2-methylheptane , octane and 2,2,4-trimethylpentane in order of increasing boiling point?

Good question. The boiling points of the alkanes should increase in the order, ##”2,2,4-trimethylheptane”##, ##”2-methylheptane”##, ##”octane”##.

The longer, and straighter the chain (i.e. the less unbranched) the greater should be the interaction between chains, and thus the greater the boiling point.
Now of course I did not know these boiling points off the top of my head, but I can account for their order:
##”2,2,4-trimethylheptane,”## ##99## ##””^@C##
##”2-methylheptane,”## ##116## ##””^@C##
##”octane”, 125## ##””^@C##
Longer, less branched chains have greater opportunity for intermolecular dispersion forces, and this is certainly reflected in the boiling point. That the longest chain alkane, ##”octane”##, is the most involatile supports our analysis. And even though ##”2,2,4-trimethylheptane”## is the most massive molecule, branching prevents as effective intermolecular interaction as exists in the other pair.
The boiling point of ##n-“heptane”## is ##98.5## ##””^@C## (this I did know off the top of my head, because I found it to be a highly useful laboratory solvent), which is comparable to the boiling point of
##”2,2,4-trimethylheptane”##. Once again, branching serves to decrease the boiling point.

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