# Chapter 16: Kinetic Theory of Gases¶

## Example Problem 16.2, Page Number 400¶

In :
from math import sqrt

#Variable Declaration
R = 8.314         #Ideal Gas Constant, J/(mol.K)
T = 298           #Temperatureof Gas, K
MNe = 0.020       #Molecular wt of Ne, kg/mol
MKr = 0.083       #Molecular wt of Kr, kg/mol

#Calculations
vmpNe = sqrt(2*R*T/MNe)
vmpKr = sqrt(2*R*T/MKr)

#Results
print 'Most probable speed of Ne and Krypton at 298 K are %4.0f, %4.0f m/s'%(vmpNe,vmpKr)

Most probable speed of Ne and Krypton at 298 K are  498,  244


## Example Problem 16.2, Page Number 401¶

In :
from math import sqrt,pi

#Variable Declaration
R = 8.314         #Ideal Gas Constant, J/(mol.K)
T = 298           #Temperatureof Gas, K
M = 0.040         #Molecular wt of Ar, kg/mol

#Calculations
vmp = sqrt(2*R*T/M)
vave = sqrt(8*R*T/(M*pi))
vrms = sqrt(3*R*T/M)

#Results
print 'Maximum, average, root mean square speed of Ar\nat 298 K are %4.0f, %4.0f, %4.0f m/s'%(vmp,vave,vrms)

Maximum, average, root mean square speed of Ar
at 298 K are  352,  397,  431 m/s


## Example Problem 16.4, Page Numbe 403¶

In :
from math import sqrt,pi

#Variable Declaration
R = 8.314         #Ideal Gas Constant, J/(mol.K)
T = 298           #Temperature of Gas, K
M = 0.040         #Molecular wt of Ar, kg/mol
P = 101325        #Pressure, N/m2
NA = 6.022e23     #Number of particles per mol
V = 1.0           #Volume of Container, L

#Calculations
Zc = P*NA/sqrt(2*pi*R*T*M)
Nc = Zc*A
#Results
print 'Number of Collisions %4.2e  per s'%(Nc)

Number of Collisions 2.45e+27  per s


## Example Problem 16.5, Page Number 404¶

In :
from math import sqrt, pi

#Variable Declaration
R = 8.314         #Ideal Gas Constant, J/(mol.K)
T = 298           #Temperature of Gas, K
M = 0.040         #Molecular wt of Ar, kg/mol
P0 = 1013.25      #Pressure, N/m2
NA = 6.022e23     #Number of particles per mol
V = 1.0           #Volume of Container, L
k = 1.38e-23      #Boltzmann constant, J/K
t = 3600          #time of effusion, s
A = 0.01          #Area, um2

#Calculations
A = A*1e-12
V = V*1e-3
expo = (A*t/V)*(k*T/(2*pi*M/NA))
P = P0*exp(-expo)
#Results
print 'Pressure after 1 hr of effusion is %4.3e Pa'%(P/101325)

Pressure after 1 hr of effusion is 1.00e-02 Pa


## Example Problem 16.6, Page Number 407¶

In :
from math import sqrt, pi

#Variable Declaration
R = 8.314         #Ideal Gas Constant, J/(mol.K)
T = 298           #Temperature of Gas, K
M = 0.044         #Molecular wt of CO2, kg/mol
P  = 101325       #Pressure, N/m2
NA = 6.022e23     #Number of particles per mol
sigm = 5.2e-19    #m2

#Calculations
zCO2 = (P*NA/(R*T))*sigm*sqrt(2)*sqrt(8*R*T/(pi*M))
#Results
print 'Single particle collisional frequency is %4.1e per s'%(zCO2)

Single particle collisional frequency is 6.9e+09 per s


## Example Problem 16.7, Page Number 407¶

In :
from math import sqrt, pi

#Variable Declaration
R = 8.314         #Ideal Gas Constant, J/(mol.K)
T = 298           #Temperature of Gas, K
MAr = 0.04        #Molecular wt of Ar, kg/mol
MKr = 0.084       #Molecular wt of Kr, kg/mol
pAr  = 360        #Partial Pressure Ar, torr
pKr  = 400        #Partial Pressure Kr, torr
rAr = 0.17e-9     #Hard sphere radius of Ar, m
rKr = 0.20e-9     #Hard sphere radius of Kr, m
NA = 6.022e23     #Number of particles per mol
k = 1.38e-23      #Boltzmann constant, J/K

#Calculations
pAr = pAr*101325/760
pKr = pKr*101325/760
p1 = pAr*NA/(R*T)
p2 = pKr*NA/(R*T)
sigm = pi*(rAr+rKr)**2
mu = MAr*MKr/((MAr+MKr)*NA)
p3 = sqrt(8*k*T/(pi*mu))
zArKr = p1*p2*sigm*p3

#Results
print 'Collisional frequency is %4.2e m-3s-1'%(zArKr)

Collisional frequency is 3.14e+34 m-3s-1