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l09 - CH 203 O R G A N I C C H E M I S T R Y I Homodesmotic...

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Homodesmotic reactions © Bruno I. Rubio 1 CH 203 O R G A N I C C H E M I S T R Y I Homodesmotic reactions Homodesmotic reactions Homodesmotic reactions are hypothetical reactions used to calculate strain energy. The technique involves setting up a reaction where a strained mole- cule is transformed into a molecule that has no strain. The standard enthalpy ! H º r of a homodesmotic reaction is a measure of strain. A homodesmotic reac- tion has the following constraints: (1) It must be stoichiometrically balanced. (2) The molecule whose E strain is being calculated must be the only strained species in the reaction. (3) The number and type (e.g., Csp 3 –Csp 3 " , Csp 3 –H1s " , Csp 2 –Csp 2 # , Csp 2 –H1s " , etc.) of all bonds must be conserved. (4) The number of methyl (CH 3 ), methylene (CH 2 ) and methine (CH) groups must be conserved. The constraints are enforced so that the quantity being calculated reflects strain energy only, and not bond energy. Calculating the strain energy of monocyclic cycloalkanes Let’s set up a homodesmotic reaction to calculate the strain energy of cyclo- hexane. The basic idea is this: cyclohexane $ something with no strain A good choice for “something with no strain” would be a straight-chain al- kane. Because cyclohexane has six CH 2 groups and because the number of CH 2 groups must be conserved, an appropriate choice of straight-chain alkane might be octane: H 3 C CH 3 6 Csp 3 –Csp 3 " 7 Csp 3 –Csp 3 " 12 Csp 3 –H1s " 18 Csp 3 –H1s " 6 alkane CH 2 6 alkane CH 2 0 CH 3 2 alkane CH 3
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Homodesmotic reactions © Bruno I. Rubio 2 On the left-hand side of the equation we now need a molecule that has two strain-free CH 3 groups; a molecule of ethane fits the bill perfectly: H 3 C CH 3 + H 3 C CH 3 6 Csp 3 –Csp 3 " 1 Csp 3 –Csp 3 " 7 Csp 3 –Csp 3 " 12 Csp 3 –H1s " 6 Csp 3 –H1s " 18 Csp3–H1s " 6 alkane CH 2 0 alkane CH 2 6 alkane CH 2 0 alkane CH 3 2 alkane CH 3 2 alkane CH 3 The reaction is now balanced and homodesmotic. It will truly calculate the strain of cyclohexane because cyclohexane is the only strained molecule in the reaction. We perform a Hess’s Law computation using standard enthalpy of formation ! H º f values: H 3 C CH 3 + H 3 C CH 3 ! H º f –123 kJ/mol –85 kJ/mol –208 kJ/mol ! H º r = (–208 kJ/mol) – (–123 kJ/mol) – (–85 kJ/mol) = 0 kJ We arrive at the conclusion that cyclohexane has no strain! Cyclohexane puck- ers into the chair conformation because it is strain–free. That cyclohexane has no strain will make setting up other homodesmotic reac- tions easier because we can use it as a source of strain-free alkane CH 2 groups. Problem Calculate the strain energy of cyclopropane ( ! H º f = 53 kJ/mol). Answer The basic idea is cyclopropane $ something with no strain The balanced homodesmotic reaction is
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Homodesmotic reactions © Bruno I. Rubio 3 1/2 3 Csp 3 –Csp 3 " 3 Csp 3 –Csp 3 " 6 Csp 3 –H1s " 6 Csp 3 –H1s " 3 alkane CH 2 3 alkane CH 2 ! H º f 53 kJ/mol –123 kJ/mol ! H º r
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