Symbol |
|---|---|---|
| Atomic Mass | atomic mass unit | u (6.022 x 1023 u = 1 g) |
| Volume | liter | L (1000 L = 1 m3 |
| Energy | calorie | cal (1 cal = 4.184 J) |
| electron Volt | eV (1 eV = 1.60 x 10-19 J) | |
| Amount of Substance | mole | mol (1 mol = 6.022 x 1023 things) |
| Example |
|---|
| Question: How many L are in 3.24 m3? |
Solution:
1000 L
2.34 m3 x -------- = 2340 L
m3
|
The most common measurements in a chemistry laboratory are of mass and volume. However, many different type of measurements are made and hence many different types of units are necessary.
Oftentimes, it is more convenient to express a measurment in terms of units which are not the standard SI units. For example, a measured volume may be so small, that we need to write it as
It would be more convenient to define a smaller unit of volume so the number we record in our notebook doesn't need to be so ridiculously tiny. Since SI is based on the metric system, SI uses the same Greek prefixes used in the metric system to define smaller or larger units of measure. In our example above, we might write
where the symbol mL stands for milliliters. (A milliliter is 1/1000th of a liter.) There are many such Greek prefixes used in science. With the proliferation of personal computers, many of the prefixes are used commonly in everyday langue now as well. While it is easy to joke about these prefixes, there are a number of common Greek prefixes which every chemistry student is expected to know:
| Prefix | Symbol | Value | |
|---|---|---|---|
| tera | t | 1012 | 1 000 000 000 000 |
| giga | g | 109 | 1 000 000 000 |
| Mega | M | 106 | 1 000 000 |
| kilo | k | 103 | 1 000 |
| hecta | h | 102 | 100 |
| Deca | D | 101 | 10 |
| deci | d | 10-1 | 0.1 |
| centi | c | 10-2 | 0.01 |
| milli | m | 10-3 | 0.001 |
| micro | μ | 10-6 | 0.000 001 |
| nano | n | 10-9 | 0.000 000 001 |
| pico | p | 10-12 | 0.000 000 000 001 |
| femto | m | 10-15 | 0.000 000 000 000 001 |
A more complete discussion of the origins of these roots is also available.
Converting between units using Greek prefixes is actually quite easy. For example:
| Example |
|---|
| Question: How many femtoseconds are in a millisecond? |
Solution:
10-3 s 1 fs
1 ms x --------- x --------- = 1012 fs
1 ms 10-15 s
|
| Note: Pay attention to how the units are cancelled in the above example. The easiest way to prevent silly errors in calculations is to be meticulous with the use of units. The easiest way to generate silly and frustrating errors is to leave units off of calculations. Omitting units is a very bad habit. Don't get into it. You'll be glad later on! |
Some units are defined in terms of others. For example, one liter was originally defined as the volume occupied by a cube with an edge length of 1 dm. This definition allows us to write a very useful conversion factor:
| Example |
|---|
| Question: What is the edge length (in cm) of a cube which has a volume of 22.4 L? |
Solution:
1 dm3 103 cm3
22.4 L x ------- x --------- = 22 400 cm3
1 L 13 dm3
(22 400 cm3)1/3 = 28.8 cm
|
| Note: Pay attention to how the units are cancelled when powers of units are involved. This situation is common. There are not 10 cm3 in 1 dm3. There are 1000 cm3 in 1 dm3! (1000 = 103.) Raising the unit to a power requires raising the conversion factor to the same power in order to properly cancel the units. |
There are many important relationships between units which every chemistry student should know.
| A gram is the mass of 1 mL of water at 3.96 oC. | 1 g water = 1 mL (at 3.96 oC) |
| A Newton is the force necessary to accelerate 1 kg by 1 m/s2. | 1 N = 1 kg m s-2 |
| A Joule is the energy required to accelerate 1 kg by 1 m/s2 over a distance of 1 m. | 1 J = 1 kg m2 s-2 = 1 N m |
| A Pascal is the pressure generated by a force of 1 N when spread out over an area of 1 m2. | 1 Pa = 1 N m-2 = 1 J s-2 = 1 kg m-1 s-2 |
Other important relationships are used to relate physical properties to basic units although they do not define units themselves.
| Velocity is given by the distance traveled per unit time. | v = distance/time | m s-1 N kg-1 s J kg-1 m-1 s |
| Momentum is given by the mass times the velocity of an object. | p = mv | kg m s-1 N s J m-1 s |
| Kinetic energy is given by one half the mass times the velocity squared. | K.E = 1/2 mv2 | kg m2 s-2 N m J |
Now try some problems! You may find it necessary to look up some of the required formulae in a math text. You will be expected to know these. Be careful to properly cancel all units. You'll be glad you did!