Density

For liquids, density is usually measured as the number of grams per milliliter—expressed as g/mL. Density is a useful tool in the laboratory. Its most common use is in extractions, the transfer of a solute from one solvent to a better one. To do an extraction, choose a solvent that is better than the one the solute is currently dissolved in. The two solvents must be insoluble in one another. Then shake the two together and separate them. Because you know the density of each solvent and which solvent best dissolves the solute, you know which one to keep. You may also use density, as you do boiling or melting points, to help identify unknown liquids.

Density of Solids
You can easily estimate the relative density of many organic liquids, but you cannot do so as readily with solids because the density of a solid depends on too many factors. Two generalizations that relate to the density of solids are: organic solids typically have lower densities than inorganic solids, and nonionic solids typically have lower densities than ionic solids. Beyond these generalizations, this book does not consider the density of solids.

The density of an organic liquid depends on three factors: the molecular weight of the substance, the ratio of the number of heavy atoms to the number of carbons in the molecule, and how well the molecules pack together. The first two factors are very closely related because, when determining the density of a liquid, there is more to the picture than just the molecule's actual weight. Of greater importance is the ratio of the number of heavy atoms to carbon atoms in the molecule. For example, the van der Waals radius of a methyl group is

200 pm, and the van der Waals radius of a bromine atom is 195 pm. The formula weight of a methyl group is 15, and the atomic weight of the bromine is 80. Bromine weighs more than five times as much as the methyl group, yet it takes up a smaller volume of space. This leads to a dramatic increase in density for bromine compared to a methyl group. Thus, when you compare the two in compounds pentane and 1-bromobutane, for example, you find that both compounds have nearly the same molecular volume, but the density of pentane is 0.62 g/mL, and that of 1-bromobutane is 1.27 g/mL.

This type of difference holds true for any set of molecules with similar sizes—the molecule with the heavier atoms is the molecule with the higher density. For example, cyclohexane and cyclohexane-d12 (in which all of the hydrogens have been replaced with deuterium, 2H) have densities of 0.78 and 0.89 g/mL respectively.
The third factor that determines a liquid's density is how efficiently its molecules pack together. The closeness of packing

depends on how readily each molecule fits into an aggregation of molecules. For example, hexane, with a density of 0.66 g/mL, has many more stable conformations than does cyclohexane, with a density of 0.78 g/mL. Cyclohexane packs more efficiently because it is more symmetrical than hexane.
Intermolecular attractions affect the packing efficiency of a molecule. The greater these attractions, the more readily the molecules pack together. Dipolar attractions and, especially, hydrogen bonding increase the density of a liquid. For example, compare the isomers diethyl ether and 1-butanol. Diethyl ether, which has van der Waals and dipolar attractions, has a density of 0.71 g/mL. 1-Butanol, which has hydrogen bonding in addition to van der Waals and dipolar attractions has a density of 0.81 g/mL.

Chemists often perform extractions using a two-phase liquid system consisting of water and some organic liquid. They use an estimate of the density of the organic liquid relative to that of water. They work with estimates rather than precise densities because that is all they need to know to decide which layer is which. Here is a rule for estimating the densities of molecules relative to water. Any molecule containing bromine, iodine, or multiple chlorine atoms (e.g., CHCl3) has a density greater than that of water (1 g/mL). All other organic solvents generally have a density less than that of water. This rule, of course, is less effective for large molecules. In a large molecule, the functional group becomes less important, and all the physical properties tend to converge to the same values. Table 4.3 illustrates how chain length affects densities. Note that the density changes rapidly for molecules containing between two and ten carbons, but above ten carbons, the density does not change very much.