Appendix 2 Units and Dimensions

The units used in Science are part of the International System of Units (System International - SI) which has been adopted throughout the world. The units which are basic to the SI system are tablated below.

Property	Dimensions	Basic Unit	Symbol for Unit
Mass	M	kilogram	kg
Length	L	metre	m
Time	T	second	s
Temperature	K	kelvin	K
Amount of Substance	N	mole	mol
Electric Charge	Q	Coulomb	C

The basic units can be qualified by various prefixes if the scale of the basic unit is not appropriate to the value of some particular quantity. A complete list of the prefixes is given below:

Factor	Prefix	Symbol
10-18	atto-	a
10-15	femto-	f
10-12	pico-	p
10-9	nano-	n
10-6	micro-	µ
10-3	milli-	m
10-2	centi-	c
10-1	deci-	d
10	deca-	da
102	hecto	h
103	kilo-	k
106	mega-	M
109	giga-	G
1012	tera-	T
1015	peta-	P
1018	exa-	E

More details of the definitions of standard units can be found in Beran and Atkins. You should be sure that you are familiar with the elementary material in on 'Measurements and Units'. This is seen in Atkins starting on p.11 to the end of Chapter 1.

Moles and Molar Quantities

The unit used in Chemistry to measure the amount of substance is the mole (mol), which is defined as:

1 mol of any substance contains the same number of atoms or molecules as there are in 12g of ¹²C.

Avogadro's constant N_A is defined as the number of species in 1 mol, and therefore

N= 6.022 14 x 10²³ mol^-1

Note that Avogadro's constant has units of mol^-1. It is obvious that if we know how many moles there are in a sample, then it is trivial to calculate the number of molecules. Hence the number of molecules N_A, corresponding to n moles is

N = nN_A

We can also define a whole range of molar quantities which refer to just a single mole of substance. Hence, the molar volume

V_m = V / n

where as before n is the number of moles, and V is the total volume of the sample. (NB. the unit of volume in SI is m³, but frequently it is more practical to use the litre - 1L = 1000cm³ = 1 dm³, 1mL = 1cm³). The molar mass

M = m /n

where m is the mass of the sample in kg. Molar mass is the modern term for what used to be called atomic or molecular weight. It is usual, in fact, to quote molar masses in units of gmol^-1, although kgmol^-1 are useful units for very large molecules (macromolecules), such as polymers and proteins. We can also report concentration in molar units. The molar concentration, usually known as the molarity, is defined as

c = n / V

where the units are usually defined as mol dm^-3, or as mol L^-1. The units are often written in a short form as 'M', which is to be read as 'molar'. Hence

1M = 1 mol dm^-3

Molar concentration is usually just known as 'concentration'. Note that the molar concentration of a pure substance is just the inverse of the molar volume.

There are various 'derived' units in the SI scheme, for example the unit of force. We shall define the derived units we need when we need them. Be sure that you understand the units that are used in your learning. They are the basis of all of the quantitative work done in Science. You should also be aware that the SI system has only been in operation since the 70's. Many textbooks are still in use that refer to older unit systems, such as the 'c.g.s.' system (which was based upon the centimetre, the gram and the second as basic units). There has also been resistance to the introduction of SI, particularly from the USA. The greatest difficulty in the introduction of SI units has been in those units dealing with electrical and magnetic quantities. In the theory of electromagnetism even the fundamental equations look different in SI and the older unit systems, so it is important to beware. You will certainly sometimes meet quantities quoted in non-SI units, and it is wise to be familiar with some of these non-standard units.