What is the solubility order of isomeric alcohols in water?

Question

The order for the solubility of isomeric alcohols in a book was given as:

Primary alcohol >Secondary alcohol >Tertiary alcohol

After this I found a question:

(1) Which is more soluble in water?
(a) 3-ethyl-3-hexanol
(b) 2-octanol

Ans: (a)

The reason was that (a) has a more compact alkyl portion than (b). But as (a) is a tertiary alcohol while (b) is a secondary one, so according to the order given above the answer should be the reverse.

Also, while comparing 2-methyl-2-propanol and 1-butanol, 1-butanol had higher solubility which matched the given order.

I am not understanding what's wrong about the first case. Please explain.

Answer 1

The reasons that you cite are both important for the solubility of an alcohol. Generally speaking, if the molecule is branched its (hydrophobic) surface exposed to water is less than in a linear molecule. This effect is more pronounced when the number of atoms is bigger. On the other hand the effect of the degree of substitution on the solubility is less pronounced when the molecular size rise.

This would partially justify your second question, but the problem here is that your second question is wrong, 2-methyl-2-propanol is soluble with water in every ratio, while n-butanol is not.

The statement primary > secondary > tertiary is valid when comparing ethanol > isopropanol > t-butanol or similar series. The hydrophobic surface in the series stays relatively unchanged this is why we can say that the effect on the solubility is caused by the degree of substitution of the alcohol. In the comparison between alcohols with the same number of carbons branched > linear is a much more important factor.

Answer 2

This is probably an entropic effect because water is involved. If it is to dissolve in water a (hydrophobic) linear alkyl chain has to be bridged by hydrogen bonds between several water molecules. This bridging severely restricts the normal hydrogen bonding behaviour of water and when compared to normal water behaviour is a low entropy situation. In the tertiary alcohol fewer water molecules are needed to surround the alkyl groups and so while still a low entropy situation is nevertheless more favourable that the linear chain and so solubility is greater. The enthalpy needed to dissolve in water is often small, either positive or negative, so in terms of the free energy the entropy term, $-T\Delta S$, dominates and makes this negative.