In addition to having synthetic applications, catalytic hydrogenation is useful for analytical and thermochemical purposes. The analysis of a substance for the number of carbon-carbon double bonds it contains is carried out by measuring the uptake of hydrogen for a known amount of sample. Measurement of the heat evolved in the hydrogenation of alkenes gives information as to the relative stabilities of alkenes, provided that the differences in \(\Delta S^0\) values are small. The experimental values of \(\Delta H^0\) for hydrogenation of a number of alkenes and alkynes are listed in Table 11-2. The \(\Delta H^0\) calculated from average bond energies is \(-30 \: \text{kcal/mol}\) for a double bond and \(-69 \: \text{kcal/mol}\) for a triple bond. The divergences from these values reflect the influence of structure on the strengths of multiple bonds. Some important generalizations can be made: The more alkyl groups or other substituents there are on the multiple bond, the less heat is evolved on hydrogenation. Because less heat evolved signifies a stronger, more stable bond, it appears that alkyl substitution increases the stability (strength) of the multiple bond. Trans isomers of 1,2-dialkyl-substituted ethenes evolve less heat (are more stable) than the corresponding cis isomers. This is the result of molecular overcrowding in the cis isomers from nonbonded interactions between two alkyl groups on the same side of the double bond. The effect amounts to almost \(10 \: \text{kcal/mol}\) with two cis - tert -butyl groups. This effect is another manifestation of steric hindrance and can be seen most clearly with space-filling models (Figure 11-3). 3. Conjugated dienes are more stable than isolated dienes (compare 1,3- and 1,4-pentadiene). 4. Cumulated dienes appear to be less stable than conjugated or isolated dienes (see 1,2-propadiene). Table 11-2: Heats of Hydrogenation of Gaseous Alkenes and Alkynes \(\left( \text{kcal/mol}, \: 1 \: \text{atm}, \: 25^\text{o} \right)\)