This document discusses ideal and non-ideal gases, focusing on how they behave according to the combined gas law and Van der Waals equation. It also covers vapour pressure and how Raoult's law describes the relationship between vapour pressure and composition in ideal solutions. Non-ideal behaviour is examined for mixtures like hydrocarbon propellants, anaesthetic agents, and drug-solvent combinations, which can show positive or negative deviations from Raoult's law due to intermolecular interactions.

1. GASES AND VOLATILE
AGENTS (1)
Dr Mohd Cairul Iqbal Mohd Amin
Gases and volatile substances are
encountered in pharmacy mainly as
anaesthetic gases or as propellants in
aerosols
Ideal and non-ideal gases
Ideal gases obey the combined gas law
PV = nRT (eqn 1.1)
Where P is the pressure in N m-2, V is
the volumes in m3, n is the number of
moles of gas, T is the temperature in
Kelvins and R is the gas constant (8.314
J mol-1)
Ideal and non-ideal gases
The equation may be derived from the
kinetic theory of gases assuming the
gas molecules to behave as perfectly
elastic spheres having negligible volume
with no intermolecular attraction or
repulsion

2. Ideal and non-ideal gases
For a given number of moles of gas the
quantity PV/RT should, according to
equation 1.1, be independent of
changes in P, V or T providing such
changes do not involve a change of
state.
Ideal and non-ideal gases
A convenient means of expressing
departure from ideality is by plots such
as that shown in figure 1.1 in which
PV/RT is plotted as a function of
pressure for 1 mole of each gas.
Ideal and non-ideal gases
It is important to note that the
magnitude of the pressures involved in
figure 1.1.
The narrow shaded area represents the
pressure normally met in
pharmaceutical systems and it is clear
that the ideal gas laws are sufficient for
most purposes.

3. Ideal and non-ideal gases
Where it is clear that equation 1.1 is
inadequate in describing the behaviour
of a gaseous system, a better
approximation to real behaviour may be
achieved using the Van der Waal’s
equation:
Ideal and non-ideal gases
(P + an2/V2) (V – nb) = nRT (eqn 1.2)
where a and b are constants for a
particular gas.
Ideal and non-ideal gases
At the moment of impact of a molecule
with the container wall the molecule is
subjected to an imbalance of forces
which tend to pull it back into the bulk
of the gas and so lessen the force of
impact.
Ideal and non-ideal gases
Since pressure is the consequence of
collisions of molecules with walls there
is a resultant reduction of pressure
which may be corrected by addition of
the a/V2 term.

4. Ideal and non-ideal gases
Around each molecule of a gas is a
particular volume from which other
molecules are excluded for purely
physical reasons.
Ideal and non-ideal gases
The bulk molar volume, V, of the gas is
consequently an over-estimation of the
true molar volume.
In the Van der Waal’s equation
allowance is made for the excluded
volume by substraction of the constants
b.
Ideal and non-ideal gases
Table 1.1 gives values of a and b for
some common gases.

5. Vapour pressure
Vapour pressure and solution
composition – Raoult’s law
Vapour pressure and solution
composition – Raoult’s law
In pharmaceutical systems in which an
equilibrium exists between a liquid and
its vapour, such as in certain types of
aerosols, it is important to be able to
calculate the vapour pressure from a
knowledge of the composition of the
solution.
Vapour pressure and solution
composition – Raoult’s law
In an ideal solution, the relationship between
the partial vapour pressure, pi, of a
component i in the vapour phase and the
mole fraction of that component in solution,
xi, is expressed by Raoult’s law as
pi=pi
Øxi (eqn 1.3)
where pi
Ø is the vapour pressure of the pure
component.
Vapour pressure and solution
composition – Raoult’s law
Binary mixtures of the fluorinated
hydrocarbon aerosol propellants show
behaviour which approaches ideality.
Figure 1.2a shows the vapour pressure-
composition plots for a mixture of the
propellants 12 and 114.

6. Vapour pressure and solution
composition – Raoult’s law
Deviation from the Raoult’s law plot
does not exceed 5 percent.
In aerosol systems consisting of a
binary mixture of a propellant and a
solvent such as acetone or alcohol,
there is a pronounced departure from
ideal behaviour.
Vapour pressure and solution
composition – Raoult’s law
Figure 1.2b shows a large positive
deviation from the Raoults law plot for
mixtures of propellant 12 and ethanol.
Such positive deviations usually arise
when the attraction between molecules
of one component is greater than that
between the molecules of the two
components.
Vapour pressure and solution
composition – Raoult’s law
This form of interaction is referred to as
association.
Vapour pressure-concentration curves
for mixtures of two anaesthetic agents
also show positive deviations from
ideality (figure 1.3).

7. Vapour pressure and solution
composition – Raoult’s law
These are greatest for enflurane and at
least for halothane.
Such curves are of value in assessing
errors which may arise through the
incorrect usage of agent-specific
anaesthetic vaporisers.
Vapour pressure and solution
composition – Raoult’s law
As the name suggests, these vaporisers
are specifically calibrated for a
particular anaesthetic gas.
Vapour pressure and solution
composition – Raoult’s law
If a vaporiser partly filled with the
correct gas is mistakenly replenished
with another, then it is clear from figure
1.3. that, because of the facilitation of
vaporisation in the gas mixtures, more
of each agent will be delivered than
would be the case if ideal mixtures
were formed.

8. Vapour pressure and solution
composition – Raoult’s law
The clinical consequences of this error
will of course depend upon the
potencies of each agent as well as the
delivered vapour concentrations.
Another system which shows positive
deviation is the binary mixture of the
volatile drug, methylamphetamine, and
eucalyptol.
Vapour pressure and solution
composition – Raoult’s law
Combinations of these volatile
compounds are used in nasal
inhalations and an examination of the
vapour pressure of such systems is of
interest since the partial pressure
exerted by the drug in the presence of
other volatile constituents is a major
factor governing the dose delivered to
the patient.
Vapour pressure and solution
composition – Raoult’s law
The slight positive deviation from
Raoult’s law exhibited by this system
(figure 1.4) may be explained by
hydrogen bonding between the amine
groups of methylamphetamine
molecules.

9. Vapour pressure and solution
composition – Raoult’s law
Negative deviations from Raoult’s law
may arise when the specific attractions
between the component molecules
exceed the normal attractions which
exist between the molecules of each
pure component.
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