# Chemistry - Why is the molar entropy of hexane lower than that of butane?

## Solution 1:

There are two factors to consider. Certainly, the dominant factor is that the degrees of freedom available for the molecule to disperse energy into increases as the carbon chain extends. Thinking along these lines, one would expect a monotonic increase of entropy with carbon chain length.

However, we must also consider phase. As the carbon chain increases in length, the equilibrium phase at RTP changes from gas to liquid. This occurs between butane and pentane. At this point, there is a drop in the standard entropy, which then proceeds to increase monotonically from this point (pentane). The cause for this drop in entropy upon phase-change is due to the motional degrees of freedom being more constrained by proximity to other molecules in liquids compared to gasses.

See this link, where you can see some nice plots of standard entropy vs. carbon chain length.

## Solution 2:

It is a problem of phase. The standard entropy of butane is $$\pu{310 J mol-1 K-1}$$ in the gaseous phase.

The standard entropy of hexane is $$\pu{296 J mol-1 K-1}$$ in the liquid phase. But it is $$\pu{389 J mol-1 K-1}$$ in the gaseous phase. So the entropy increases from butane to hexane in the gaseous phase, as expected.