Chapter2: Properties of Gases

1
Chapter2 Properties of Gases

• Kinetic Molecular Model
• Speed of gas
• Combining Kinetic Molecular Model and Ideal gas
  Law
• Real gas
• Virial equation
• PV-plot for real gas
• Van der Waals equation
• Comparing ideal and real gas

2
Kinetic molecular model of Gases

• Assumption
• 1) gas molecules in ceaseless random motion ( no
  phase change)
• 2) molecular size is negligible (no repulsion)
• 3) molecules do not interact (no attraction)
• All gases at same T and P have the same
  properties

3

• Definition of pressure
• gas pressure is caused by collective collision
  of gas molecules with containers wall

4
gas molecule has mass m and velocity v
5
Let V Volume of container and N Number of
molecules At equilibrium N/2 travel left with
IvI speed N/2 travel
right with -IvI speed Number of molecules that
hit wall per second number of molecules at
distance IvxI from walls In volume V there are
N molecules
IvxIA there are NIvxIA
V A ? surface area of a wall
6
force exerted on right wall per second F
1 NvxA (2 mvx) 2 V only 1
NvxA hit right wall (N/2 out of N travel
right) 2 V F mNvx2A V P
F Nmvx2 A V
7

• Vetcor v can be written as
• v vx i vy j vz k
• c2 v2 vx 2 vy 2 vz 2
• c gas speed
• assume velocity in all 3 axes are equal
• vx vy vz
• or c2 3 vx 2
• vx 2 1/3 c2
• P 1 Nmc2
• 3 V
• or PV 1/3Nmc2 n number of
  moles
• 1/3nMc2 M molar
  mass

8
Speed of gas
every gas does not travel at the same speed
The Maxwell distribution of speeds and its
variation with the temperature.
9
Average velocity
wil ? frequency (weight)
root mean square (rms) velocity
More accurate than average if molecules do not
travel in same direction most probable velocity
(highest population) vmp
10

• Maxwell distribution of gas velocity
• distribution of gas speed can be presented by a
  mathematical function call Maxwell distribution

11
(No Transcript)
12
(No Transcript)
13
Combining Kinetic Molecular Model and Ideal Gas
Law average kinetic energy from
equipartition theory thus
14
from
Ideal gas Law
15

• Real gas
• molecules not always in motion (condense phase
  can be formed)
• molecular size is non-negligible (there is
  molecular repulsion)
• Molecules do interact (there is molecular
  attraction)

16
- Compression factor (Z)
Vm molar volume or volume per mole If Z lt 1
molar volume of real gas is less than ideal gas
molecular attraction is dominant Z gt 1 molar
volume of real gas is larger than ideal gas
molecular repulsion is dominant Substitute
17
The variation of the compression factor, Z, with
pressure for several gases at 0 oC
18

• Equation of state
• is equation that represents the state of
  system
• Ideal gas equation is the equation of state for
  gas

19
Virial equation

• in search for equation of state for real gas,
  one looks at P dependent of Z

or
Since
and are 2nd, 3rd, , virial
coefficient respectively
20
Replacing Z by
virial equation of state
virial coefficients vary with gas type So does
the virial equation of state
21
PV plot for real gas
The experimental isotherms of CO2 at several
temperatures.
22
Critical constants
23

• Reduced properties

The compression factors of four gas.
24
Van der waals equation another attempt to find
equation of state for real gas To correct whats
wrong in kinetic molecular model, Van der waals
proposed
molecular attraction reduces impact force to wall

• volume of gas is the space where gas can travel
  in a container
• Ideal gas has no molecular volume, volume of gas
  is volume of container
• real gas has molecular volume (repulsion), space
  that gas can travel is
• less than volume of container

25
(rate of collision) x (impact force
P
Attraction reduces rate of collision and impact
force Reduction in pressure (due to attraction)
From ideal gas equation
26
real gas volume is less than ideal gas Given b
as molecular volume
Substitute V in (1) with V - nb
then
Van der waals s equation
a, b van der waals parameter (obtained from
experiment)
27
Since Van der Waals equation comes from
modification of kinetic molecular model (theory)
while a, b comes from experiment Van der waals
equation is semi-empirical virial equation is
empirical
28
Van der waals parameters of gas.
29

• Van der waals loop

Isotherms calculated by using the van der waals
equation of state.
30
Comparing ideal and real gas V 10 L , n
1 mol

AIR 80N2 20O2
31
Example 2.1 Estimate the molar volume of CO2 at
500 K and 100 atm by treating it as a van der
waals gas.
From
32
must solve for roots of cubic equation
a 3.610 L2 atm mol-2 b 4.29 x 10-2 L mol-1
33
(No Transcript)
34
assume
Vm 0.366 L mol-1