Page 52 - Physical chemistry understanding our chemical world

THE PRACTICE OF THERMODYNAMIC MEASUREMENT 19

A variable (mass, length, velocity, etc.) is written in a standard format, according
to Equation (1.2):

Variable or physicochemical quantity = number × units (1.2)

We sometimes call it a ‘phrase’. Because some numbers are huge
and others tiny, the SI system allows us a simple and convenient ‘Giga’ comes from the
Latin gigas, meaning
shorthand. We do not need to write out all the zeros, saying the
−1 ‘giant’ or ‘huge’. We
velocity of light c is 300 000 000 m s : we can write it as c = 3 × also get the every-
8
−1
10 ms −1 or as 0.3Gm s , where the capital ‘G’ is a shorthand
day words ‘giant’ and
for ‘giga’, or 1 000 000 000. The symbol G (for giga) in this context ‘gigantic’ from this
is called a ‘factor’. In effect, we are saying 300 000 000 m s −1 = root.
−1
0.3Gm s . The standard factors are listed on pp. xxviii–xxxi.
Most people find that writing 300 000 000 m s −1 is a bit long
winded. Some people do not like writing simple factors such as G In physical chemistry,
for giga, and prefer so-called scientific notation. In this style, we a ‘factor’ is a number
by which we multiply
write a number followed by a factor expressed as ten raised to an
−1
8
appropriate power. The number above would be 3.0 × 10 ms . the numerical value of
avariable. Factors are
usually employed with
Worked Example 1.2 Identify the variable, number, factor and unit a shorthand notation.
−1
in the phrase, ‘energy = 12 kJ mol ’.
Energy = 12 k J mol −1

Variable Number Factor Compound
unit

Reasoning

Variable – in simple mathematical ‘phrases’ such as this, we almost always write
the variable on the left. A variable is a quantity whose value can be altered.
Number – the easy part! It will be made up of numbers 1, 2, 3,..., 0.
Factor – if we need a factor, it will always be written between the number and
the units (compound or single). A comprehensive list of the simple factors is
given on pp. xxviii–xxxi.
Units – the units are always written on the right of a phrase such as this. There
−1
are two units here, joules (J) and moles (as ‘mol ’, in this case). We should
leave a space between them.

A factor is simply shorthand, and is dispensable. We could have dispensed with the
−1
factor and written the number differently, saying energy = 12 000 J mol . This same
−1
3
energy in scientific notation would be 12 × 10 Jmol . But units are not dispensable.