milligram (mg) = 1,000 micrograms (µg)
1 gram (g) = 1,000 milligrams (mg)
1 kilogram (kg) = 1,000 grams (g)
Some common English-to-SI-system mass conversions are
1 pound (lb) = 454 grams (g)
1 ounce (oz) = 28.4 grams (g)
1 pound (lb) = 0.454 kilograms (kg)
1 grain (gr) = 0.0648 grams (g)
1 carat (car) = 200 milligrams (mg)
Units of volume
In the SI system, volume is measured in base units called cubic meters. However, chemists normally use the liter, 0.001 m3, to measure volume. Here are some SI units of volume:
1 milliliter (mL) = 1 cubic centimeter (cm3) = 1,000 microliters (μL)
1 liter (L) = 1,000 milliliters (mL)
Some common English-to-SI-system volume conversions are
1 quart (qt) = 0.946 liters (L)
1 pint (pt) = 0.473 liters (L)
1 fluid ounce (fl oz) = 29.6 milliliters (mL)
1 gallon (gal) = 3.78 liters (L)
Units of temperature
Kelvin is the base unit for temperature in the SI system. 0 K is called absolute zero, the temperature at which all atomic/molecular motion ceases. Water freezes at 273 K and boils at 373 K. Following are the three major temperature conversion formulas:
Celsius to Fahrenheit:
Fahrenheit to Celsius:
Celsius to Kelvin:
Units of pressure
The SI unit for pressure is the pascal, where 1 pascal equals 1 newton per square meter. (A newton is a unit of force equal to 1 kg·m/s2.) But pressure can also be expressed in a number of ways, so here are some common pressure conversions:
1 millimeter of mercury (mm Hg) = 1 torr
1 atmosphere (atm) = 760 millimeters of mercury (mm Hg) = 760 torr
1 atmosphere (atm) = 29.9 inches of mercury (in. Hg)
1 atmosphere (atm) = 14.7 pounds per square inch (psi)
1 atmosphere (atm) = 101 kilopascals (kPa)
Units of energy
The SI unit for energy (heat being one form) is the joule, but most folks still use the metric unit of heat, the calorie. Here are some common energy conversions:
1 calorie (cal) = 4.184 joules (J)
1 nutritional (food) Calorie (Cal) = 1 kilocalorie (kcal) = 4,184 joules (J)
1 British thermal unit (BTU) = 252 calories (cal) = 1,053 joules (J)
SI base units
In case you’re looking for a simple and handy way to keep track of the most common SI base units, look at Table 2-2 to see them all nicely arranged for your enjoyment.
Table 2-2 SI Base Units
Examples
Q. You measure a length to be 0.005 m. How can this be better expressed using a metric system prefix?
A. 0.005 is
Q. What metric base unit would be the most appropriate to use if you were going to measure the distance a runner covers during a marathon?
A. Meters are used to measure how long something is or how much distance is covered. When taking and reading measurements, remember which units you’re using and understand which unit best applies.
Practice Questions
1. How many nanometers are in 1 cm?
2. Your lab partner has measured the mass of your sample to be 2,500 g. How can you record this more nicely (without scientific notation) in your lab notebook using a metric system prefix?
Practice Answers
1.
2. 2.5 kg. Because 1,000 g are in 1 kg, simply divide 2,500 by 1,000 to get 2.5.
Looking at Density
Sometimes units combine two or more units of measurement. These kinds of quantities are called derived units, and they’re built from combinations of different base units. Area, volume, and pressure, which we cover in detail later in the book, are considered to be derived units. There’s one derived unit, however, that’s almost universally discussed early in every chemistry class. It’s quite important and quite useful. We are, of course, talking about density.
Getting to the bottom of density basics
Density (d) is the ratio of the mass (m) to the volume (V) of a substance. Mathematically, it looks like this:
Usually, mass is described in grams (g) and volume is described in milliliters (mL), so density is g/mL. Because the volumes of liquids vary somewhat with temperature, chemists also usually specify the temperature at which a density measurement is made. Most reference books report densities at 20 degrees Celsius, because it’s close to room temperature and easy to measure without a lot of heating or cooling. The density of water at 20 degrees, for example, is 1 g/mL.
Another term you may hear is specific gravity (sg), which is the ratio of the density of a substance to the density of water at the same temperature. Specific gravity is just another way for you to get around the problem of volumes of liquids varying with the temperature. Specific gravity is used with urinalysis in hospitals and to describe automobile battery fluid in auto repair shops. Note that specific gravity has no units of measurement associated with it, because the unit g/mL appears in both the numerator and the denominator and therefore
