Page 25 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:35 9in x 6in b985-ch01 Elementary Physical Chemistry

10 Elementary Physical Chemistry

b) Calculate the ratio of the rate of diffusion of

O 2 (M =32.0g mol −1 )to N 2 (M =28.0g mol −1 )
The ratio is proportional to the ratio of the speeds of the molecules, and
if P and T are the same for both molecules,

(D of O 2 /D of N 2 )= c (O 2 )/c(N 2 )= [3RT/M(O 2 )]/[3RT/M(N 2 )]

= [M(N 2 )/M(O 2)] = (28.0/32.0) = 0.95

1.11. Real Gases
So far attention was focused on ideal gases. From a molecular point of
view, ideal gases consist of molecules that do not attract or repel each
other. This is obviously unrealistic. In a real gas (even if the molecules
have no dipoles, quadrupoles, etc. or electrical charges), there are short-
range repulsive forces and long-range attractive forces, which invalidates
the ideal equation of state.

An equation of state that takes into account these interactions is the
a) van der Waals equation of state
2
2
(P +an /V )(V − nb) = nRT (1.22)
where a and b are constants.

Another equation of state is the
b) Virial equation of state

2
PV m = RT [1 + B/V m + C/V + ··· ] (1.23)
m
where V m is the molar volume of the gas, B the second virial coefficient,
C the third virial coefficient, etc.

Attractive forces are needed to account for liquefaction of gases. When a
compressed gas in a container is forced through a porous plug into another
where it is less compressed (the Joule–Thomson Experiment), the gas cools.
Why? In the compressed state the molecules are close to each other; there
is great attraction. In the dilute state, the molecules are farther apart.
Therefore, when the gas expands the attractive van der Waals bonds are
broken. It takes energy to do that. The energy comes from the gas — the
gas cools!