Page 67 - Physical chemistry understanding our chemical world

34 INTRODUCTION TO PHYSICAL CHEMISTRY

It is important to appreciate that this energy relates to the average energy of 1 mol
of gas molecules. The concept of temperature has no meaning when considering a
single molecule or atom. For example, the velocity (and hence the kinetic energy)
of a single particle changes with time, so in principle its temperature also changes.
Temperature only acquires any thermodynamic meaning when we consider average
velocities for a large number of particles.
Provided we know the temperature of the gas, we know its energy – the energy it
has simply by existing at the temperature T .

Worked Example 1.6 What is the energy of 1 mol of gas in a warm room at 310 K?

The energy per mole is 3 × R × T ; so, inserting values, energy =
2
3 −1 −1
The ‘room energy’ 3 RT 2 × 8.314 J K mol × 310 K.
2
derives from the kinetic
(movement) energy of Energy = 3866 J mol −1 ≈ 3.9kJ mol −1
a gas or material.
−1
The molar energy of these molecules is about 4 kJ mol ,which is
extremely slight compared with the energy of the bonds connecting
the respective atoms within a molecule (see Chapters 2 and 3). There is little chance of
this room energy causing bonds to break or form.

SAQ 1.12 What is the room energy per mole on a cold winter’s day, at
◦
−8 C (265 K)?

What do we mean by ‘room temperature’?

Standard temperature and pressure

Suppose two scientists work on the same research project, but one resides in the far
north of the Arctic Circle and the other lives near the equator. Even if everything
else is the same – such as the air pressure, the source of the chemicals and the
manufacturers of the equipment – the difference between the temperatures in the two
laboratories will cause their results to differ widely. For example, the ‘room energy’
RT will differ. One scientist will not be able to repeat the experiments of the other,
which is always bad science.
An experiment should always be performed at known tempera-
An experiment should ture. Furthermore, the temperature should be constant throughout
always be performed at the course of the experiment, and should be noted in the labora-
aknown,fixedtemper- tory notebook.
ature. But to enable complete consistency, we devise what is called a set
O
of standard conditions. ‘Standard pressure’ is given the symbol p ,
5
and has a value of 10 Pa. We sometimes call it ‘1 bar’. Atmospheric pressure has a
value of 101 325 Pa, so it is larger than p . We often give atmospheric pressure the
O
symbol ‘atm’.