how can you account for the differences in the entropies of combination of methyl propane (-1465J/mol K) and butane (1465J/mol K)​

Explanation:

The change in entropy is a measure of temperature. When the temperature of a compound or a system increases, there will be more randomness in the system.

The boiling point is directly related to the number of carbon atoms but is indirectly proportional to the branching in a hydrocarbon.

Butane and methyl propane, both have 4 carbon atoms.

But, butane has 4 carbon atoms in a straight chain while methyl propane has 3 carbon atoms in a straight chain and 1 methyl substituent which makes it a branched hydrocarbon.

Thus, the boiling point of methyl propane will be less than the butane. Likewise, the pattern in entropies will be seen.