Unit 3.3 Metric System (System International)

How long is a yard? It depends on whom you ask and when you asked the question. Today we have a standard definition of the yard, which you can see marked on every football field. If you move the ball ten yards, you get a first down and it doesn’t matter whether you are playing in Los Angeles, Dallas, or Green Bay. But at one time that yard was arbitrarily defined as the distance from the tip of the king’s nose to the end of his outstretched hand. Of course, the problem there is simple: new king, new distance (and then you have to remark all those football fields).

Metric Base Units

All measurements depend on the use of units that are well known and understood. The English system of measurement units (inches, feet, ounces, etc.) are not used in science because of the difficulty in converting from one unit to another. The metric system is used because all metric units are based on multiples of 10, making conversions very simple. The metric system was originally established in France in 1795. The International System of Units is a system of measurement based on the metric system. The acronym SI is commonly used to refer to this system and stands for the French term, Le Système International d’Unités. The SI was adopted by international agreement in 1960 and is composed of seven base units.

Length: meter

1 The distance light travels in a vacuum in /299,792,458 s Volume: liter A cube that is 10 cm per side = 1 liter, 1 cm3 = 1 mL Mass: kilogram o 1 gram is the mass of 1 mL of H2O at 4 C Time: second

Temperature: Celsius or Kelvin Amount of Substance: mole 6.02 x 1023 number of particles

The map shown to the right, shows the adoption of the SI units in countries around the world. The United States has legally adopted the metric system for measurements, but does not use it in everyday practice. Great Britain and much of Canada use a combination of metric and imperial units.

The table below is a list of prefixes used with metric units.

SI Prefixes

Prefix Unit Abbrev. Exponential Factor Meaning Example

giga G 109 1,000,000,000 1 gigameter (Gm) = 109 m

mega M 106 1,000,000 1 megameter (Mm) = 106 m

kilo k 103 1000 1 kilometer (km) = 1000 m

hecto h 102 100 1 hectometer (hm) = 100 m

deka da 101 10 1 dekameter (dam) = 10 m

100 1 1 meter (m)

deci d 10-1 1/10 1 decimeter (dm) = 0.1 m

centi c 10-2 1/100 1 centimeter (cm) = 0.01 m

milli m 10-3 1/1000 1 millimeter (mm) = 0.001 m

micro μ 10-6 1/1,000,000 1 micrometer (μm) = 10-6 m

nano n 10-9 1/1,000,000,000 1 nanometer (nm) = 10-9 m

pico p 10-12 1/1,000,000,000,000 1 picometer (pm) = 10-12 m

Length is the measurement of the extent of something along its greatest dimension. The SI basic unit of length, or linear measure, is the meter (m). All measurements of length may be made in meters, though the prefixes listed in various tables will often be more convenient. The width of a room may be expressed as about 5 meters (m), whereas a large distance, such as the distance between New York City and Chicago, is better expressed as 1150 kilometers (km). Very small distances can be expressed in units such as the millimeter or the micrometer. The width of a typical human hair is about 20 micrometers (μm).

Volume is the amount of space occupied by a sample of matter. The volume of a regular object can be calculated by multiplying its length by its width by its height. Since each of those is a linear measurement, we say that units of volume are derived from units of length. The SI unit of volume is the cubic meter (m3), which is the volume occupied by a cube that measures 1 m on each side. This very large volume is not very convenient for typical use in a chemistry laboratory. A liter (L) is the volume of a cube that measures 10 cm (1 dm) on each side. A liter is thus equal to both 1000 cm3 (10 cm × 10 cm × 10 cm) and to 1 dm3. A smaller unit of volume that is commonly used is the milliliter (mL – note the capital L which is a standard practice). A milliliter is the volume of a cube that measures 1 cm on each side. Therefore, a milliliter is equal to a cubic centimeter (cm3). There are 1000 mL in 1 L, which is the same as saying that there are 1000 cm3 in 1 dm3.

Mass is a measure of the amount of matter that an object contains. The mass of an object is made in comparison to the standard mass of 1 kilogram. The kilogram was originally defined as the mass of 1 L of liquid water at 4°C (volume of a liquid changes slightly with temperature). The density of water is the greatest when it is at 4 °C. In the laboratory, mass is measured with a balance which must be calibrated with a standard mass so that its measurements are accurate.

Other common units of mass are the gram and the milligram. A gram is 1/1000th of a kilogram, meaning that there are 1000 g in 1 kg. A milligram is 1/1000th of a gram, so there are 1000 mg in 1 g.

Mass is often confused with the term weight. Weight is a measure of force that is equal to the gravitational pull on an object. The weight of an object is dependent on its location. On the moon, the force due to gravity is about one sixth that of the gravitational force on Earth. Therefore, a given object will weigh six times more on Earth than it does on the moon. Since mass is dependent only on the amount of matter present in an object, mass does not change with location. Weight measurements are often made with a spring scale by reading the distance that a certain object pulls down and stretches a spring.

Temperature is a measure of the average kinetic energy of the particles in matter. In everyday usage, temperature indicates a measure of how hot or cold an object is. Temperature is an important parameter in chemistry. When a substance changes from solid to liquid, it is because there was an increase in the temperature of the material. Chemical reactions usually proceed faster if the temperature is increased. Many unstable materials (such as enzymes) will be viable longer at lower temperatures.

Temperature Scales

The first thermometers were glass and contained alcohol, which expanded and contracted as the temperature changed. The German scientist, Daniel Gabriel Fahrenheit used mercury in the tube, an idea put forth by Ismael Boulliau. The Fahrenheit scale was first developed in 1724 and tinkered with for some time after that. The main problem with this scale is the arbitrary definitions of temperature. The freezing point of water was defined as 32°F and the boiling point as 212°F. The Fahrenheit scale is typically not used for scientific purposes.

The Celsius scale of the metric system is named after Swedish astronomer Anders Celsius (1701-1744). The Celsius scale sets the freezing point and boiling point of water at 0°C and 100°C respectively. The distance between those two points is divided into 100 equal intervals, each of which is one degree. Another term sometimes used for the Celsius scale is “centigrade” because there are 100 degrees between the freezing and boiling points of water on this scale. However, the preferred term is “Celsius.”

The Kelvin temperature scale is named after Scottish physicist and mathematician Lord Kelvin (1824-1907). It is based on molecular motion, with the temperature of 0 K, also known as absolute zero, being the point where all molecular motion ceases. The freezing point of water on the Kelvin scale is 273.15 K, while the boiling point is 373.15 K. Notice that here is no “degree” used in the temperature designation. Unlike the Fahrenheit and Celsius scales where temperatures are referred to as “degrees F” or “degrees C,” we simply designated temperatures in the Kelvin scale as kelvins.

As can be seen by the 100 kelvin difference between the two, a change of one degree on the Celsius scale is equivalent to the change of one kelvin on the Kelvin scale. Converting from one scale to another is easy, as you simply add or subtract 273.

Temperature conversions can easily be made using the formulas below.

O C + 273 = K

O 5 o C = /9 ( F – 32 )

O 9 o F = /5 C + 32

A mole is a quantity of particles, such as atoms, molecules, electrons, etc. Similar to going to the grocery store to purchase eggs, they are sold by the dozen. Atoms are so small that a very large quantity must be used. One mole of atoms is 6.02 x 1023 atoms. The concept of moles will be explored in depth in Unit 5.

Summary

The SI system is based on multiples of ten. The basic units are commonly used in chemistry. Length is the measurement of the extent of something along its greatest dimension. Volume is the amount of space occupied by a sample of matter. Volume can be determined by knowing the length of each side of the item. Mass is a measure of the amount of matter that an object contains. Temperature is a measure of the average kinetic energy of the particles in matter. The Fahrenheit scale defines the freezing point of water as 32°F and the boiling point as 212°F. The Celsius scale sets the freezing point and boiling point of water at 0°C and 100°C respectively. The Kelvin scale is based on molecular motion, with the temperature of 0 K, also known as absolute zero, being the point where all molecular motion ceases.

Review

1. What does SI stand for? 2. Which of the units are commonly used in chemistry? 3. What is the basic unit of length? 4. What are the dimensions of length for one mL? 5. An object measures 6.2 cm x 13.7 cm x 26.9 cm.. What is the volume of the object? 6. Why is the mass of 1 mL of water taken at 4 oC? 7. What is the basic unit of mass? 8. Define weight. 9. What is absolute zero on the Celsius temperature scale? 10. What are the freezing and boiling points of water in the Celsius and Kelvin scales? 11. Convert the following Kelvin temperatures to degrees Celsius. a. 188 K b. 631 K 12. What is the Celsius temperature outside on a warm day (88°F)? 13. Convert the following Celsius temperatures to Kelvin. a. 1075 oC b. 254 oC

Answers

1. System International (This is also called the Metric System) 2. Chemistry uses meter, liter, kilogram, second, Celsius or Kelvin, and moles 3. meter 4. 1 cm x 1 cm x 1 cm 5. 2285 cm3, or 2285 mL, or 2.285 L 6. Water is the densest at 4 oC. At temperatures above and below 4 oC, water expands. 7. Kilogram 8. Weight is a measure of force that is equal to the gravitational pull on an object. 9. -273 oC = 0 K, absolute zero 10. For water: Freezing = 0 oC or 273 K, Boiling = 100 oC or 373 K 11. Convert the following Kelvin temperatures to degrees Celsius. 1. 188 K – 273 = -85 oC 2. 631 K – 273 = 358 oC 12. (5/9) (88 oF – 32) = 31 oC 13. Convert the following Celsius temperatures to Kelvin. a. 1075 oC + 273 = 1348 K b. 254 oC + 273 = 527 K