Benson Model
Starting with simple linear and branched alkanes and alkenes the method works by collecting a large number of experimental heat of formation data (see: Heat of Formation table) and then divide each molecule up into distinct groups each consisting of a central atom with multiple ligands:
- X-(A)i(B)j(C)k(D)l
To each group is then assigned an empirical incremental value which is independent on its position inside the molecule and independent of the nature of its neighbors:
- P primary C-(C)(H)3 -10.00
- S secondary C-(C)2(H)2 -5.00
- T tertiary C-(C)3(H) -2.40
- Q quaternary C-(C)4 -0.10
- gauche correction +0.80
- 1,5 pentane interference correction +1.60
- in kcal/mol and 298 K
The following example illustrates how these values can be derived.
The experimental heat of formation of ethane is -20.03 kcal/mol and ethane consists of 2 P groups. Likewise propane (-25.02 kcal/mol) can be written as 2P+S, isobutane (-32.07) as 3P+T and neopentane (-40.18 kcal/mol) as 4P+Q. These four equations and 4 unknowns work out to estimations for P (-10.01 kcal/mol), S (-4.99 kcal/mol), T (-2.03 kcal/mol) and Q (-0.12 kcal/mol). Of course the accuracy will increase when the dataset increases.
the data allow the calculation of heat of formation for isomers. For example the pentanes:
- n-pentane = 2P + 3S = -35 (exp. -35 kcal/mol)
- isopentane = 3P + S + T + 1 gauche correction = -36.6 (exp. -36.7 kcal/mol)
- neopentane = 4P + Q = 40.1 (exp. 40.1 kcal/mol)
The group additivities for alkenes are:
- Cd-(H2) +6.27
- Cd-(C)(D) +8.55
- Cd-(C)2 +10.19
- Cd-(Cd)(H) +6.78
- Cd-(Cd)(C) +8.76
- C-(Cd)(H)3 -10.00
- C-(Cd)(C)(H)2 -4.80
- C-(Cd)(C)2(H) -1.67
- C-(Cd)(C)3 +1.77
- C-(Cd)2(H)2 -4.30
- cis correction +1.10
- alkene gauche correction +0.80
In alkenes the cis isomer is always less stable than the trans isomer by 1.10 kcal/mol.
More group additivity tables exist for a wide range of functional groups.
Read more about this topic: Heat Of Formation Group Additivity
Famous quotes containing the word model:
“...that absolutely everything beloved and cherished of the bourgeoisie, the conservative, the cowardly, and the impotent—the State, family life, secular art and science—was consciously or unconsciously hostile to the religious idea, to the Church, whose innate tendency and permanent aim was the dissolution of all existing worldly orders, and the reconstitution of society after the model of the ideal, the communistic City of God.”
—Thomas Mann (1875–1955)