Part I
Methane Notes
1
Hydrogen
Electronegativity = 2.20 (Pauling scale)
Free Radius = 53 pm(1.000000000 bohr)
Covalent Radius = 31pm(0.585815056 bohr)
Vanderwalls Radius = 120 pm(2.267671186 bohr)
1.0.1
Molecular Hydrogen Data
The bond dissociation energy for molecular hydrogen is 436 kJ/mole
Conversion
Mathematica In:= Convert[(436000 Joule/Mole)/AvogadroConstant, ElectronVolt]
Mathematica Out:= 4.58812 eV
Therefore at the average interatomic distance of .7414 Angstroms the Zero
Point Vibrational Energy is:
1
2 ~ωH = 4.58812eV
This corresponds to the ultraviolet region at about 21.5041nm.
But the ionization potential of H2 is NISTl[1] averaged to 15.46946131 eV
The Methane appearance energy of H+ is NIST[1] averaged to 17.786 eV
H2 anion
Vibrational Zero Point Energy 2200.6cm−1 [2]
Vibration level 4401cm−1 [2]
2
Carbon
Electronegativity = 2.55 (Pauling scale)
Free Radius = 53 pm(1.000000000 bohr)
Covalent radius = 77(sp³) pm(1.455089011 bohr), 73(sp²) pm(1.379499972
bohr), 69(sp) pm(1.303910932 bohr)
Vanderwalls Radius = 170 pm(3.212534181 bohr)
2.0.2
3
Carbon Spectrum Data
Methane
1
Arm Lengths = 108.70 pm(2.05413215 bohr)
Arm Covalent radius = 77(sp³) pm(1.455089011 bohr)
Arm Angles = 109.5 degrees
Molar Mass = 16.0425 g/mol
3.1
sp3
orbital hybridization
The valence bond theory would predict, based on the existence of two half-lled
p-type orbitals (the designations px py or pz are meaningless at this point, as
they do not ll in any particular order), that C forms two covalent bonds, i.e.,
CH2 (methylene). However, methylene is a very reactive molecule (see also:
carbene) and cannot exist outside of a molecular system. Therefore, this theory
alone cannot explain the existence of CH4.The rst step in hybridisation is the
excitation of one (or more) electrons (we consider the carbon atom in methane,
for simplicity of the discussion):
The solution to the Schrödinger equation for this conguration is a linear
combination of the s and p wave functions, or orbitals, known as a hybridized
orbital. In the case of carbon attempting to bond with four hydrogens, four
orbitals are required. Therefore, the 2s orbital (core orbitals are almost never
involved in bonding) "mixes" with the three 2p orbitals to form four sp3 hybrids
(read as s-p-three).
2
In CH4, four sp3 hybridised orbitals are overlapped by hydrogen's 1s orbital,
yielding four (sigma) bonds (that is, four single covalent bonds). The four bonds
are of the same length and strength.
to
The actual space lling model appears to be
3
3.1.1
Methane Bond and Ionization Energy
Ionization Energy = 12.7 eV (one electron pair), 23 eV (three electron pairs)
Generally the CO bond is 410 kJ/mole
The Methyl Group C-H bond-dissociation energy is 439 kJ/mol
Conversion
Mathematica In:= Convert[(439000 Joule/Mole)/AvogadroConstant, ElectronVolt]
Mathematica Out:= 4.54991 eV
But the ionization potential of methane is NISTl[1] averaged to 12.84139286
eV
The Methane appearance energy of CH−
3 is NIST[1] averaged to 14.11866667
eV
3.1.2
Methane Spectrum Data
1cm−1 = 2.99793 · 1010 Hz[12]
Symmetric Stretch v1 , A1
[7]
v1 , A1 = 2917cm−1 [7]
v1 , A1 = 3025.5cm−1 [12]
v1 , A1 = 2916.5cm−1 [9]
v1 , A1 = 3023.3cm−1 [10]
v4 , F2 = 1306cm−1 [7]
so 2917cm−1 → 8744.95MHz
NIST[12] and Widener[11] do not have v1 , A1
So using the Energies from above we can predict conditions for transition
state saturation in a bath of Methane and Hydrogen. Using the CH−
3 appearance
energy of 14.11866667 eV we can nd the temperature of a mixture of 1 mole of
Hydrogen with 1 mole of Methane. This corresponds to the ultraviolet region
at about 87.8158nm.
4
1
3
mv 2 = kT
2
2
At this energy Methane would have an avg. speed of 13,049.2m/s and Hydrogen would get 52,196.6 m/s. But really it's their relative kinetic energy we
want to match to 14.11866667 eV.
3.2
Reaction Rates
The geometries of the two modes v1 , A1 and v4 , F2 seen previously are postulated
to be the dominant modes in the SN2 reaction.
CH4 +H'=CH3 H'+H
In this case the following energies should be considered in experiment.
Form
Value
Symmetric Stretch Vibration mode v1 , A1
Wagging Bend Modev4 , F2
J [16]
Dissociation Energy of CH3 − H Methyl C-H bond 439, 000 mole
J [17]
C-H bond dissociation energy
410, 000 mole
J [17]
H-H bond dissociation energy
436, 000 mole
+
NIST Appearance energy for CH3
Appearance energy for H+
What I might have to study is
Wavenumber
2917cm−1
1306cm−1
113875cm−1
Crossed Molecula
0.0000361662
.0000161923e
4.54991 eV
4.24935 eV
4.51882 eV
12.84139286
17.786 eV
CH4 +D=CH3 D+H
Real Data for the reaction
CH4 +H=CH3− +H2
Activation = 7.4 ± 1.1kcal/mole(P5)
Steric Factor = 10−3 (P5)
That's only 1.25664% of the total spherical surface. Imagine keeping Zenith
constant at 1.44015 degrees and sweeping a cone around an axis with the azimuthal angle.
3.2.1
Reference Papers
1. Mechanism of isotope exchange reaction between methane and deuterium
(a) http://onlinelibrary.wiley.com/doi/10.1002/kin.550080112/abstract?systemMessage=Wiley+Online
14+BST+for+monthly+maintenance
2. THE REACTION OF DEUTERIUM ATOMS WITH METHANE AT
HIGH TEMPERATURES
5
(a) http://www.nrcresearchpress.com/doi/abs/10.1139/cjr37b-029?journalCode=cjr
3. Mechanism for the catalytic exchange of methane with deuterium on
Pt(111) surfaces
(a) http://www.springerlink.com/content/m6kk705752605067/
4. Calculation of reaction rate constants for hydrogendeuterium exchange
reactions of methane catalysed by acid zeolites
(a) http://pubs.rsc.org/en/content/articlelanding/2001/cc/b102249k/unauth
5. THE KINETICS OF THE REACTION OF ATOMIC HYDROGEN WITH
METHANE J. W. S. J A ~ ~ I E S O NAN D G. R. BROWN Departnze?lt
of Chenlistry, St. John's College, Utziversity of Manitoba, Winnipeg,
il6anitoba Received July 29, 1963
(a) http://www.nrcresearchpress.com/doi/pdf/10.1139/v64-247
Part II
References
References
[1] http://webbook.nist.gov/chemistry/
[2] http://webbook.nist.gov/cgi/cbook.cgi?ID=C74828&Mask=20
[3] http://cccbdb.nist.gov/exp2.asp?casno=1333740
[4] http://en.wikipedia.org/wiki/Hydrogen
[5] http://en.wikipedia.org/wiki/Carbon
[6] http://en.wikipedia.org/wiki/Methane
[7] http://en.wikipedia.org/wiki/Orbital_hybridisation
[8] http://physics.nist.gov/cgi-bin/MolSpec/mole.pl?prex=hydro&molecule=CH4
[9] http://courses.chem.psu.edu/chem210/mol-gallery/methanevib/methane-vibrations.html
[10] http://www.cfa.harvard.edu/hitran/vibrational.html
[11] http://icb.u-bourgogne.fr/omr/SMA/methane/vib_qt.html
[12] http://www2.ess.ucla.edu/~schauble/MoleculeHTML/CH4_html/CH4_page.html
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[13] http://science.widener.edu/svb/ftir/ir_ch4.html
[14] http://physics.nist.gov/cgi-bin/MolSpec/hydrosearch.pl?molecule=CH4&xCH4=1&lowerfreq=1&
[15] http://mccammon.ucsd.edu/~dzhang/energy-unit-convtable.html
[16] http://en.wikipedia.org/wiki/Bond-dissociation_energy#Tabulated_data
- Morrison & Boyd Organic Chemistry 4th Ed. ISBN 0-205-058388 - Blanksby, S. J.; Ellison, G. B.; (2003). "Bond Dissociation
Energies of Organic Molecules". Acc. Chem. Res. 36 (4): 255263.
doi:10.1021/ar020230d. PMID 12693923.
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