User:Mc2916

Introduction of Haber-Bosch process

Haber-Bosch process is a reaction that commonly used in industry to make ammonia by Nitrogen gas and Hydrogen gas. K2O, CaO, SiO2, and Al2O3 are usually used as catalyst to speed up the reaction. The reaction equation is as shown below

N2 + 3 H2 → 2 NH3 

A brief image describing how Haber-Bosch process work in industry.

NH3

Information about NH3 molecular

A Gaussview image of an optimised NH3 molecule.

NH3 optimisation

NH3 optimisation

Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
E(RB3LYP)	-56.55776873
Point Group	C3V

The bond length of NH3=101.2 Bond angle of NH3=106.7

         Item               Value     Threshold  Converged?
 Maximum Force            0.000004     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000072     0.001800     YES
 RMS     Displacement     0.000035     0.001200     YES
 Predicted change in Energy=-5.986295D-10

NH3 after optimisation

The optimisation file is liked to here

vibration of NH3

The vibrations of NH3

mode1	mode2	mode3
mode4	mode5	mode6

For NH3 molecule, 6 vibration modes are expected. In these 6 modes, mode1, mode2 and mode3 are banding vibrations while the rest 3 modes are stretching vibrations. Some modes have the special features, mode4 is highly symmetric, and mode1 is know as umbrella mode. Furthermore, some modes show similar energy levels, mode2 and mode3 are degenerate, mode5 and mode6 are degenerate. Four different energies are obtained from the vibration modes, therefore four bands are expected to be seen. However, in experiment only 3 peaks are observed in the spectra. The reason for this observation is due to only vibration that contains dipole can be detected. Among the four vibrations, mode4 doesn't have the dipole, then the peak is not shown on the spectra.

expenriment gaseous ammonia spectra

charge distribution of NH3

the charege distribution of NH3 molecule.

The charge of N is expected to be negative due to its high electronegativity, and H is expected to be positive dur to its low electronegativity.

N2

Information about N2 molecular

A Gaussview image of an optimised N2 molecule.

N2 optimisation

Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
E(RB3LYP)	-109.52412868
Point Group	D*H

The bond length of N2=1.10 Bond angle of NH3=180

         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000450     YES
 RMS     Force            0.000000     0.000300     YES
 Maximum Displacement     0.000000     0.001800     YES
 RMS     Displacement     0.000000     0.001200     YES
 Predicted change in Energy=-1.025171D-15

H2 after optimisation

The optimisation file is liked to here

vibration of N2

H2

Information about H2 molecular

A Gaussview image of an optimised H2 molecule.

H2 optimisation

Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
E(RB3LYP)	-1.17853936
Point Group	D*H

The bond length of N2=0.74 Bond angle of NH3=180

         Item               Value     Threshold  Converged?
 Maximum Force            0.000039     0.000450     YES
 RMS     Force            0.000039     0.000300     YES
 Maximum Displacement     0.000052     0.001800     YES
 RMS     Displacement     0.000073     0.001200     YES
 Predicted change in Energy=-2.025007D-09

H2 after optimisation

The optimisation file is liked to here

vibration of H2

Haber-Bosch reaction energy calculation

E(NH3)=-56.55776873
2*E(NH3)=-113.11553746	
E(N2)=-109.52412868
E(H2)=-1.17853936
3*E(H2)=-3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]=-0.0557907
Final ΔE is -0.06 KJ 

Since the result is negative, it is an exothermic reaction, the equilibrium is prefer to move to the right. In a conclusion, it is more stable in ammonia product.

F2

Information about F2 molecular

A Gaussview image of an optimised F2 molecule.

F2 optimisation

Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
E(RB3LYP)	-199.49825220
Point Group	D*H

The bond length of N2=1.42 Bond angle of NH3=180

         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000450     YES
 RMS     Force            0.000000     0.000300     YES
 Maximum Displacement     0.000000     0.001800     YES
 RMS     Displacement     0.000001     0.001200     YES
 Predicted change in Energy=-1.347176D-13

F2 after optimisation

The optimisation file is liked to here

vibration of F2

Charge distribution of F2

The charges on both F atom are zero due to they have the same electronegativity.

Molecular orbitals of F2

Molecular orbitals of F2

MO1 is a bonding orbital,it is 3σg which contributed by F2pzA - F2pzB. It is lower than the HOMO, and is occupied. Since the electron is occupied in this bongding MO, the stablisation of the bond increases	MO2is an antibonding orbital,it is 2πg* which is occupied by F2pxA - F2pxB. It is in HOMO orbital and is occupied by electrons. Since the electron is occupied in this antibongding MO, the stablisation of the bond decreases	MO3 is a bonding orbital. It is 1πu which is occupied by F2pxA + F2pxB. It is lower than the HOMO, and is occupied. Since the electron is occupied in this bongding MO, the stablisation of the bond increases
MO4 is an antibonding orbital, it is 2σu* and is occupied by F2sA - F2sB. It is lower than the HOMO, and is occupied. Since the electron is occupied in this antibongding MO, the stablisation of the bond decreases	MO5is a bonding orbital, it is 2σg which is occupied by F2sA + F2sB. It is lower than the HOMO, and is occupied. Since the electron is occupied in this bongding MO, the stablisation of the bond increases