Page 85 - Physical chemistry understanding our chemical world

52 INTRODUCING INTERACTIONS AND BONDS

As the temperature rises above the critical temperature and the pressure drops
below the critical pressure, so the gas approximates increasingly to an ideal gas,
i.e. one in which there are no interactions and which obeys the ideal-gas equation
(Equation (1.13)).

How do we liquefy petroleum gas?

Quantifying the non-ideality

Liquefied petroleum gas (LPG) is increasingly employed as a fuel. We produce it by
applying a huge pressure (10–20 × p ) to the petroleum gas obtained from oil fields.
O
Above a certain, critical, pressure the hydrocarbon gas condenses; we say it reaches
the dew point, when droplets of liquid first form. The proportion of the gas liquefying
increases with increased pressure until, eventually, all of it has liquefied.
Increasing the pressure forces the molecules closer together, and the intermolecular
interactions become more pronounced. Such interactions are not particularly strong
because petroleum gas is a non-polar hydrocarbon, explaining why it is a gas at room
temperature and pressure. We discuss other ramifications later.
The particles of an ideal gas (whether atoms or molecules) do
We often call a gas that not interact, so the gas obeys the ideal-gas equation all the time.
is non-ideal, a real gas. As soon as interactions form, the gas is said to be non-ideal,
with the result that we lose ideality, and the ideal-gas equation
(Equation (1.13)) breaks down. We find that pV = nRT .
When steam (gaseous water) is cooled below a certain tem-
The physical chem- perature, the molecules have insufficient energy to maintain their
istry underlying the high-speed motion and they slow down. At these slower speeds,
liquefaction of a gas
is surprisingly compli- they attract one another, thereby decreasing the molar volume.
cated, so we shall not Figure 2.9 shows a graph of the quotient pV ÷ nRT (as y)
return to the question against pressure p (as x). We sometime call such a graph an
until Chapter 5. Andrews plot. It is clear from the ideal-gas equation (Equa
tion (1.13)) that if pV = nRT then pV ÷ nRT should always
equal to one: the horizontal line drawn through y = 1, therefore,
We form a ‘quotient’ indicates the behaviour of an ideal gas.
when dividing one thing But the plots in Figure 2.9 are not horizontal. The deviation of a
by another. We meet trace from the y = 1 line quantifies the extent to which a gas devi-
the word frequently ates from the ideal-gas equation; the magnitude of the deviation
when discussing a depends on pressure. The deviations for ammonia and ethene are
person’s IQ, their ‘intel-
clearly greater than for nitrogen or methane: we say that ammo-
ligence quotient’, which
we define as: (a per- nia deviates from ideality more than does nitrogen. Notice how
son’s score in an intel- the deviations are worse at high pressure, leading to the empiri-
ligence test ÷ the aver- cal observation that a real gas behaves more like an ideal gas at
age score) × 100. lower pressures.
Figure 2.10 shows a similar graph, and displays Andrews plots
for methane as a function of temperature. The graph clearly