Transcript Thail 1 - University of Missouri

Adventures in Thermochemistry
James S. Chickos*
Department of Chemistry and Biochemistry
University of Missouri-St. Louis
Louis MO 63121
E-mail: [email protected]
Formation Enthalpies
Eads Bridge
1867-72
Estimations of Enthalpies and Entropies of Formation
Basic concept in Chemistry
1. Conservation of Mass
Basic concept in Thermochemistry
2. Conservation of Energy
Fundamental types of Energy
1. Kinetic energy
2. Potential energy
Basic Definitions in Thermochemistry
E = internal energy; ΔE = change in internal energy
H = E + PV;
ΔH = ΔE + Δ(PV);
ΔH = ΔE + P ΔV
For an exothermic process, H is negative;
In thermochemistry, usually we are usually dealing with heat; q
Reference Points: Elevation
The standard enthalpy of formation of a compound is the change of enthalpy
during the formation of 1 mole of the compound from its constituent elements, with
all substances in their standard states at 1 atmosphere (1 atm or 101.3 kPa) and
temperature 298.15 K.
Standard states are as follows:
For a gas: the hypothetical state it would have if it obeyed the ideal gas equation at a
pressure of 1 atm
For a solute present in an ideal solution: a concentration of exactly one mole per liter
(1 M) at a pressure of 1 atm.
For a pure substance or a solvent in a condensed state (a liquid or a solid): the
standard state is the pure liquid or solid under a pressure of 1 atm
Standard States of Reference Materials in Calorimetry
Enthalpy H varies with temperature.
At constant pressure, the change in enthalpy with temperature (𝜕𝐻/𝜕𝑇)𝑝 = 𝐶𝑝
H(𝑇) = H298 +
𝑇
𝐶 𝑑𝑇
298 𝑝
Entropy as a function of temperature ((𝜕𝑆/𝜕𝑇)𝑝 = 𝐶𝑝/𝑇
S(𝑇) =
𝑇
𝐶𝑝/𝑇𝑑𝑇
0
= Cpln(T2/T0)
Entropy is a measure of randomness and disorder. Together with enthalpy and
temperature, they are a mathematical method of predicting of whether a change,
a chemical reaction for example, is
possible to occur spontaneously.
ΔG = ΔH - T ΔS
if ΔG < 0, the process is thermodynamically possible
if ΔG > 0, the process is thermodynamically possible but the reverse process can
occur spontaneously
if ΔG = 0, the system is in equilibrium and not net change is thermodynamically
possible
If we burn methane in the open
CH4 +2O2
= CO2(g) + 2H2O(g)
heat given off q
In an enclosed container at 298.15
CH4 + 2O2
= CO2(g) + 2H2O(l)
more heat is given off
Why?
The final product is liquid water; it takes 40.65 kJ/mol to vaporize water (18 g)
In the open container, there is no change in volume, ΔH = q
However if the products were CO2 and liquid water, but carried out at constant pressure,
the enthalpy change for this process however would be –(q + 2(40.65) kJ/mol + 2RT )
What is the enthalpy of formation of different substances, how are they determined and
why are we interested in them?
Why the interest?
Used to evaluate bond energies
0.5 H2  H·
+218 kJ
0.5 Cl2 
Cl·
+122 kJ
HCl  0.5 H2 + 0.5 Cl2
92 kJ
_________________________________
HCl  H· + Cl·
432 kJ
0.5 H2 + 0.5 Cl2  HCl -92 kJ
The enthalpy of formation governs how much potential energy is is available
How is the enthalpy of formation of organic
compounds actually measured experimentally?
The bomb is charged with 3.0 MPa O2
From: Stull, Westrum & Sinke “The
Chemical Thermodynamics of Organic
Compounds
C7H6O2(s) + 7.5 O2(g) = 7 CO2(g) + 3 H2O (l) ΔcH = - 3228.1 kJ mol-1
7 CO2
3 H2O
= 7 C + 7 O2
= 3 H2 + 1.5O2
ΔfH = 7(393.5) kJ mol-1
ΔfH = 3(285.8) kJ mol-1
C7H6O2
= 7C + 3 H2 + O2
ΔHf =
____________________________________________________________________________________
7C + 3 H2 + O2 = C7H6O2
383.9 kJ mol-1
ΔHf (cr) = -383.9 kJ /4.184 kJ mol-1/kcal = -91.77 kcal mol-1
ST(cr) = 0TtCp(I)/TdT + ΔcrcrHm/Tt + Tt298Cp(II)/TdT
S(298.15 K)benzoic acid = 40.05 cal mol-1 K
ΔfS (298)(cr) = S(298.15 K)benzoic acid - [S (298)(7C)) + S (298)(3H2) + S (298)(O2)]
ΔfS (298)(cr) = 40.05 – [7(1.361) + 3(31.211+ (49.003)] = -112.11 cal-1 mol K-1
ΔfG (298) = ΔHf - T ΔSf (298) ΔfG(298)(cr)= -91.77 – (298.15)(-112.11) = -58.3 kcal mol-1
TABLE 3: Derived Standard (p° ) 0.1 MPa) Molar Values of
Substituted Thiopheneacetic Acid Methyl Esters in the
Condensed Phase, at T = 298.15 K
2-thiopheneacetic acid
methyl ester (l)
- Δ cUm(l)
(kJ·mol-1)
4163.2±2.2
- Δ cHm(l)
- Δ fHm(l)
4169.4±2.2
330.4±2.4
The combustion reaction was performed at constant volume. If carried out open to the
atmosphere and the products were the same:
Δ cHm = - Δ cUm(l) + PΔV;
For an ideal gas PΔV = nRT = -6.2 kJ·mol-1
M.V. Roux,* M. Temprado, R. Notario, J. S. Chickos, A. Filipa L. O. M. Santos and M.A.V. Ribeiro da Silva, J. Phys. Chem.
2007, 111, 5280-5286
Estimations of Enthalpies of Formation
An experiment as just described requires a great deal of patience, perseverance and
attention to detail. It is not a favorite of many chemists.
Estimations of Enthalpies of Formation
1. From first principles: ab initio calculations
These calculation require a theoretical chemist.
2. Bond additivity
It has been known for some time that the properties of large molecules can be
considered made up of the additive contribution of atoms or bonds. The physical
basis for this appears to be that the forces between atoms are fairly short range, of
the order of 1 to 3 Å.
3. Group additivity
Group additivity is based on the assumption that each group in the molecule
contributes a constant amount to the property being estimated. it was pioneered by
Sidney Benson, It is still probably the most widely used method for estimating
various thermochemical properties.
All simple groups methods generally provide approximate values. Efforts have been
made to improve the estimation by adding additional parameters. This has been
successful but at a cost. The beauty of group additivity has been its simplicity. By
introducing second and third order approximations, the complexity of the method
becomes a deterrent in its use.
Zero order
approximation
S. W. Benson and J. H. Buss
J. Chem. Phys. 1958, 29, 546
Cp
ΔHf
Soint
Cp
300
Entropy Correction
σ (symmetry number): If each atom was
numbered, the symmetry number would
provide the number of difference
arrangement of numbers that would produce
the identical structure
In most cases the correction is due to ring stain
Bond Additivity
ΔfH (g, 298) = -134.5±0.5 kJ mol-1 (exp, Stull)
S298 = 294.6 J K-1mol-1 (exp, Stull)
Cp(g, 298) = 98 J K-1mol-1 (exp, NIST)
10 CH + 3 C-C
ΔfH o (298) = [10*(-3.83) + 3(2.73)]*4.184 kJ mol-1 = -126 kJ mol-1 (calc)
S298 = [10*(12.9) + 3(-16.4) – 4*1.987*ln(3)]*4.184 kJ mol-1 = 306.5 J K-1 mol-1 (calc)
Cp (g, 300) = [ 10*1.74 +3(1.98)] *4.184 kJ mol-1 = 97.6 J K-1 mol-1 (calc)
Group Additivity
ΔHf o (298)/kJ mol-1
3 C(H3)(C) + 4 C(H)(C3)
[3*(-10.2) + 4*(-1.90] *4.184
ΔHf o (298) = -159.8 kJ mol-1
Cp
So
C-H 1.74 12.9
C-C 1.98 -16.4
C(H3)(C) 6.19 30.41
C(H)(C3) -1.9 -12.07
ΔHf
-3.83
2.73
-10.2
4.54
S298 = [3*(30.41) -12.07 – 4*1.987*ln(3)]*4.184 kJ mol-1 = 294.7 J K-1 mol-1 (calc)
Cp (l, 300) = [ 3*6.19 + (4.54)] *4.184 kJ mol-1 = 96.7 J K-1 mol-1 (calc)
CH3CH2CH2CH2CH3
ΔHf o (298) = -147.1 kJ mol-1 (exp, NIST)
S298 = 347.8 J K-1mol-1 (exp, NIST)
Cp298(g) = 120 J K-1mol-1 (exp, NIST)
Bond additivity:
ΔfH o (298)/kJ mol-1
12 CH + 4 C-C
[12(-3.83) + 4(2.73)]*4.184 = -146.6 kJ mol-1
So (298) J mol-1 K-1
12 CH + 4 C-C – Rln(σ)
[12(12.9) + 4(-16.4) - 2Rln(3) - Rln(2)]*4.184 = 349.2 J K-1mol-1
Cp(g, 298) [12(1.74) + 4(1.98)] = 28.8*4.184 = 120.5 J K-1mol-1
Cp
So
ΔHf
Group additivity:
C-H
1.74 12.9 -3.83
ΔfH o (298)/kJ mol-1
C-C
1.98 -16.4
2.73
[2 C(H3)(C) + 3 C(H2)(C2)]
C(H3)(C) 6.19 30.41 -10.2
[2(-10.2) + 3(-4.93)]*4.184 = -147.2 kJ mol-1
C(H2)(C2) 5.5 9.42 -4.93
So (298) J mol-1 K-1
2 C(H3)(C) + 3 C(H2)(C2)
[2(30.41) + 3(9.42) - 2Rln(3) –Rln(2)]*4.184 = 348.7 J K-1mol-1
Cp(g, 300
[2(6.19) +3(5.5)]*4.184 = 120.8
σ (symmetry number): If each atom was numbered, the symmetry number would
provide the number of difference arrangement of numbers that would produce the
identical structure
ΔHf o (298) = -312.4±2.8 kJ mol-1 (exp, NIST)
S298 = 326.3 J K-1mol-1 (exp)
Cp(g, 298) = 113.6 J K-1mol-1 (exp, NIST)
Bond additivity:
ΔHf o (g,298)/kJ mol-1
[9 CH + 3 C-C + C-O +O-H]
[9(-3.83) + 3( 2.73) - 12 - 27] *4.184 kJ mol-1 = -273.1
\ So (298) J mol-1 K-1
[9 CH + 3 C-C + C-O +O-H - Rln(σ)]
[9(12.9) + 3(-16.4) - 4 + 24 - 4*Rln(3)]*4.184 = 327.1 J K-1mol-1
Cp(g, 298) J K-1mol-1
[9(1.74+3*1.98+2.7+2.7] *4.184 = 113.0 J K-1mol-1
Group Additivity
ΔHf o (298) = [3* C(H3)(C) + C(C3)(O) + O(H)(C)]
= [3(-10.2) + (-6.6 - 37.9] *4.184 kJ mol-1 = -314.2 kJ mol-1
So (298) J mol-1 K-1
= [3(30.41) - 33.56 29.07 - 4Rln(3)]*4.184 = 326.4 J K-1mol-1
Cp(g, 298) J K-1mol-1
= [3(6.19) + 4.33 + 4.3]*4.184 = 113.8 J K-1mol-1
Cp
C-H
1.74
C-C
1.98
C(H3)(C) 6.19
C(H2)(C2) 5.5
C(C4)
4.37
So
12.9
-16.4
30.41
9.42
-35.1
ΔHf
-3.83
2.73
-10.2
-4.93
0.5
Calculate Cp, So, and ΔHf for by bond and group
additivity for:
ΔfH o (298)/kJ mol-1 16 CH + 6 C-C
[16(-3.83) + 6(2.73)] = -44.9 kcal mol-1
So (298) J mol-1 K-1
16 CH + 6 C-C – 5Rln(σ)
[16(12.9) + 6 (-16.4) - 5Rln(3)] = 97.1 cal K-1mol-1
Lit.
-1
-1
Cp(g, 298) [16(1.74) + 6(1.98)] = 39.7 cal K mol
ΔHf = -49.27 kcal/mol
So = 93.9 cal mol-1 K
ΔfH o (298)/kJ mol-1
Cp (g) not known
[4 C(H3)(C) + 2 C(H2)(C2) + C(C4)]
[4(-10.2) + 2(-4.93) + 0.5 ] = -50.1 kcal mol-1
So (298) J mol-1 K-1
[4(30.41) + 2(9.42) -35.1 - 5Rln(3)] = 94.5 cal K-1mol-1
Cp(g, 300)
[4(6.19) +2(5.5) + 4.37] = 40.13 cal K-1mol-1
ΔHf o (298) = - 177.8 ±1.0 kJ mol-1 (exp, NIST)
S298 = 365.7 J K-1mol-1 (exp, Stull)
Cp(g, 298) = 139.4 J K-1mol-1 (exp, NIST)
Bond additivity:
ΔfH o(g, 298)/kcal mol-1
14 CH + 5 C-C + 2 gauche interactions
2,3-Dimethylbutane
[14(-3.83) + 5( 2.73) + 2(0.8)]*4.184 = -160.7 kJ mol-1
So (g,298) J mol-1 K-1
[12 CH + 5 C-C – Rln(σ)]
[12(12.9) + 5(-16.4) - 4Rln(3) –Rln(2)] = 370.2 J K-1mol-1
Cp(g, 298) J K-1mol-1
[12(1.74) + 5(1.98)]*4.184 = 128.8 J K-1mol-1
Group additivity:
ΔfH o (g,298)/kJ mol-1
4 C(H3)(C) + 2 C(H)(C3) + 2 gauche interactions
[4(-10.2) + 2(-1.9) + 2(0.8)]*4.184 = -179.9 kJ mol-1
So (298) J mol-1 K-1
4 C(H3)(C) + 2 C(H)(C3) – Rln(σ)
[4( 30.41) + 2(9.42) - 4Rln(3) –Rln(2)]*4.184 = 365.6 J K-1mol-1
Cp(g, 300) J K-1mol-1
[4(6.19) + 2(4.54)]*4.184 = 141.6 J K-1mol-1
σ (symmetry number): If each atom was numbered, the symmetry number would provide
the number of difference arrangement of numbers would provide the identical structure
ΔHf o (g,298) = -172.3 kJ mol-1 (exp, Pedley)
S298 = 374.3 J K-1mol-1 (exp, NIST)
Cp(g, 298) = 151.2 J K-1mol-1 (exp, NIST)
Bond additivity:
cis 1,2-Dimethylcyclohexane
ΔfH o(g, 298)/ kJ mol-1
8 C-C + 16 C-H + cis and gauche corrections
[8(2.73) + 16(-3.83) + 1 + 0.9]*4.184 = -157 kJ mol-1
So (298) J mol-1 K-1
[8(-16.4) + 16(12.9) – 2Rln(3) +18.8] = 371.7 J K-1mol-1
Cp(g, 298) J K-1mol-1
[8(1.98) + 16(1.74) – 5.8]*4.184 = 158.5 J K-1mol-1
Group additivity:
ΔHf o (298)/ kJ mol-1
2 C(H3)(C) + 4 C(H2)(C2) + 2 C(H)(C3) + cis + gauche corrections
[2(-10.2) + 4(-4.93) + 2(-1.9) + 1 + 0.8 ]*4.184 = -176.2 kJ mol-1
So (298) J mol-1 K-1
2 C(H3)(C) + 4 C(H2)(C2) + 2 C(H)(C3) – Rln(σ) + ring corr
[2( 30.41) + 4(9.42) + 2*(-12.07) - 2Rln(3) + 18.8]*4.184 = 371.5 J K-1mol-1
Cp(g, 298) J K-1mol-1
[2( 6.19) + 4(5.5) + 2*(4.54) - 5.8]*4.184 = 157.6 J K-1mol-1
S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O'Neal, A. S. Rodgers, R. Shaw, and R.
Walsh, Chem . Rev. 69 (1969) 279-324.
Isodesmic Reactions
An isodesmic reaction is a chemical reaction in which the type of chemical bonds
broken in the reactant are the same as the type of bonds formed in the product. This is
usually a hypothetical reaction in thermochemistry.
A homodesmic reaction is a reaction in which the type of bonds broken in the
reactants are the same as the type of bonds formed in the reaction product.
Reactants - Products
ΔHf o (g, 298)/kJ mol-1 = (50.1±0.3)
(29.2±0.5)
(82.9±0.3)
(-3.2±1.3)
(-1.8±1.1) kJ mol-1
ΔHf
o (g,
298)/kJ
mol-1
= (50.1±0.3) + (29.2±0.5) – (82.9 ±0.3)
= -3.6±0.7
(1.3±1.0) kJ mol-1
Δ fHm(l) = (330.4±2.4 ) kJ mol-1
Δ vapHm(l) = ?
Δ fHm(cr) = -383.9 kJ kJ mol-1
Δ subHm(l) = ?
Δ vapHm(l), Δ subHm(cr) can be measured directly
ΔsubHm(298.15) can be obtained from = ΔvapHm(l,298) + Δ fusHm(298)
Fusion enthalpies are measured at the melting temperature and vaporization
enthalpies are frequently measured above 298 K over a range of temperatures
How does one measure vaporization enthalpies or sublimation enthalpies and
since enthalpies are a function of temperature, how does one adjust them to a
common or standard temperature (298.15 K)?
In future periods we will discuss about how some of these measurements are made
as well as some of the efforts directed toward estimating them.
Are there methods for estimating vaporization and sublimation enthalpies?
Vaporization Enthalpies
There are numerous method for estimating vaporization enthalpies ranging from
additivity methods from either less sophisticated to more sophisticated methods.
The method chosen depends on the purpose of the estimation.
Tb boiling
temperature and
ΔvapHm is the
vaporization at the
boiling temperature
What is critical
temperature and
critical pressure?
Guthrie, J. P.; Tylor, K. F. Can. J.
Chem. 1983, 61 602
Bond Method
ΔvapH = 6*(CB-CB) + 5*CB-H + CB-C + 3 C-H
ΔvapH = [6*0.72+ 5*0.6+.49+3*.43]*4.184 = 38.1. kJ mol-1 (lit 37.9)
Group Method
5 CB-H + CB-C + CH3(X)
[5*1.34 + 1.11 + 1.36]*4.184 = 38.4 kJ mol-1
Bond Method
ΔvapH = 9*(C-C) + 27*C-H + 3C-N
ΔvapH = [9*0.31 + 27*0.43 + 3*0.36]*4.184 = 64.8 kJ mol-1 (lit 56.4)
N
Group Method
6 CH3(X) +3 CH(C)3 + 3 CH2(C)(N) + N(C)3
[6*1.36 + 3*0.73 + 3*0.43 + 2.88]*4.184 = 60.8 kJ mol-1 (lit 56.4)
O
Group Method
4 CH2(C)2 + CH(C)3 + CH2CCO + CH(C)2CO + CO(C)2
[4*1.21 + 0.73 + 0.37 – 0.18 – 1.01 +4.79]*4.184 = 44.1 kJ mol-1
Simple Methods
Hydrocarbons:
ΔvapH (298) = (4.69±0.8)(nC – nQ) + 1.3 nQ + (3.0±0.2)
± 5% Good to up to 15-20 carbon atoms
ΔvapH (298) = [4.69*7 + 3] = 35.8±1.8 kJ mol-1 (lit. 37.9)
Monosubstituted Hydrocarbon Derivatives Containing O, N, S heteroatoms
ΔvapH (298) = (4.69±0.8)(nC – nQ) + 1.3 nQ + (3.0±0.2) + b + C
nC = number of carbon atoms
nQ = number of quaternary carbon atoms
b = function group value
C = corrections
a Enthalpy
increment to b for functional groups on rings; one correction per molecule ;
bbranching and ortho alkyl branching corrections are applied for each carbon branch;
branching due to an acyclic quaternary carbon center is counted as one branch; branching
due to a cyclic quaternary carbon center is ignored; a branch resulting from attachment of a
functional group is ignored.
O
N
_____________________________________________________________________
C12H27N triisobutylamine
 (298.15 K)
 vap Hm
lit: 56.4 kJ mol-1
calcd: 56.6±2.8 kJ mol-1
[4.69]12+[3.0]+
[3.3] -3[2]}
Bond Additivity
ΔvapH = 64.8 kJ mol-1
Group Additivity
ΔvapH = 60.8 kJ mol-1
C8H12O bicyclo[3.3.0]octan-2-one

 vap Hm
(298.15 K)
cis lit: 54.4 kJ mol-1
trans lit: 53.6 kJ mol-1
calcd: 53.9±2.7 kcal mol-1
{[4.69]8+[3.0]+[10.5]
+[2.9]}
Bond Additivity:
Bonds not all available
Group Additivity:
ΔvapH = 44.1 kcal mol-1