Chapter 2: Atomic Bonding

Exa 2.1

In [1]:
from __future__ import division
import math
#Python Ex2.1 Stability of molecule on bond dissociation energy:Page-61 (2010)

 
#Variable declaration
 

e = 1.6*10**-19;           # Electronic charge, C
N = 6.023*10**+23;            # Avogadro's number
#Absolute Electrical permitivitty of free space,
#coulomb square per newton per metre square
e0 = 8.854*10**-12;
Re = 3*10**-10;  # Equilibrium separation, m 
IE = 502;      # First ionization energy of A, kJ/mol
EA = 335;     # Electron affinity for atom B, kJ/mol
IS = 3*10**-10;  # Interatomic separation between A+ and B-, m


#Calculation

 # Potential energy at equilibrium separation of A+B- molecule, kJ/mol
Ue = -(e**2*N)/(4*math.pi*e0*Re*1*10**+3);
DE = Ue + IE - EA;  # Bond dissociation energy of A+B- molecule, kJ/mol

#Result

print"\nThe bond dissociation energy of A+B- molecule is :",round(DE)," kJ/mol"
if(DE<0):
  print "The molecule A+B- is stable.."
else: 
  print "The molecule A+B- is unstable.."   
 
The bond dissociation energy of A+B- molecule is : -295.0  kJ/mol
The molecule A+B- is stable..

Exa 2.2

In [2]:
from __future__ import division
import math
 #  Python  Code  Ex2.2  Conversion  of  eV  into  kcal/mol:  Page-64  (2010)
 
 
#Variable declaration
  
e  =  1.6*10**-19;                   #  Electronic  charge,  C
N  =  6.023*10**+23;                  #  Avogadro's  number
J  =  4.184*10**+3;        #  Joule's  mechanical  equivalent  of  heat
V  =  1;                       #  Potential  difference,  V

#Calculation

eV  =  e*V;          #  Energy  equivalent  of  1  electron-volt,  J
eVpm  =  eV*N;              #  Electron-volt  per  mole,  J/mol
Ecal  =  eVpm/J;      #  Energy  equivalent  of  1eV,  kcal/mole

#Result

print"\n1  eV  is  approximately  equal  to :",round(Ecal,2),"kcal/mol"
     
1  eV  is  approximately  equal  to : 23.03 kcal/mol

Exa 2.3

In [3]:
from __future__ import division
import math
 #  Python  Code  Ex2.3  Potential  energy  of  the  system  of 
# Na+  and  Cl-  ions:  Page-68  (2010)


 
#Variable declaration
 
e  =  1.6*10**-19;                         #  Electronic  charge,  C
ep_0  =  8.854*10**-12;#Absolute electrical  permittivity  of  free  space,  
#coulomb  square  per  newton  per  metre  square
Re  =  2*10**-10;#Equilibrium  separation  between  Na+  and  Cl-  ions,  m


#Calculations

#Potential energy of NaCl molecule at equilibrium  separation,  electron-volt
U  =  -e/(4*math.pi*ep_0*Re);


#Result

print"\nThe  potential  energy  of  NaCl  molecule  " 
print "at  equilibrium  separation5  is  :",round(U,1),"eV"

 
The  potential  energy  of  NaCl  molecule  
at  equilibrium  separation5  is  : -7.2 eV

Exa 2.4

In [4]:
from __future__ import division
import math
#Python CodeEx2.4Compressibility and ionic energy of NaCl crystal:Page-68(2010)

 
#Variable declaration
 

e  =  1.6*10**-19;                    #  Electronic  charge,  C
ep_0  =  8.854*10**-12; # Absolute  electrical  permittivity  of  free  space, 
# coulomb  square  per  newton  per  metre  square
Re  =  2.81*10**-10;#Equilibrium  separation  between  Na+  and  Cl-  ions,  m
A  =  1.7496;                                   #  Madelung  constant
n  =  9;#Power of R in the repulsive term of potential energy of two particles  
IP_Na  =  5.14;       #  Ionization  potential  of  sodium,  eV
EA_Cl  =  3.61;                   #  Electron  Affinity  of  chlorine,  eV


#Calculation

#  Compressibilty  of  NaCl  crystal,  metre  square  newton
K0  =  (72*math.pi*ep_0*Re**4)/((n  -  1)*A*e**2);
# Potential energy of NaCl molecule  at equilibrium  separation,electron-volt
U  =  -(A*e)/(4*math.pi*ep_0*Re)*(1-1/n);
U_bar  =  U/2;         #  Potential  energy  per  ion,  electron-volt
delta_E  =  IP_Na  -  EA_Cl;#Energy  required  to  produce  the  ion-pair,  eV
E_ion  =  delta_E/2;      #  Energy  required  to  produce  per  ion,  eV
C_E  =  U_bar  +  E_ion;           #  Cohesive  energy  per  ion,  eV


#Result

print"\nThe  compressibility  of  NaCl  crystal  is"
print round(K0*10**(11),2)*10**-11,"metre  square  newton"
print"\nThe  cohesive  energy  of  NaCl  crystal  is",round(C_E,2),"eV"
The  compressibility  of  NaCl  crystal  is
3.48e-11 metre  square  newton

The  cohesive  energy  of  NaCl  crystal  is -3.21 eV

Exa 2.5

In [5]:
from __future__ import division
import math
#Python CodeEx2.5 Potential energy and dissociation energy
# of a diatomic molecule:  Page-69  (2010)

 
#Variable declaration
 

e  =  1.6*10**-19;                       #  Electronic  charge,  C
A  =  1.44*10**-39;#Constant corrsponding to the attractive term 
# in  potential  energy,  joule  metre  square
B  =  2.19*10**-115; #  Constant  corresponding  to  the  repulsive  term  
#in  potential  energy,  joule  metre  raised  to  power  10


#Calculation

Re  =  (5*B/A)**(1/8);#Equilibrium  spacing  of  diatomic  molecule,  m
n  =  2;#Power of R in the attractive term of potential energy of two particles
m  =  10;#Power of R in the repulsive term of potential energy of two particles
D  =  A/(Re**2*e)*(1-n/m) #Dissociation  energy  of  diatomic  molecule,  eV


#Result

print"\nThe  equilibrium  spacing  of  diatomic  molecule  is"
print round((Re*10**10),2)*10**-10,"m"
print"\nThe  dissociation  energy  of  diatomic  molecule  is",round(D,3),"eV"

 
The  equilibrium  spacing  of  diatomic  molecule  is
4.08e-10 m

The  dissociation  energy  of  diatomic  molecule  is 0.043 eV

Exa 2.6

In [6]:
from __future__ import division
import math
 #  Python  Code  Ex2.6  Binding  force  and  critical  separation  of  
 #a  diatomic  molecule:  Page-69  (2010)
 
 
 
#Variable declaration
 
Re  =  3*10**-10;   #  Equilibrium  spacing  of  diatomic  molecule,  m
e  =  1.6*10**-19;            #  Electronic  charge,  C
n  =  2;#Power of R in the attractive term of potential energy of two particles
m  =  10;#Power of R in the repulsive term of potential energy of two particles


#Calculations

D  =  4*e;          #  Dissociation  energy  of  diatomic  molecule,  eV
Ue = -D;#Potential energy of diatomic molecule at equilibrium separation,joule
A  =  -(Ue*Re**n)/(1-n/m);#Constant corrsponding to the attractive  term
#  in  potential  energy,  joule  metre  square
B  =  A*Re**8/5; #  Constant  corresponding  to  the  repulsive  term 
# in  potential  energy,  joule  metre  raised  to  power  10
Rc  =  (55/3*B/A)**(1/8);  #  Critical  separation  between  the  nuclei,  m
F_min  =  -2*A/Rc**3*(1-(Re/Rc)**8);#  The  minimum  force  required  to
#  dissociate  the  moleule,  N


#Results

print "The constant A corresponding to " 
print "the attractive potential energy, in joule metre square, is :",A
print "The constant B corresponding to"
print"the repulsive potential energy,in joule metre raised to power 10,is:"
print round((B*10**115),2)*10**-115
print "The critical separation between the nuclei, in angstrom, is : "
round ((Rc*10**10),2)*10**-10
print "The minimum force required to dissociate the molecule,in N,is:"
print round((F_min*10**9),2)*10**-9

 
The constant A corresponding to 
the attractive potential energy, in joule metre square, is : 7.2e-38
The constant B corresponding to
the repulsive potential energy,in joule metre raised to power 10,is:
9.45e-115
The critical separation between the nuclei, in angstrom, is : 
The minimum force required to dissociate the molecule,in N,is:
-2.38e-09

Exa 2.7

In [7]:
from __future__ import division
import math
#Python Code Ex2.7Bond  formation Energy for K+ and Cl- ion pair:Page-70(2010)



#Variable declaration
 
eps_0  =  8.854*10**-12;# Absolute  electrical  permittivity  of  free  space,
#  coulomb  sqaure  per  newton  per  metre  square
e  =  1.6*10**-19;                 #  Electronic  charge,  C
IP_K  =  4.1;      #  Ionization  potential  of  potassium,  electron-volt
EA_Cl  =  3.6;    # Electron  affinity  of  chlorine,  electron-volt


#Calculations

delta_E  =  IP_K  -  EA_Cl; #  Net  energy  required  
#to  produce  the  ion-pair,  electron-volt
Ec  =  delta_E;  #  Coulomb  energy  equals  net  energy  required 
# to  produce  the  ion  pair,  in  electron-volt
 #  Since  Ec  =  -e/(4*%math.pi*eps_0*R),  solving  for  R
R  =  -e/(4*math.pi*eps_0*Ec);#Separation between K+ and Cl- ion pair,  m


#Results

print "The bond formation energy for K+ and Cl- ion pair, in eV, is : ",Ec
print"The separation between K+ and Cl- ion pair,in angstrom,is"
print round(R/(1*10**-10),2)

 
The bond formation energy for K+ and Cl- ion pair, in eV, is :  0.5
The separation between K+ and Cl- ion pair,in angstrom,is
-28.76

Exa 2.8

In [8]:
from __future__ import division
import math
 #  Python  Code  Ex2.8    Energy  liberated  during  electron  transfer
#  between  ions  of  a  molecule:    Page-71  (2010)



#Variable declaration
 
eps_0  =  8.854*10**-12; #  Absolute electrical permittivity  of  free  space,                                                       #  Electronic  charge,  C
R  =  5*10**-10; #  Separation  between  the  ions  M  and  X,  m
e=1.6*10**-19
IP_M  =  5;              #  Ionization  potential  of  M,  eV
EA_X  =  4;                       #  Electron  affinity  of  X,  eV


#Calculations

U  =  -e/(4*math.pi*eps_0*R); #  The  potential  energy  of  MX  molecule,  eV
delta_E  =  IP_M  -  EA_X;#The net energy required to produce the ion pair, eV
Er  =  delta_E  +  U;#Energy required to transfer an electron from M to X  eV

#Result

print"\nEnergy to transfer an electron from M to X atom=",round(Er,2)," eV"

 
Energy to transfer an electron from M to X atom= -1.88  eV