If there is no experimental data available, are there any
other methods of estimating thermochemical data?
Group Additivity
ab initio calculations
molecular mechanics calculations
Reasons for the Development of Estimation Techniques
1. To provide a value for the property when no
experimental values are available
2. To provide a means of distinguishing between two or
more discordant experimental values.
3. The parameters generated by the estimation technique
may provide a handle to measure or understand some
molecular property that can not be measured directly.
4. As a diagnostic tool to identify and sometimes
quantify unusual interactions.
Question: Can thermochemical properties be subdivided
into small increments so that the total molecular
property in question can be calculated from the sum of
its parts?
1. How small can the increments be?
2. Are these group increments interchangable so that
they can be used to calculate similar properties of
distinctively different molecules?
3. What properties are subject to this treatment?
Some Thermochemical properties that have been
modeled by group additivity
1. Molecular weight
2. Atomic weight
3. Enthalpy of formation
4. Entropy of formation
4. Enthalpy of vaporization
5. Total phase change entropy
6. Heat capacity
7. Vapor pressure
Bond additivity
1. Bond Additivity: An assignment of a value
associated with each type of bond.
Group additivity
2. Values are associated with a series of atom
combinations is various structural environments.
Bond Additivity
Butane
C3H8 Hf(298) = 8 C-H + 2C-C
Hf(298) = [8(-3.83) + 2(2.73)]4.184
= -105.4 kJ mol-1
Hf(298)expt = -104.6 kJ mol-1
Bond Additivity
Butadiene
CH2=CH-CH=CH2
Hf(298) = 6 Cd-H + Cd-C
Hf(298) = [6(3.2) + 6.7]*4.184 = 109.4 kJ mol-1
Hf(298)expt = 110 kJ mol-1
Bond Additivity
Styrene
Hf(298) = 5 -H + -C +3 Cd-H
Hf(298) = 4.184[5(3.25) + 7.25 + 3(3.2)]
Hf(298) = 138.5 kJ mol-1
Hf(298)expt = 147.9 kJ mol-1
Benson’s Group Additivity
Values are assigned to groups based on their constitution
and on their neighboring environment
Group Additivity
Styrene
Hf(298) = 5 CB-(H) + CB-(Cd) + Cd-(Cd)(H)+ Cd-(H2)
Hf(298) = 4.184[5(3.3) + 5.68 + 6.78 + 6.26]
Hf(298) = 147.4 kJ mol-1
Hf(298)expt = 147.9 kJ mol-1
Group Additivity
Butane
Hf(298) = 2 C-(H)3(C) + 2 C-(H)2(C)2
Hf(298) = 4.184[2(-10.2) +2(-4.93)]
Hf(298) = -126.6
Hf(298)expt = -125.5
Group Additivity
Cyclobutane
Hf(298) = 4 C-(H)2(C)2
Hf(298) = 4.184[4(-4.93)] = -82.5
Hf(298)expt = 28.4
Hf(298) = -82.5-28.4 = -111 kJ mol-1
-CH2CH2CH2CH2- vs
CH2CH2
| |
CH2CH2
Hf(298) = strain energy in cyclobutane
Cp(g)
Calculation of heat capacity follows the same rules as
enthalpy.
What is the heat capacity of 2-methylhexane?
Cp(g)(298) = 3 C-(H)3C+3 C-(H)2(C)2 +C-(H)(C)3
Cp(g)(298) = 4.184[3(6.19) + 3(5.5) +4.54]
Cp(g)(298) = 165.7 J mol-1K-1
Entropy: (S(298)(g)
The calculation of entropy follows the same rules as for
enthalpy and heat capacity but has two additional
corrections.
Correction terms: (1) symmetry (-Rln)
(2) mixing (-Riniln(ni))
where ni refers to the mol fraction and  is the symmetry
number. The symmetry number is the number of identical
structures that can be obtained by a symmetry operation
such as rotation.
S(298) (g)
What is the entropy of 2-methylhexane?
S(298) (g) = 3 C-(H)3C+3 C-(H)2(C)2 +C-(H)(C)3 + corrections
S(298) (g) = 4.184[3(30.41)+3(9.42)-12.07] + corrections
S(298) (g) = 449.4
corrections = -3Rln(3) =-27.4
S(298) (g) = 449.4 - 27.4 = 422 J mol-1 K-1
S(298) (l)expt = 314.6, 315.1, 323.3
S(298) (l)
TB=363 K; Cp(l)=222.9J mol-1K-1;
Hv= 34.9 J mol-1K-1
S(298)(g) = S(298)(l) + Cp(l)lnTB/298) + Hv/TB +Cp(g)ln(298/TB)
S(298)(l) = S(298)(g) - [Cp(l)lnTB/298) + Hv/TB+Cp(g)ln(298/TB)]
S(298)(l) = 422 -[222.9ln(363/298)+34900/363+165.7ln(298/363)]
S(298)(l) = 314.6 J mol-1K-1
S(298) (l)expt = 314.6, 315.1, 323.3
What is the entropy of 3-methylhexane?
S(298) (g) = 3 C-(H)3C+3 C-(H)2(C)2 +C-(H)(C)3 + corrections
S(298) (g) = 4.184[3(30.41)+3(9.42)-12.07] + corrections
S(298) (g) = 449.4
corrections = -3Rln(3) =-27.4; +Rln(2)
S(298) (g) = 449.4 - 27.4 +5.76 = 427 J mol-1 K-1
S(298) (l)expt = 309.6
S(298) (l)
TB=364 K; Cp(l)=216.7J mol-1K-1;
Hv= 35.1 J mol-1K-1
S(298)(g) = S(298)(l) + Cp(l)lnTB/298) + Hv/TB +Cp(g)ln(298/TB)
S(298)(l) = S(298)(g) - [Cp(l)lnTB/298) + Hv/TB+Cp(g)ln(298/TB)]
S(298)(l) = 427 -[216.7ln(364/298)+35100/364+165.7ln(298/364)]
S(298)(l) = 320.4 J mol-1K-1
S(298) (l)expt = 309.6 J mol-1K-1
What is the enthalpy of formation of 3-methylhexane?
Hf(298)(g) = 3 C-(H)3C+3 C-(H)2(C)2 +C-(H)(C)3 + corrections
Hf(298)(g) = 4.184[3(-10.2)+3(-4.93)-1.9] + corrections
Hf(298)(g) = -197.9 + corrections
correction = 0.8*4.184
Hf(298)(g) = -194.5 kJ mol-1
Hf(298)(g)expt = -191.3  1.3
CH3
H2C
CH2
CH3
H
H
H
CH3
1 gauche interaction
Summary on Using Benson Group Values
1. Identify the groups: Hf, Cp, S
2. Add non-bonded interactions: Hf, Cp, S
3. Add symmetry and chirality considerations: S