Units and Dimensions in Physical Chemistry
Units and dimensions tend to cause untold amounts of grief to many chemists throughout the
course of their degree.
My hope is that by having a dedicated tutorial on them we can avoid this
for Hertford chemists.
It is very important that you understand everything in this tutorial and that
you (eventually) find the associated problems quite straightforward.
Please make sure you ask lots
of questions if there are things you don’t understand (this goes for all tutorials, of course).
SECTION A – Reading and notes
Read the material taken from the book ‘Quantities, units and symbols in physical chemistry’ (often
called the ‘Green Book’), and also the overview below.
Read them in any order you like, and take
notes if it helps you.
A physical quantity is the product of a numerical value and a unit.
(Physical quantity) = (numerical value) x (unit)
(mass of an average person) = (70) x (kg)
Obviously, this is usually just written 70 kg.
(speed of light) = (2.99792458 x 10
) x (ms
If you are one of the many people who, up until now, has always thought of units as something you
have to tack onto the end of your calculations, appreciating the significance of the above is even
In science, we are generally dealing with physical quantities, not with pure
numbers (we’ll leave that to the mathematicians).
This means that virtually every number you write
down should have units with it.
The numerical value of a physical quantity will vary depending on
what units you choose to use (for example, an energy of 1 kJ could equally well be expressed as
1000 J, or 6.242 x 10
eV, or 2.294 x 10
Hartree), which means that just writing down a number
without also stating its units is completely meaningless.
Units are not optional!
The good news is that by thinking of units in this way, all the calculations and conversions and
conventions that you previously may have found tortuous and completely incomprehensible should
suddenly become much more straightforward.
All calculations to do with units now essentially just
become very basic algebra.
For example, the tick marks along the axis of a graph are generally
only labelled with numerical values.
The axis label must therefore be consistent with this.
Rearranging the above equation gives (numerical value) = (physical quantity)/(unit), so axes
should always be labelled to be consistent with this e.g. speed / ms
, or mass / kg.
alternative, often seen in publications from the US and written e.g. speed (ms) or mass (kg) is
technically incorrect and unfortunately shows that the authors do not understand physical
Before we move onto calculations, we need a short recap of the SI (Système Internationale)
system of units.