Heats of combustion cycloalkanes

Figure 4.3 Cycloalkane strain energies, calculated by taking the difference between cycloalkane heat of combustion per CH2 and acyclic alkane heat of combustion per CH2, and multiplying by the number of CH2 units in a ring. Small and medium rings are strained, but cyclohexane rings are strain-free.

Cycloalkane Number of CH2 groups Heat of combustion per CH2 group... 

Conformational analysis is far simpler m cyclopropane than m any other cycloalkane Cyclopropane s three carbon atoms are of geometric necessity coplanar and rotation about Its carbon-carbon bonds is impossible You saw m Section 3 4 how angle strain m cyclopropane leads to an abnormally large heat of combustion Let s now look at cyclopropane m more detail to see how our orbital hybridization bonding model may be adapted to molecules of unusual geometry... 

At one time all cycloalkanes were believed to be planar It was expected that cyclopentane would be the least strained cycloalkane because the angles of a regular pentagon (108°) are closest to the tetrahedral angle of 109 5° Heats of combustion established that this is not so With the exception of cyclopropane the rings of all cycloalkanes are nonplanar... 

What are the facts To measure the amount of strain in a compound, we have to measure the total energy of the compound and then subtract the energy of a strain-free reference compound. The difference between the two values should represent the amount of extra energy in the molecule due to strain. The simplest way to do this for a cycloalkane is to measure its heat of combustion, the amount of heat released when the compound burns completely with oxygen. The more energy (strain) the compound contains, the more energy (heat) is released on combustion. 

Because the heat of combustion of a cycloalkane depends on size, we need to looJk at heats of combustion per CH2 unit. Subtracting a reference value derived from a strain-free acyclic alkane and then multiplying by the number of CH2 units in the ring gives the overall strain energy7. Figure 4.3 shows the results. 

The amount of strain in cycloalkanes is shown in Table 4.6, which lists heats of combustion per CH2 group. As can be seen, cycloalkanes larger than 13 membered are as strain-free as cyclohexane. 

TABLE 4.6 Heats of Combustion A/f in the Gas Phase for Cycloalkanes per CHj group... 

Table 4.6 Heats of Combustion and ring Strain of Cycloalkanes...

In marked contrast to the n-alkanes, the cycloalkanes exhibit thermodynamic properties where such regularities are no longer present. Heats of formation (AH ) for a substantial number of cycloalkanes are available from heats of combustion. With the exception of cyclohexane, AH°f is always more positive than the quantity — 4.926n. The difference between the two quantities leads to a quantitative assessment of the important notion of ring strain. The AH -values and strain energy data listed in Table 1 were taken from Skinner and Pilcher (1963). Other references give different but usually comparable... 

Thus -butane which liberates more heat than isobutane must have more potential energy and so is less stable than isobutane. Similarly the heat of combustion of cycloalkanes can be written in the following form ... 

Since cycloalkanes do not have isomers, the heat evolved has been calculated per CH2 group. First we find the heat of combustion of cyclohexane which is most stable and then the heat of combustion per CH2 group. It comes to 157.4 K cals/mole. Now to calculate the ring strain for other cycloalkanes, we multiply 157.4 K cal/mole by n and then subtract it from the heat of combustion of cycloalkane. 

Cycloalkane n Heat of combustion K cal/mole Heat of combustion/ CH2 group K cals/mole Ring strain K cals/mole... 

TABLE 2-7 Heats of Combustion and Strains of Cycloalkanes per Methylene Group"... 

TABLE 4.S Heats of combustion in the gas phase for cycloalkanes, per CH2 group3 2... 

Cycloalkane. (CH2) n Angle strain at each CH2, dega Heat of combustion,b A/-/0, kcal mole-1 Heat of combustion per CH2, AH°/n, kcal Total strain,0 kcal mole-1... 

We expect that the total strain in cycloalkanes of the type (CH2) should decrease rapidly in the order = 2>ra = 3> = 4. However, the data of Table 12-3 show that the order actually is 3 = 4 > 2. This difference in order often is disguised by dividing the heats of combustion by the numbers of CH2 groups and showing that the heats of combustion per CH2 are at least in the order expected from bond-angle strain. This stratagem does not really solve the problem. 

Exercise 12-17 Use the heats of combustion to liquid water given in Table 12-3 and appropriate bond energies to calculate AH° (vapor) for ring-opening of the cycloalkanes with bromine in the range n = 2 to n = 6 ... 

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