Adventures in Thermochemistry James S. Chickos* Department of Chemistry and Biochemistry University of Missouri-St. Louis Louis MO 63121 E-mail: jsc@umsl.edu 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 + 298 𝑇 𝐶𝑝𝑑𝑇 Entropy as a function of temperature ((𝜕𝑆/𝜕𝑇)𝑝=𝐶𝑝/𝑇 S(𝑇) = 0 𝑇 𝐶𝑝/𝑇𝑑𝑇 = 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 _________________________________ 0.5 H2 + 0.5 Cl2  HCl -92 kJ HCl  H· + Cl· 432 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

ST(cr) = 0TtCp(I)/TdT + ΔcrcrHm/Tt + Tt298Cp(II)/TdT C7H6O2(s) + 7.5 O2(g) = 7 CO2(g) + 3 H2O (l) ΔcH = - 3228.1 kJ mol-1 7 CO2 = 7 C + 7 O2 ΔfH = 7(393.5) kJ mol-1 3 H2O = 3 H2 + 1.5O2 ΔfH = 3(285.8) kJ mol-1 ____________________________________________________________________________________ C7H6O2 = 7C + 3 H2 + O2 ΔHf = 383.9 kJ mol-1 7C + 3 H2 + O2 = C7H6O2 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

- Δ cUm(l) - Δ cHm(l) - Δ fHm(l) (kJ·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 - Δ cUm(l) - Δ cHm(l) - Δ fHm(l) (kJ·mol-1) 2-thiopheneacetic acid 4163.2±2.2 4169.4±2.2 330.4±2.4 methyl ester (l) 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 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) Cp So ΔHf C-H 1.74 12.9 -3.83 C-C 1.98 -16.4 2.73 C(H3)(C) 6.19 30.41 -10.2 C(H)(C3) -1.9 -12.07 4.54 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 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) Bond additivity: Cp298(g) = 120 J K-1mol-1 (exp, NIST) 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 Group additivity: [2 C(H3)(C) + 3 C(H2)(C2)] [2(-10.2) + 3(-4.93)]*4.184 = -147.2 kJ mol-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 Cp So ΔHf C-H 1.74 12.9 -3.83 C-C 1.98 -16.4 2.73 C(H3)(C) 6.19 30.41 -10.2 C(H2)(C2) 5.5 9.42 -4.93

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

Calculate Cp, So, and ΔHf for by bond and group additivity for: Cp So ΔHf C-H 1.74 12.9 -3.83 C-C 1.98 -16.4 2.73 C(H3)(C) 6.19 30.41 -10.2 C(H2)(C2) 5.5 9.42 -4.93 C(C4) 4.37 -35.1 0.5 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 Cp(g, 298) [16(1.74) + 6(1.98)] = 39.7 cal K-1mol-1 Lit. ΔHf = -49.27 kcal/mol So = 93.9 cal mol-1 K Cp (g) not known ΔfH o (298)/kJ mol-1 [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 [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 2,3-Dimethylbutane

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 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 [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) = -3.6±0.7

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) 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) 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.  

C12H27N triisobutylamine C8H12O bicyclo[3.3.0]octan-2-one (298.15 K) _____________________________________________________________________ C12H27N triisobutylamine C8H12O bicyclo[3.3.0]octan-2-one    (298.15 K) lit: 56.4 kJ mol-1 calcd: 56.6±2.8 kJ mol-1 [4.69]12+[3.0]+ [3.3] -3[2]}   (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 ΔvapH = 64.8 kJ mol-1 Group Additivity ΔvapH = 60.8 kJ mol-1 Bond Additivity: Bonds not all available Group Additivity: ΔvapH = 44.1 kcal mol-1