Page 35 - Physical chemistry eng

12 CHAPTER 1 Fundamental Concepts of Thermodynamics

In Example Problem 1.4, a comparison is made of the molar volume for N 2 calcu-
lated at low and high pressures, using the ideal gas and van der Waals equations of state.

EXAMPLE PROBLEM 1.4

a. Calculate the pressure exerted by N 2 at 300. K for molar volumes of 250. L mol -1
and 0.100 L mol -1 using the ideal gas and the van der Waals equations of state.
6
The values of parameters a and b for N 2 are 1.370 bar dm mol -2 and
3
0.0387 dm mol -1 , respectively.
b. Compare the results of your calculations at the two pressures. If P calculated
using the van der Waals equation of state is greater than those calculated with the
ideal gas law, we can conclude that the repulsive interaction of the N 2 molecules
outweighs the attractive interaction for the calculated value of the density. A
similar statement can be made regarding the attractive interaction. Is the attrac-
tive or repulsive interaction greater for N 2 at 300. K and V m = 0.100 L ?

Solution
a. The pressures calculated from the ideal gas equation of state are
-1
-2
nRT 1mol * 8.314 * 10 L bar mol K -1 * 300. K
P = = = 9.98 * 10 -2 bar
V 250. L
-1
-2
nRT 1 mol * 8.314 * 10 L bar mol K -1 * 300. K
P = = = 249 bar
V 0.100 L
The pressures calculated from the van der Waals equation of state are
2
nRT n a
P = -
V - nb V 2
-2
-1
1mol * 8.314 * 10 L bar mol K -1 * 300. K
=
3
250. L - 1mol * 0.0387 dm mol -1
2
6
(1mol) * 1.370 bar dm mol -2
-
(250. L) 2
= 9.98 * 10 -2 bar
-1
-2
1mol * 8.314 * 10 L bar mol K -1 * 300 K
P =
3
0.100 L - 1mol * 0.0387 dm mol -1
6
2
(1mol) * 1.370 bar dm mol -2
-
(0.100 L) 2
= 270. bar
b. Note that the result is identical with that for the ideal gas law for V m = 250. L ,
and that the result calculated for V m = 0.100 L deviates from the ideal gas law
result. Because P real 7 P ideal , we conclude that the repulsive interaction is more
important than the attractive interaction for this specific value of molar volume
and temperature.

Vocabulary

absolute temperature scale Celsius scale elastic collision
adiabatic centigrade scale equation of state
Boltzmann constant closed system equilibrium
boundary diathermal extensive variable