IIT-JEE 2011 - Career Point

KEY CONCEPT
Physical
Chemistry
Fundamentals
GASEOUS STATE
& REAL GASES
Real Gases :
Deviation from Ideal Behaviour :
Real gases do not obey the ideal gas laws exactly
under all conditions of temperature and pressure.
Experiments show that at low pressures and
moderately high temperatures, gases obey the laws of
Boyle, Charles and Avogadro approximately, but as
the pressure is increased or the temperature is
decreased, a marked departure from ideal behaviour
is observed.
Ideal gas
p
V
Plot of p versus V of hydrogen, as
compared to that of an ideal gas
The curve for the real gas has a tendency to coincide
with that of an ideal gas at low pressures when the
volume is large. At higher pressures, however,
deviations are observed.
Compressibility Factor :
The deviations can be displayed more clearly, by
plotting the ratio of the observed molar volume V m to
the ideal molar volume V m,ideal (= RT/p) as a function
of pressure at constant temperature. This ratio is
called the compressibility factor Z and can be
expressed as
Z =
V
V
m
m,ideal
p
= RT
Vm
Plots of Compressibility Factor versus Pressure :
For an ideal gas Z = 1 and is independent of pressure
and temperature. For a real gas, Z = f(T, p), a
function of both temperature and pressure.
A graph between Z and p for some gases at 273.15 K,
the pressure range in this graph is very large. It can
be noted that:
(1) Z is always greater than 1 for H 2 .
(2) For N 2 , Z < 1 in the lower pressure range and is
greater than 1 at higher pressures. It decreases with
increase of pressure in the lower pressure region,
passes through a minimum at some pressure and then
H 2
increases continuously with pressure in the higher
pressure region.
(3) For CO 2 , there is a large dip in the beginning. In
fact, for gases which are easily liquefied, Z dips
sharply below the ideal line in the low pressure
region.
1.0
t = 0ºC
H 2
N 2
CH 4
ideal gas
CO 2
Z
0 100 200 300
p/101.325 bar
Plots of Z versus p of a few gases
This graph gives an impression that the nature of the
deviations depend upon the nature of the gas. In fact,
it is not so. The determining factor is the temperature
relative to the critical temperature of the particular
gas; near the critical temperature, the pV curves are
like those for CO 2 , but when far away, the curves are
like those for H 2 (below fig.)
Z
1.0
T 1 >T 2 >T 3 >T 4
ideal gas
0 200 400 600
p/101.325 kPa
T 4
T 3
T 2
Plots of Z versus p of a single gas
at various temperatures
Provided the pressure is of the order of 1 bar or less,
and the temperature is not too near the point of
liquefaction, the observed deviations from the ideal
gas laws are not more than a few percent. Under
these conditions, therefore, the equation pV = nRT
and related expressions may be used.
Van der Waals Equation of state for a Real gas
Causes of Deviations from Ideal Behaviour :
The ideal gas laws can be derived from the kinetic
theory of gases which is based on the following two
important assumptions:
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XtraEdge for IIT-JEE 33 MAY 2010