Concise Physical Chemistry

c21 JWBS043-Rogers September 13, 2010 11:30 Printer Name: Yet to Come

356 PHOTOCHEMISTRY AND THE THEORY OF CHEMICAL REACTIONS

Solution 21.1 The term “G3(MP2) model chemistry” means that G3(MP2) calcu-

lations are used for all molecular and radical species. In the case of ethane, homolytic

cleavage of the C C bond

CH 3 CH 3 →2CH• 3

has adissocH^298 and a BDE:

BDE[CH 3 CH 3 ]=dissocH^298 [CH 3 CH 3 ]= 2 fH^298

[

CH• 3

]

−fH^298 [CH 3 CH 3 ]

= 2 H^298

[

CH• 3

]

−H^298 [CH 3 CH 3 ]

= 2 (− 39. 752873 )−(− 79. 646716 )= 0. 1410 Eh

= 88 .4 kcal mol−^1 = 370 .0kJmol−^1

Calculated enthalpies of formation of the molecule and radicals from the nuclei

and electronsH^298 can be substituted forfH^298 of the molecule and radicals in

Example 21.1 because the enthalpies of formation of the atoms cancel in the homolytic

cleavage reaction (they are the same for 2 CH• 3 as for CH 3 CH 3 ). The experimental

value for this BDE is 89.7 kcal mol−^1 = 375 .3kJmol−^1 , so the difference between

the experimental value and calculated value is 1.4%.

Example 21.2 An Isodesmic Reaction

Find the enthalpy of formation oftert-butylmethane (2,2-dimethylpropane) by an

isodesmic reaction using known values offH^298 (methane)=− 17 .8 kcal mol−^1

andfH^298 (ethane)=− 20 .1 kcal mol−^1.

Solution 21.2 Cheng and Li (2003) calculatedfH^298 ofn-tert-butyl methanes,

wheren=1, 2, 3, and 4. FindfH^298 of the simplest exampletert-butylmethane

(2,2-dimethylpropane). The isodesmic reaction is

CH 3

|

CH 3 −C−CH 3 +3CH 4 −→ 4C 2 H 6

|

CH 3

− 197. 35354 − 40. 42210 − 79. 65120

− 17. 8 − 20. 1

Computed values offH^298 are in the first line below the reaction, and experimental

values offH^298 for CH 4 and C 2 H 6 are in the second line.

On the reactant side, two alkanes have a total of 24 C H bonds and 4 C C bonds.

On the product side, one molecule has a total of 4(6)=24 C H bonds and 4(1)=

4CC bonds. The reaction is isodesmic because the number and types of bonds on