The heat of hydrogenation of cyclohexene is \(127 \mathrm{~kJ} \mathrm{~mol}^{-1} .\) When a second double bond is introduced in the molecule, the heat of hydrogenation of the diene is found to be \(231 \mathrm{~kJ} \mathrm{~mol}^{-1} .\) The diene is most likely (a) Hexa- 1,4 -diene (b) Hexa- 1,3 -diene (c) Hexa- 1,5 -diene (d) Hexa-1, 2-diene

We have the heat of hydrogenation of the diene as \(231 \mathrm{~kJ}\mathrm{~mol}^{-1}\). Since there are two double bonds in the diene, we can find the average heat of hydrogenation per double bond by dividing this value by 2: Average heat of hydrogenation per double bond for diene = \(\frac{231 \mathrm{~kJ}\mathrm{~mol}^{-1}}{2} = 115.5 \mathrm{~kJ}\mathrm{~mol}^{-1}\)

Cyclohexene has a heat of hydrogenation of \(127 \mathrm{~kJ}\mathrm{~mol}^{-1}\). To find the most likely diene, we need a molecule that has a double bond with a heat of hydrogenation close to that of cyclohexene. Given the heat of hydrogenation per double bond for the diene is 115.5, the double bond with the least difference is more likely to be present in the diene.

The difference in the heat of hydrogenation between each double bond of the dienes in the options and that of cyclohexene we have: (a) Hexa-1,4-diene: Conjugated diene, the double bonds are isolated from each other which gives more stability, and has a similar heat of hydrogenation to that of cyclohexene. (b) Hexa-1,3-diene: Conjugated diene, the double bonds are close to each other and share stability, thus having a lower heat of hydrogenation. (c) Hexa-1,5-diene: Non-conjugated diene, the double bonds are isolated and have a similar heat of hydrogenation to cyclohexene. (d) Hexa-1,2-diene: Cumulative diene, the double bonds are in direct contact and give more stability, resulting in a lower heat of hydrogenation to that of other dienes. Among these options, Hexa-1,4-diene has a structure that will result in a heat of hydrogenation per double bond close to that of cyclohexene. Therefore, the diene that is most likely present is Hexa-1,4-diene (Option a).