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Which has higher rate of hydrogenation- methyl propene or trans-2-butene?
I know that cis-2-butene has a higher rate of hydrogenation than both of these due to steric reasons, but here, both of these compounds have the same steric hindrance.
So, when they come in contact with the hydrogen adsorbed catalyst, they both should behave in a similar manner. Is this correct?
We should be able to determine which molecule will hydrogenate faster by comparing the activation energies for hydrogenation of these two molecules. A catalyst does not alter the reaction mechanism, it merely reduces the activation energy for the process.
The heat of formation of 2-methyl-propene is ca. 1.3 kcal/mol higher than that of trans-2-butene, presumably because of the adverse steric interaction between the geminal methyl groups in 2-methyl-propene. The transition state for this reaction will start to resemble the corresponding alkane in its eclipsed conformation (due to the cis-hydrogen delivery). If we only consider methyl-methyl steric interactions, then for 2-methyl-propene as we approach the transition state the two geminal methyl groups, initially separated by a 120 degree ($\ce{sp^2}$) angle, will displace towards a 109 degree ($\ce{sp^3}$) angular separation. Therefore, the methyl-methyl steric interaction should increase in 2-methyl-propene as we approach the transition state. 2-methyl-propene's transition state will be more destabilized than the ground state, consequently increasing the activation energy required to reach it. With trans-2-butene, there are no methyl-methyl steric interactions in the ground state or transition state; its activation energy, the energy separating the ground state and transition state, should not be increased or decreased.
Based on this analysis, the ground state - transition state energy separation would be expected to increase (slightly) for 2-methyl-propene as compared to trans-2-butene. Consequently, faster hydrogenation of trans-2-butene would be predicted. However the effect is expected to be very small.
The Cis-2-butene has the higher hydrogenation rate because both hydrogens on the double bond are on the same side, so you can get these close to the catalyst and transfer two more hydrogens on relatively easily. You can mimic this by building a molecular model of the cis-2-butene and use a table as your catalyst. Clearly, the hydrogen side of the double bond fits pretty well. Now build the 2-methyl-propene and trans-2-butene, and try to fit those against the surface as well.
It would also be good to keep in mind that the 2-methyl-propene has a terminal alkene. I'm trying not to answer the question outright and make you do the work, but that terminal alkene is probably very important for determining which reacts more readily.
You need to consider an actual hydrogenation system rather than generics. Hydrogenation is often much more difficult than adding a substrate, finely divided metal and then throwing in hydrogen gas for good fun.
Take a look at Wilkinson's catalyst and its corresponding catalytic cycle (an old catalyst, but one which has plenty of literature). I expect tentatively for the transition state of the migratory insertion of the alkene to play a huge part in the relative reaction rates.
If you consider a four-membered transition state at this stage, then we can possibly imagine a build up of charge on the carbon where the hydride inserts (the more hindered end, the metal on the less) which would be more stabilised if there are additional alkyl chains due to hyperconjugation.
