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

Entropy is dependent on the complexity of the molecule.

Due to this, I expected entropy to increase as the complexity of the molecule increased.

According to p 918 of Atkins' Physical Chemistry (9th ed.), I noticed that the standard molar entropy of n-hexane at is $$\pu{204.3 J mol-1 K-1}$$, whereas that for n-butane is $$\pu{310.23 J mol-1 K-1}$$.

How can butane have a higher standard molar entropy, even though it is a smaller molecule?

• Thing is butane is gas! – Mithoron Jul 30 '20 at 16:58
• I should also point out that standard molar entropies must be specified with a temperature, as the word "standard" by itself does not indicate a temperature. If your book does not point out that these entropies apply to 298 K (or whatever temperature they used), then it is doing you a disservice. – orthocresol Jul 31 '20 at 9:44
• Also, annoyingly, there's some disagreement over the value of the molar entropies in the sources I have on hand (neither is given in the CRC Handbook), but I think the general idea that butane > hexane appears to be valid. For now I've stuck with values which I can actually cite; if anybody has better values please go ahead and update it. – orthocresol Jul 31 '20 at 10:16

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.

• The next question that arises is why a gas and a liquid would have so little difference in entropies but I guess hexane being much more complex would compensate it. – Manit Agarwal-El psy congroo Aug 1 '20 at 3:02

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.

• Where did you get the number 389 from? – orthocresol Jul 31 '20 at 10:13
• The entropy of gaseous n-hexane is given in the reference : D.W. Scott, Correlation of the Chemical Thermodynamic Properties of Alkane Hydrocarbons, J. Chem. Phys. 1974, 60, 3144 - 3165. – Maurice Jul 31 '20 at 11:29