# 3.1: The International System of Units

Difficulty Level: At Grade Created by: CK-12

## Lesson Objectives

• Identify the seven base units of the International System of Units.
• Know the commonly used metric prefixes.
• Convert between the Celsius and Kelvin temperature scales.
• Understand volume and energy as combinations of SI Units.
• Distinguish between mass and weight.

## Lesson Vocabulary

• energy
• International System of Units (SI)
• joule
• kinetic energy
• liter
• measurement
• scientific notation
• temperature
• weight

### Recalling Prior Knowledge

• Why is the metric system easier to use than the English system of units?
• How is scientific notation used to represent very large or very small numbers?
• What units are used to measure length, mass, and volume in the metric system?

The temperature outside is 52 degrees Fahrenheit. Your height is 67 inches and your weight is 145 pounds. All are examples of measurements. A measurement is a quantity that includes both a number and a unit. If someone were to describe the height of a building as 85, that would be meaningless. 85 meters? 85 feet? Without a unit, a measurement does not convey enough information to be useful. In this lesson, we will begin an exploration of the units that are typically used in chemistry.

## SI 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.) is 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 (Table below).

SI Base Units of Measurement
Quantity SI Base Unit Symbol
Length meter m
Mass kilogram kg
Temperature kelvin K
Time second s
Amount of a Substance mole mol
Electric Current ampere A
Luminous Intensity candela cd

The first five units are frequently encountered in chemistry. The amount of a substance, the mole, will be discussed in detail in a later chapter. All other measurement quantities, such as volume, force, and energy, can be derived from these seven base units.

### Metric Prefixes and Scientific Notation

As stated earlier, conversions between metric system units are straightforward because the system is based on powers of ten. For example, meters, centimeters, and millimeters are all metric units of length. There are 10 millimeters in 1 centimeter and 100 centimeters in 1 meter. Prefixes are used to distinguish between units of different size. Listed below (Table below) are the most common metric prefixes and their relationship to the central unit, which has no prefix. Length is used as an example to demonstrate the relative size of each prefixed unit.

SI Prefixes
Prefix Unit Abbreviation 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

There are more prefixes, although some of them are rarely used. Have you ever heard of a zeptometer? You can learn more about metric prefixes at www.nist.gov/pml/wmd/metric/prefixes.cfm.

The table above (Table above) introduces a very useful tool for working with numbers that are either very large or very small. Scientific notation is a way to express numbers as the product of two numbers: a coefficient and the number 10 raised to a power. As an example, the distance from Earth to the Sun is about 150,000,000,000 meters—a very large distance indeed. In scientific notation, the distance is written as 1.5 × 1011 m. The coefficient is 1.5 and must be a number greater than or equal to 1 and less than 10. The power of 10, or exponent, is 11. Pictured below are two more examples of scientific notation (Figure below). Scientific notation is sometimes referred to as exponential notation.

The sun is very large and very distant, so solar data is better expressed in scientific notation. The mass of the sun is 2.0 × 1030 kg, and its diameter is 1.4 × 109 m.

Very small numbers can also be expressed using scientific notation. The mass of an electron in decimal notation is 0.000000000000000000000000000911 grams. In scientific notation, the mass is expressed as 9.11 × 10-28 g. Notice that the value of the exponent is chosen so that the coefficient is between 1 and 10.

## Typical Units in Chemistry

### Length and Volume

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 above (Table above) 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 (Figure below). 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). 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.

(A) A typical water bottle is 1 liter in volume. (B) These dice measure 1 cm on each side, so each die has a volume of 1 cm3 or 1 mL. (C) Volume in the laboratory is often measured with graduated cylinders, which come in a variety of sizes.

### Mass and Weight

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 (the volume of a liquid changes slightly with temperature). In the laboratory, mass is measured with a balance (Figure below), which must be calibrated with a standard mass so that its measurements are accurate.

An analytical balance in the laboratory takes very sensitive measurements of mass, usually in grams.

You can watch a short video about using an analytical balance at http://www.benchfly.com/video/54/how-to-weigh-small-amounts/.

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 and Energy

Touch the top of the stove after it has been on and it feels hot. Hold an ice cube in your hand and it feels cold. Why? The particles of matter in a hot object are moving much faster than the particles of matter in a cold object. An object’s kinetic energy is the energy due to motion. The particles of matter that make up the hot stove have a greater amount of kinetic energy than those in the ice cube (Figure below). Temperature is a measure of the average kinetic energy of the particles in matter. In everyday usage, temperature is how hot or cold an object is. Temperature determines the direction of heat transfer. When two objects at different temperatures are brought into contact with one another, heat flows from the object at the higher temperature to the object at the lower temperature. This occurs until their temperatures are the same.

The glowing charcoal on the left is composed of particles with a high level of kinetic energy, while the snow and ice on the right are made of particles with much less kinetic energy.

Temperature can be measured with several different scales. 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 referred to as one degree.

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. 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 273.15 (Figure below).

A comparison of the Kelvin (left) and Celsius (right) temperature scales. The two scales differ from one another by 273.15 degrees.

Energy is defined as the capacity to do work or to produce heat. As discussed previously, kinetic energy is one type of energy and is associated with motion. Another frequently encountered form of energy is potential energy, which is a type of energy that is stored in matter. The joule (J) is the SI unit of energy and is named after English physicist James Prescott Joule (1818-1889). In terms of SI base units, a joule is equal to a kilogram times a meter squared divided by a second squared (kg•m2/s2). A common non-SI unit of energy that is often used is the calorie (cal), which is equal to 4.184 J.

## Lesson Summary

• Measurements are critical to any field of science and must consist of a quantity and an appropriate unit. The International System of Units consists of seven base units.
• The metric system utilizes prefixes and powers of 10 to make conversions between units easy.
• Length (m), mass (kg), temperature (K), time (s), and amount (mol) are the base units that are most frequently used in chemistry. Quantities such as volume and energy can be derived from combinations of the base units.

## Lesson Review Questions

### Reviewing Concepts

1. Give the SI base unit of measurement for each of the following quantities.
1. mass
2. length
3. time
4. temperature
2. Convert the following numbers into scientific notation.
1. 85,000,000
2. 0.00019
3. Put the following into decimal notation.
1. 8.72 × 10-8
2. 3 × 104
4. Place the following units of mass in order from smallest to largest: g, kg, μg, g, pg, Mg, ng, cg, dg.
5. Explain what is wrong with the following statement: “This rock weighs 8 kilograms.”
6. What is absolute zero on the Celsius temperature scale?

### Problems

1. Calculate the volume in mL of a cube that is 2.20 cm on each side.
2. A rectangular solid has a volume of 80 cm3. Its length is 2.0 cm and its width is 8.0 cm. What is the height of the solid?
3. Convert the following Celsius temperatures to Kelvin.
1. 36°C
2. −104°
4. Convert the following Kelvin temperatures to degrees Celsius.
1. 188 K
2. 631 K
5. Temperature in degrees Fahrenheit can be converted to Celsius by first subtracting 32, then dividing by 1.8. What is the Celsius temperature outside on a warm 88°F day?
6. Two samples of water are at different temperatures. A 2 L sample is at 40°C, while a 1 L sample is at 70°C.
1. The particles of which sample have a larger average kinetic energy?
2. The water samples are mixed. Assuming no heat loss, what will be the temperature of the 3 L of water?

## Points to Consider

Conversions between units of the metric system are made easy because they are related by powers of ten and because the prefixes are consistent across various types of measurement (length, volume, mass, etc.).

• What is the mass in grams of a 2.50 kg book?
• What is the length in cm of a field that is 0.65 km?

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