Calculate Standard Enthalpy of Formation and the Gibbs
Free Energy of Formation of Ethene in Gaussian)
liu anjun
June 4, 2012
Abstract
Abstract: The paper tells the knowledge of "Thermochemistry in Gaussian" ,
using the Gaussian calculation method which our teacher tell us to calculate the
enthalpy of formation of ethylene and compared with the experimental value.The
main purpose is to master the way to calculate the enthalpy of formation of sub-
stances,and in order to learn the physical and chemical properties of substances
more clearly.
keyword: Gaussian ethylene enthalpy of formation
Contents
1 Introduction
In order to learn "Introduction to Chemical Engineering Thermodynamics", We
are forced to learn Gaussian and the computational process, but until now I didnt
understand what the program said, and I think I will never comprehend how to use
it. What I can do is following the pace that somebody told me, I have so much
di�cult to �nish the tough homework, I have no capacity to get the knowledge. I
think completing the work like learning English, no matter how much time I cost
on it, I still cant catch it. I dont want to write the text liking an article because I
sincerely know little about what the Gaussian is, so the paper is no sense for me to
write like that. So I hope to learn the development of Gaussian at the activity.
In order to let the student who start to learn "Introduction to Chemical Engi-
neering Thermodynamics" understand physical properties and computational method
of Standard Enthalpy of Formation more clearly, this paper will use simply words
to introduce how to use computer to calculate Standard Enthalpy of Formation of
some substance, although the date is inaccurated, it is still is a good way to count
the enthalpy.
2 Methods and Process
2.1 Download"Thermochemistry in Gaussian", you also need to download a thing
called puttywhich you can search it on Google. Then let your teacher open a server
1
in the net, so every student can have chance to operate in the net.
2.2 Students load the sever and manger their own ID.
2.3 Load WWW.pubChem.com, input what you want to search for its coordi-
nate, it is on the top right corner, click on the SDF connect, you can �nd it.
2.4 What I get from the "pubchem" is:
C1 -0.6672 0.0000 0.0000
C2 0.6672 0.0000 0.0000
H1 -1.2213 -0.9290 0.0708
H2 -1.2212 0.9290 -0.0708
H3 1.2213 0.9290 -0.0708
H4 1.2213 -0.9290 0.0708
2.5 After loading, input pico, click enter button, you will into a manger desk,
click the words in the right order carefully.it is :
#b3lyp/6-31+g* opt freq
blank space
blank space
0,1
the 3D coordinate
2.6 Click "Ctrl O", save name like yixi.in
2.7 Click "Ctrl X", come back to the primitive desk.
2.8 Input "g09 yixi.out",the computer will calculate what you need.
waiting until you can entry words, it indicates that the work is �nished, you can
click "more yixi.out". then look for the date loke like this:
- Thermochemistry -
||||||-
Temperature 298.150 Kelvin. Pressure 1.00000 Atm.
Atom 1 has atomic number 6 and mass 12.00000
Atom 2 has atomic number 6 and mass 12.00000
Atom 3 has atomic number 1 and mass 1.00783
Atom 4 has atomic number 1 and mass 1.00783
Atom 5 has atomic number 1 and mass 1.00783
Atom 6 has atomic number 1 and mass 1.00783
Molecular mass: 28.03130 amu.
Principal axes and moments of inertia in atomic units:
Eigenvalues { 12.23787 60.49340 72.73126
X 0.00000 1.00000 0.00000
Y 1.00000 0.00000 0.00000
Z 0.00000 0.00000 1.00000
This molecule is an asymmetric top.
Rotational symmetry number 1.
Rotational temperatures (Kelvin) 7.07753 1.43179 1.19087
Rotational constants (GHZ): 147.47189 29.83369 24.81383
Zero-point vibrational energy 135528.6 (Joules/Mol)
32.39212 (Kcal/Mol)
Vibrational temperatures: 1236.72 1437.81 1443.18 1543.21 1825.79
(Kelvin) 2035.42 2185.71 2464.35 4535.19 4562.37
4643.76 4687.15
Zero-point correction= 0.051620 (Hartree/Particle)
2
Thermal correction to Energy= 0.054643
Thermal correction to Enthalpy= 0.055587
Thermal correction to Gibbs Free Energy= 0.029437
Sum of electronic and zero-point Energies= -78.520417
Sum of electronic and thermal Energies= -78.517394
Sum of electronic and thermal Enthalpies= -78.516450
Sum of electronic and thermal Free Energies= -78.542600
E (Thermal) CV S
KCal/Mol Cal/Mol-Kelvin Cal/Mol-Kelvin
Total 34.289 7.945 55.037
Electronic 0.000 0.000 0.000
Translational 0.889 2.981 35.927
Rotational 0.889 2.981 18.627
Vibrational 32.511 1.984 0.483
Q Log10(Q) Ln(Q)
Total Bot 0.288355D-13 -13.540072 -31.177168
Total V=0 0.159766D+11 10.203485 23.494393
Vib (Bot) 0.188189D-23 -23.725406 -54.629766
Vib (V=0) 0.104268D+01 0.018151 0.041795
Electronic 0.100000D+01 0.000000 0.000000
Translational 0.583338D+07 6.765920 15.579107
Rotational 0.262672D+04 3.419414 7.873491
2.9 According to the page 8-10 of Thermochemistry in Gaussian you can know
what the date meanings.
2.10 You can use the same way to get the hydrogen information. Using the
graphite and the hydrogen atom dates to calculate what you need.
3 Computational Process
3.1 Calculate standard enthalpy of formation and the Gibbs free energy of for-
mation of ethene in Gaussian
design equation: 2H2 + 2C ! C2H4
List the date which you need:(refer to table 1 in the page 12 ofThermochemistry
in Gaussian):
Table 1
H2 C(graphite) C2H4
�0 + �ZPE -1.165341 -37.851335 -78.520417
�0 + Etot -1.162980 -37.849918 -78.517394
�0 +Hcorrt -1.162036 -37.848974 -78.516450
�0 +Gcorrt -1.176828 -37.865880 -78.542600
Standard enthalpy of formation andthe Gibbs free energy of formation of Ethene:
4rH0(298K) =
P
("0 +Hcorr)products +
P
("0 +Hcorr)rectants
= (�78:516450� 2 � (�37:848974� 1:162036)) � 627:5095 � 4:186 = �1298:7kJ=mol
4rG0(298K) =
P
("0 +Gcorr)products +
P
("0 +Gcorr)rectants = (�78:542600� 2 �
(�37:865880� 1:176828)) � 627:5095 � 4:186 = �1200:9kJ=mol
But in the experimental value is 4rH0(298K) = 52:510kJ=mol;4rG0(298K) =
68:640kJ=mol
3
3.2 Break up the molecular to atoms, then composing the atom to calculate
standard enthalpy of formation and the Gibbs free energy of formation.
Table 2
H2 C(atom) C2H4
�0 -0.500273 -37.851335 0.054643
�ZPE 0.000000 0.000000 0.051620
Etot 0.001416 0.001416 -78.516450
Hcorrt 0.002360 0.002360 -0.055587
Gcorrt -0.010654 -0.014545 0.029437
�0 + �ZPE -0.500273 -37.851335 -78.520417
�0 + Etot -0.498857 -37.849918 -78.517394
�0 +Hcorrt -0.497912 -37.848974 -78.516450
�0 +Gcorrt -0.510927 -37.865880 -78.542600
4fH(0K) 51.63 169.98
H0(298K)�H0(0K) 1.01 0.25
3.2.1 Calculate the molar enthalpy of formation of 0K:
4fH0(C2H4; 0K) =
X
�"04f (0K)� (�"0(C2H4; 0K)) = 2 � 169:98 + 4 � 51:63�
627:5095 � (2 � (�37:851335) + 4 � (�0:500273)� (�78:520417)) = 34:02kcal=mol
3.2.2 Calculate the molar enthalpy of formation of 298K:
4fH0(C2H4;298K) = 4fH0(C2H4; 0K)+H0C2H4(298K)�H0C2H4(298K)�
P
�(H0x(298k)�
H0x(0K)) = 34:02 + 627:5095 � (0:055587 � 0:051620) � (2 � 0:25 + 4 � 1:01) =
31:96kcal=mol = 133:78kJ=mol
3.2.3 Calculate the molar Gibbs free energy:
4fG0(C2H4;298K) = 4fH0(C2H4; 298K)�298:15�(S0(C2H4; 0K)�
P
S0(x; 298k))
= 34:02+627:5095 � (0:055587� 0:051620)� (2 � 0:25+4 � 1:01) = 31:96kcal=mol =
133:78kJ=mol
But in the experimental value is 4rH0(298K) = 52:510kJ=mol;4rG0(298K) =
68:640kJ=mol. The di�erence is so big.
4 Conclusion
This paper use the simply algorithm of G09, the result is di�erent in page 425
ofIntroduction to Chemical Engineering Thermodynamics. But after a week painful
studying, letting me know it is di�cult for me to learn a new knowledge which I
have not touched before. Thank my teacher gave us a good chance to advance our
skills to live in the world.
5 Reference
[1]J.M.Smith,H.C.Van Ness,M.M.Abbott.Introduction to Chemical Engineer-
ing Thermodynamics,7th Ed[M].Chemical industry.Beijing.
November 11, 2007:425-427.
[2]JosephW,Ochterski, Ph.D.Thermochemistry in Gaussian[A].April 19,2000:8-
10.
[3]osephW,Ochterski, Ph.D.Thermochemistry in Gaussian[A].April 19,2000:8-
4
10.
[4]JosephW,Ochterski, Ph.D.Thermochemistry in Gaussian[A].April 19,2000:8-
10.
6 Appendix
The data of Graphite
||||||-
- Thermochemistry -
||||||-
Temperature 298.150 Kelvin. Pressure 1.00000 Atm.
Atom 1 has atomic number 6 and mass 12.00000
Molecular mass: 12.00000 amu.
Zero-point vibrational energy 0.0 (Joules/Mol)
0.00000 (Kcal/Mol)
Vibrational temperatures:
(Kelvin)
Zero-point correction= 0.000000 (Hartree/Particle)
Thermal correction to Energy= 0.001416
Thermal correction to Enthalpy= 0.002360
Thermal correction to Gibbs Free Energy= -0.014545
Sum of electronic and zero-point Energies= -37.851335
Sum of electronic and thermal Energies= -37.849918
Sum of electronic and thermal Enthalpies= -37.848974
Sum of electronic and thermal Free Energies= -37.865880
E (Thermal) CV S
KCal/Mol Cal/Mol-Kelvin Cal/Mol-Kelvin
Total 0.889 2.981 35.581
Electronic 0.000 0.000 2.183
Translational 0.889 2.981 33.398
Rotational 0.000 0.000 0.000
Vibrational 0.000 0.000 0.000
Q Log10(Q) Ln(Q)
Total Bot 0.490172D+07 6.690348 15.405096
Total V=0 0.490172D+07 6.690348 15.405096
Vib (Bot) 0.100000D+01 0.000000 0.000000
Vib (V=0) 0.100000D+01 0.000000 0.000000
Electronic 0.300000D+01 0.477121 1.098612
Translational 0.163391D+07 6.213227 14.306484
Rotational 0.100000D+01 0.000000 0.000000
The ate of hydrogen atom
||||||-
- Thermochemistry -
||||||-
Temperature 298.150 Kelvin. Pressure 1.00000 Atm.
5
Atom 1 has atomic number 1 and mass 1.00783
Molecular mass: 1.00783 amu.
Zero-point vibrational energy 0.0 (Joules/Mol)
0.00000 (Kcal/Mol)
Vibrational temperatures:
(Kelvin)
Zero-point correction= 0.000000 (Hartree/Particle)
Thermal correction to Energy= 0.001416
Thermal correction to Enthalpy= 0.002360
Thermal correction to Gibbs Free Energy= -0.010654
Sum of electronic and zero-point Energies= -0.500273
Sum of electronic and thermal Energies= -0.498857
Sum of electronic and thermal Enthalpies= -0.497912
Sum of electronic and thermal Free Energies= -0.510927
E (Thermal) CV S
KCal/Mol Cal/Mol-Kelvin Cal/Mol-Kelvin
Total 0.889 2.981 27.392
Electronic 0.000 0.000 1.377
Translational 0.889 2.981 26.014
Rotational 0.000 0.000 0.000
Vibrational 0.000 0.000 0.000
Q Log10(Q) Ln(Q)
Total Bot 0.795358D+05 4.900563 11.283963
Total V=0 0.795358D+05 4.900563 11.283963
Vib (Bot) 0.100000D+01 0.000000 0.000000
Vib (V=0) 0.100000D+01 0.000000 0.000000
Electronic 0.200000D+01 0.301030 0.693147
Translational 0.397679D+05 4.599533 10.590816
Rotational 0.100000D+01 0.000000 0.000000
The date of hydrogen
||||||-
- Thermochemistry -
||||||-
Temperature 298.150 Kelvin. Pressure 1.00000 Atm.
Atom 1 has atomic number 1 and mass 1.00783
Atom 2 has atomic number 1 and mass 1.00783
Molecular mass: 2.01565 amu.
Principal axes and moments of inertia in atomic units:
1 2 3
Eigenvalues { 0.00000 0.99310 0.99310
X 0.00000 1.00000 0.00000
Y 0.00000 0.00000 1.00000
Z 1.00000 0.00000 0.00000
This molecule is a prolate symmetric top.
Rotational symmetry number 2.
6
Rotational temperature (Kelvin) 87.21589
Rotational constant (GHZ): 1817.286482
Zero-point vibrational energy 26627.4 (Joules/Mol)
6.36410 (Kcal/Mol)
Vibrational temperatures: 6405.07
(Kelvin)
Zero-point correction= 0.010142 (Hartree/Particle)
Thermal correction to Energy= 0.012502
Thermal correction to Enthalpy= 0.013446
Thermal correction to Gibbs Free Energy= -0.001346
Sum of electronic and zero-point Energies= -1.165341
Sum of electronic and thermal Energies= -1.162980
Sum of electronic and thermal Enthalpies= -1.162036
Sum of electronic and thermal Free Energies= -1.176828
E (Thermal) CV S
KCal/Mol Cal/Mol-Kelvin Cal/Mol-Kelvin
Total 7.845 4.968 31.133
Electronic 0.000 0.000 0.000
Translational 0.889 2.981 28.080
Rotational 0.592 1.987 3.052
Vibrational 6.364 0.000 0.000
Q Log10(Q) Ln(Q)
Total Bot 0.415890D+01 0.618978 1.425251
Total V=0 0.192259D+06 5.283887 12.166600
Vib (Bot) 0.216317D-04 -4.664909 -10.741349
Vib (V=0) 0.100000D+01 0.000000 0.000000
Electronic 0.100000D+01 0.000000 0.000000
Translational 0.112481D+06 5.051078 11.630537
Rotational 0.170926D+01 0.232809 0.536063
7
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