# Hydrogen bonding in sugar acids

I recently learnt that the reason for low solubility of mucic acid as compared to glucaric acid was more hydrogen bonding in the crystal state of mucic acid as compared to glucaric acid.

I would like to know why mucic acid has more hydrogen bonding? Does symmetry of the molecule play a role? If so how?

From the abstract of an article titled "The crystal structure of galactaric acid (mucic acid) at −147°: An unusually dense, hydrogen-bonded structure"

[...] D$$_m$$ = [1.790] $$\pu{g cm−3}$$ [...] The crystal structure has a system of strong, intermolecular hydrogen-bonds, which accounts for the high crystal density and low solubility in water.

The crystal structure was solved at very low temperature, but the density D$$_m$$ is quoted for room temperature. For comparison, the density of sucrose or cellulose is around 1.5 $$\pu{g cm−3}$$.

For glucaric acid, the volume of the asymmetric unit is 421.9 Å$$^3$$ / 2, while for mucic acid it is 194.0 Å$$^3$$. As the molar mass of the two stereoisomers is the same, there is a difference in density of about 9%.

A lower density implies more attractive interactions or less repulsive interactions in the crystal state. For a complete analysis, you would also have to compare how well these compounds are solvated in aqueous solution. Typically, it is impossible to predict solubility by just looking at structures because both solvation and crystal structure are hard to predict.