# Greater entropy: an atom or macromolecule?

A question that appeared on my last chemistry exam was :

Which of the following has greater entropy A) An atom B) A macromolecule

The question doesn't specify anything else(i.e. type/size of atom or macromolecule). The macromolecules we learned class were proteins, sugars, nucleic acids(DNA/RNA) or lipids. What is the correct answer and why(hypothetical calculation, if possible) ?

There are many equations that describe the entropy of a system, one is $$\ce{S = k~ ln ~W}$$ where S is the entropy of the system, k is Boltzmann's constant and W is the number of states a system can exist in. If we take an atom, it can only move in 3 directions x, y and z - that's it. If we take a small molecule like ethane, it can also move in these same 3 dimensions but it can also rotate about any one of the atoms, the various bonds can stretch and compress and the various bond angles can expand and collapse. Clearly, there are a lot more states that ethane can exist in as compared to a single atom, clearly W is larger for ethane than a single atom, clearly S is larger for ethane than a single atom. As we increase the complexity of the molecule, W and S increase exponentially. A macromolecule will have a much larger entropy than an atom.