The natural sciences begin with ** observation,** and this usually involves

Most of these quantities have * units *of some kind associated with them, and these units must be retained when you use them in calculations.

All measuring units can be defined in terms of a very small number of fundamental ones that, through "dimensional analysis", provide insight into their derivation and meaning, and must be understood when converting between different unit systems.

1 Units of measure

The results of a measurement are always expressed on some kind of a scale that is defined in terms of a particular kind of unit. The first scales of distance were likely related to the human body, either directly (the length of a limb) or indirectly (the distance a man could walk in a day).

As civilization developed, a wide variety of measuring scales came into existence, many for the same quantity (such as length), but adapted to particular activities or trades. Eventually, it became apparent that in order for trade and commerce to be possible, these scales had to be defined in terms of standards that would allow measures to be verified, and, when expressed in different units (bushels and pecks, for example), to be correlated or converted.

The most influential event in the history of measurement was undoubtedly the French Revolution and the Age of Enlightenment that followed. This led directly to the metric system that attempted to do away with the confusing multiplicity of measurement scales by reducing them to a few fundamental ones that could be combined in order to express any kind of quantity. The metric system spread rapidly over much of the world, and eventually even to England and the rest of the U.K. when that country established closer economic ties with Europe in the latter part of the 20th Century. The United States is presently the only major country in which “metrication” has made little progress within its own society, probably because of its relative geographical isolation and its vibrant internal economy.

Science, being a truly international endeavor, adopted metric measurement very early on; engineering and related technologies have been slower to make this change, but are gradually doing so. Even the within the metric system, however, a variety of units were employed to measure the same fundamental quantity; for example, energy could be expressed within the metric system in units of ergs, electron-volts, joules, and two kinds of calories. This led, in the mid-1960s, to the adoption of a more basic set of units, the *Systeme Internationale* (*SI*) units that are now recognized as the standard for science and, increasingly, for technology of all kinds.

2 The SI units

Brief history of the SI - NIST Reference on the SI

In principle, any physical quantity can be expressed in terms of only seven base units. Each base unit is defined by a standard which is described in the NIST Web site.

length |
meter | m |

mass |
kilogram | kg |

time |
second | s |

temperature (absolute) |
kelvin | K |

amount of substance |
mole | mol |

electric current
| ampere | A |

luminous intensity |
candela | cd |

A few special points about some of these units are worth noting:

- The base unit of
**mass**is unique in that a decimal prefix (see below) is built-in to it; that is, it is not the*gram*, as you might expect. - The base unit of
**time**is the only one that is not metric. Numerous attempts to make it so have never garnered any success; we are still stuck with the 24:60:60 system that we inherited from ancient times. (The ancient Egyptians of around 1500 BC invented the 12-hour day, and the 60:60 part is a remnant of the base-60 system that the Sumerians used for their astronomical calculations around 100 BCE.) - Of special interest to Chemistry is the mole, the base unit for expressing the
**quantity of matter**. Although the number is not explicitly mentioned in the official definition, chemists define the mole as Avogadro’s number (approximately 6.0210^{23}) of anything.

Owing to the wide range of values that quantities can have, it has long been the practice to employ prefixes such as milli and mega to indicate decimal fractions and multiples of metric units. As part of the SI standard, this system has been extended and formalized.

prefix | abbreviation | multiplier |
---|---|---|

exa | E | 10^{18} |

peta | P | 10^{15} |

tera | T | 10^{12} |

giga | G | 10^{9} |

mega | M | 10^{6} |

kilo | k | 10^{3} |

hecto | h | 10^{2} |

deca | da | 10 |

prefix | abbreviation | multiplier |
---|---|---|

deci | d | 10^{–1} |

centi | c | 10^{–2} |

milli | m | 10^{–3} |

micro | μ | 10^{–6} |

nano | n | 10^{–9} |

pico | p | 10^{–13} |

femto | f | 10^{–15} |

atto | a | 10^{–18} |

3 Units outside the SI

There is a category of units that are “honorary” members of the SI in the sense that it is acceptable to use them along with the base units defined above. These include such mundane units as the hour, minute, and degree (of angle), etc., but the three shown here are of particular interest to chemistry, and you will need to know them.

liter (litre) | L | 1 L = 1 dm^{3} = 10^{–3} m^{3} |

metric ton | t | 1 t = 10^{3} kg |

united atomic mass unit | u | 1 u = 1.66054×10^{–27} kg |

Most of the physical quantities we actually deal with in science and also in our daily lives, have units of their own: volume, pressure, energy and electrical resistance are only a few of hundreds of possible examples. It is important to understand, however, that all of these can be expressed in terms of the SI base units; they are consequently known as derived units. In fact, most physical quantities can be expressed in terms of one or more of the following five fundamental units:

mass M |
length L |
time T |
electric charge Q |
temperature Θ (theta) |

Consider, for example, the unit of ** volume**, which we denote as V. To measure the volume of a rectangular box, we need to multiply the lengths as measured along the three coordinates:

V = x · y · z

We say, therefore, that volume has the dimensions of length-cubed:

dim.V = L^{3}

Thus the units of volume will be m^{3} (in the SI) or cm^{3}, ft^{3} (English), etc. Moreover, any formula that calculates a volume must contain within it the L^{3} dimension; thus the volume of a sphere is 4/3 π*r*^{3}.

4 Units and their ranges in Chemistry

In this section, we will look at some of the quantities that are widely encountered in Chemistry, and at the units in which they are commonly expressed. In doing so, we will also consider the actual range of values these quantities can assume, both in nature in general, and also within the subset of nature that chemistry normally addresses. In looking over the various units of measure, it is interesting to note that their unit values are set close to those encountered in everyday human experience

These two quantities are widely confused. Although they are often used synonymously in informal speech and writing, they have different dimensions: weight is the *force* exerted on a mass by the local gravitational field:

*f* = *m a* = *m g*

where *g* is the acceleration of gravity. While the nominal value of the latter quantity is 9.80 m s^{–2} at the Earth’s surface, its exact value varies locally. Because it is a *force*, the proper SI unit of weight is the *newton*, but it is common practice (except in physics classes!) to use the terms "weight" and "mass" interchangeably, so the units *kilograms* and *grams* are acceptable in almost all ordinary laboratory contexts.

**Important:** Please note that in this diagram and in those that follow, the numeric scale represents the *logarithm* of the number shown. For example, the mass of the electron is 10^{–30} kg.

*Time present and time past
Are both perhaps present in time future
And time future contained in time past.
If all time is eternally present
All time is unredeemable.*

T.S. Eliott, *Burnt Norton*

Most of what actually takes place in the chemist’s test tube operates on a far shorter time scale, although there is no limit to how *slow* a reaction can be; the upper limits of those we can directly study in the lab are in part determined by how long a graduate student can wait around before moving on to gainful employment.

Looking at the microscopic world of atoms and molecules themselves, the time scale again shifts us into an unreal world where numbers tend to lose their meaning. You can gain some appreciation of the duration of a nanosecond by noting that this is about how long it takes a beam of light to travel between your two outstretched hands. In a sense, the material foundations of chemistry itself are defined by time: neither a new element nor a molecule can be recognized as such unless it lasts around sufficiently long enough to have its “picture” taken through measurement of its distinguishing properties.

We all know that temperature is expressed in degrees. What we frequently forget is that the degree is really an *increment* of temperature, a fixed fraction of the distance between two defined reference points on a temperature scale.

Pressure is the measure of the *force* exerted on a unit area of surface. Its SI units are therefore newtons per square meter, but we make such frequent use of pressure that a derived SI unit, the *pascal*, is commonly used:

1 Pa = 1 N m^{–2}

The concept of pressure first developed in connection with studies relating to the atmosphere and vacuum that were first carried out in the 17th century

The molecules of a gas are in a state of constant thermal motion, moving in straight lines until experiencing a collision that exchanges momentum between pairs of molecules and sends them bouncing off in other directions.

This leads to a completely random distribution of the molecular velocities both in speed and direction— or it would in the absence of the Earth’s gravitational field which exerts a tiny downward force on each molecule, giving motions in that direction a very slight advantage. In an ordinary container this effect is too small to be noticeable, but in a very tall column of air the effect adds up: the molecules in each vertical layer experience more downward-directed hits from those above it. The resulting force is quickly randomized, resulting in an increased pressure in that layer which is then propagated downward into the layers below.

At sea level, the total mass of the sea of air pressing down on each 1-cm^{2} of surface is about 1034 g, or 10340 kg m^{–2}. The force (weight) that the Earth’s gravitational acceleration g exerts on this mass is

*f* = *ma* = *mg* = (10340 kg)(9.81 m s^{–2}) = 1.013 × 105 kg m s^{–2}

= 1.013 × 10^{5} newtons

resulting in a pressure of 1.013 × 10^{5} n m^{–2} = 1.013 × 10^{5} pa. The actual pressure at sea level varies with atmospheric conditions, so it is customary to define *standard atmospheric pressure* as

1 atm = 1.013 × 10^{5} pa or 101 kpa.

Although the standard atmosphere (atm) is not an SI unit, it is still widely employed. In meteorology, the *bar*, exactly 1.000 × 10^{5} = 0.967 atm,

is often used.

Torricelli was also the first to recognize that the space above the mercury constituted a vacuum, and is credited with being the first to create a vacuum.

One standard atmosphere will support a column of mercury that is 76 cm high, so the “millimeter of mercury”, now more commonly known as the torr, has long been a common pressure unit in the sciences: 1 atm = 760 torr.

Concept Map