## Introduction

We make measurements all the time in our daily lives without even realizing it. When we walk, we visually measure the proximity of objects in our environment. When we pick up an item, we measure its weight and adjust our muscular response according to our initial estimates. Measurements are observations of a quantitative nature that are taken by some form of equipment. Some equipment, like our five senses, can give us very approximate measurements, while other technology, like a scale, provides more exact measurements. Many types of instruments are used to measure and study our chemical world. Some of the common quantities we measure in chemistry are distance (length), volume, mass, time, velocity, temperature, density, pressure, amount, concentration, energy, and electric charge. In this chapter, we will investigate how various methods of measurement are used to study the chemical nature of matter.

## Measurement and Numbers

Measurement is a fundamental aspect of science and chemistry. Our understanding of the chemical world would not be possible if we did not compare, contrast, categorize, and analyze our observations to obtain the information we have about chemical substances. Let’s consider water as an example. Many of the qualitative (non-numerical) properties of water, including its taste, smell, texture, and color, can be observed using our senses. We can also measure quantitative (numerical) properties of water by using equipment. For example, we can use a thermometer to measure water’s boiling point in degrees Celsius or a measuring cup to measure the volume of a given liquid.

There can be different units that are used to measure the same physical quantity. For example, temperature can be expressed in degrees Fahrenheit (°F), degrees Celsius (°C), or degrees Kelvin (K). No one set of units is more correct than the other. However, as we begin measuring, calculating, and sharing measurements, we will want a standard set of values that we and others can use. An international governing body has developed a metric system of units of measurement for scientists called the **Système International (SI)**. Some of these units are listed in **Table** below.

Physical Quantity | Name of SI Unit | Abbreviation |
---|---|---|

mass | kilogram | kg |

length | meter | m |

time | second | s or sec |

temperature | Kelvin | K |

amount of substance | mole | mol |

electric current | ampere | A |

luminous intensity | candela | cd |

### Base Units vs. Derived Units

With the **base units** listed in the **Table** above, we can describe many physical details of a given chemical substance. Base units are measurements that have their own independent scale and cannot be expressed in terms of other base units. All other measurement quantities, such as volume, force, and energy, can be derived from these seven base units. For instance, volume is calculated by multiplying together three different lengths (height, width, and depth). We call these combinations of base units **derived units**. Some examples of derived units are listed in **Table** below.

Physical Quantity | Name of SI Unit | Abbreviation |
---|---|---|

area | square meter | m2 |

volume | cubic meter | m3 |

speed, velocity | meter per second | m/s |

acceleration | meter per second squared | m/s2 |

force | Newton (mass × acceleration) | N (kg m/s2) |

mass density | kilogram per cubic meter | kg/m3 |

energy | joule (force × distance) | J (kg m2/s2) |

## Magnitude and Scale

When we think about the physical quantities that are measured in chemistry, we must also consider the concepts of magnitude and scale. The following video introduces these concepts:

As the video suggests, chemistry is a discipline in which we study things that are very, very small. We measure things like the size of an atom, which is approximately 1/10000000000 of a meter. Because individual atoms are so small, the substances that we can actually see and study, even something as small as a drop of rain, are comprised of an incredibly large number of atoms. There are literally thousands of billions of billions of particles in a drop of water. In both of these examples, we expressed size in terms of fractions or multiples of the number 10. When describing very small or very large physical quantities, we use prefixes to write the unit as a power of 10. **Table** below displays most of these prefixes.

Prefix | Meaning | Abbreviation | Numeric value | Exponential Notation |
---|---|---|---|---|

exa- | billion | E | 1000000000000000000 | 1018 |

peta- | thousand trillion | P | 1000000000000000 | 1015 |

tera- | trillion | T | 1000000000000 | 1012 |

giga- | billion | G | 1000000000 | 109 |

mega- | million | M | 1000000 | 106 |

kilo- | thousand | k | 1000 | 103 |

hecto- | hundred | h | 100 | 102 |

deka- | ten | da | 10 | 10 |

n/a | one | n/a | 1 | 100 |

deci- | one tenth | d | 0.1 | 10-1 |

centi- | hundredth | c | 0.01 | 10-2 |

milli- | thousandth | m | 0.001 | 10-3 |

micro- | millionth | µ | 0.000001 | 10-6 |

nano- | billionth | n | 0.000000001 | 10-9 |

pico- | trillionth | p | 0.000000000001 | 10-12 |

femto- | quadrillionth | f | 0.000000000000001 | 10-15 |

atto- | quintillionth | a | 0.000000000000000001 | 10-18 |

## The Relative Size of Things

We can express the relative size of things with which we are familiar. For instance, the **Figure** below shows the height of a human as measured in meters, or 100 scale. We see a dust mite, measured in micrometers scale;

and a virus, measured in nanometers scale.

These are examples of length related to relative size and scale.

Relative size and scale of things. CC BY-NC 3.0 – Source: CK-12 Foundation – Credit: Zachary Wilson and Laura Guerin – Edited by Jennifer Guest

This text is **Creative Commons BY-NC 3.0 Source: CK-12** and edited / added to by Guest Hollow.