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Hydrocarbons (i.e., molecules containing carbon and hydrogen only) are generally less dense than water. Yet chloroform, which is a halogenated hydrocarbon, is more dense.

Why is this? I know water is more dense than hydrocarbons because its polar nature would cause it to pack more tightly. But ,why chloroform, which is less polar than water, has a higher density than water.

It can't be molecular weight, because larger hydrocarbons like hexane and octane have a higher molecular weight than water, yet water is denser.

So is there any theory or concept which will help me find why chloroform is denser than water?

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    $\begingroup$ Have you noticed 3 heavy chlorine atoms hanging on the central carbon ? BTW hydrocarbons do not have lower than water density because being nonpolar. It is just side attribute. $\endgroup$ – Poutnik Sep 26 '20 at 18:30
  • $\begingroup$ Rover your observations are very good. In the condensed phase, it seems logical to argue, that the volume of each molecule is a nontrivial factor. That might counteract your argument about the higher alkanes having a higher molecular weight but lower overall density. $\endgroup$ – Bertram Sep 26 '20 at 18:47
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    $\begingroup$ Not all hydrocarbons are less dense than water. Then again, chloroform is not a hydrocarbon. Now what is your question, really? $\endgroup$ – Ivan Neretin Sep 26 '20 at 21:15
  • $\begingroup$ @Rover I edited your question to make it clearer. Hopefully now it won't be closed. $\endgroup$ – theorist Sep 26 '20 at 22:13
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    $\begingroup$ @Rover. I see you removed my edits, and restored the original language. $\endgroup$ – theorist Nov 30 '20 at 7:00
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The density of a substance depends on its molecular density and packing fraction (where you need to be consistent in definiting the molar volume in calculating both attributes).

However you are looking for a simpler explanation that gets the general trends right. Just looking at molecular mass is too simple—larger molecules have greater mass, but take up more space. So what would be a simple model that works reasonably well?

I suspect the main determinant of density is the average mass of a molecule's atoms, and that relative atomic sizes, as well as packing density, while important, are secondary contributors.

Given this, let's construct our very rough model for predicting relative densities by comparing just the average atomic masses of the molecule's atoms, and see if that, by itself, can explain most of the trends.

Of course, since we are ignoring these other factors, our simple model is imperfect and thus, as expected, will have many exceptions (one of which is included, and bolded, below). Nevertheless, in spite of the very simple nature of this model, it does surprisingly well in matching the general trends (at least for the substances shown here).

In each case I have calculated the average atomic mass of the atoms (u/atom) from $\frac{\text{molecular mass}}{\text{no. of atoms}}$:

Hexane ($\ce{C6H14}$): 86.18/20 = 4.3 u/atom; density = 0.661 g/$\text{cm}^3$

Octane ($\ce{C8H18}$): 114.23/26 = 4.4 u/atom; density = 0.703 g/$\text{cm}^3$

Water ($\ce{H2O}$): 18.015/3 = 6.0 u/atom; density = 0.997 g/$\text{cm}^3$ (at 25$^\circ$C)

Methyl chloride ($\ce{CH3Cl}$): 50.485/5 = 10.1 u/atom; density = 0.911 g/$\textbf{cm}^{\bf{3}}$ (note the exception to the trend; it works well in comparing like compounds—this one vs. the ones below—but fails when comparing very unlike compounds—this one vs. water—when the average atomic masses of the atoms are too close)

Methylene chloride ($\ce{CH2Cl2})$: 84.927/5 = 17.0 u/atom; density = 1.325 g/$\text{cm}^3$

Chloroform ($\ce{CHCl3})$: 119.369/5 = 23.9 u/atom; density = 1.492 g/$\text{cm}^3$

Carbon tetrachloride ($\ce{CCl4}$): 153.8118/5 = 30.8 u/atom; density = 1.594 g/$\text{cm}^3$

Carbon tetrabromide ($\ce{CBr4}$): 331.627/5 = 66.3 u/atom; density = 3.42 g/$\text{cm}^3$ (m.p. = 89$^\circ$C, so it's solid at room temperature)

Carbon tetraiodide ($\ce{CI4}$): 519.628/5 = 103.9 u/atom; density = 6.36 g/$\text{cm}^3$ (m.p. = 168$^\circ$C, so it's solid at room temperature)

Mercury ($\ce{Hg}$): 200.592/1 = 200.6 u/atom; density = 13.534 g/$\text{cm}^3$

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    $\begingroup$ Please note that usage of unit symbols such as "amu" or "cc" is not recommended. "amu" is obsolete since 1961 (use $\pu{u}$ instead). "cc" is an old non-standardized abbreviation that still can be found in popular literature, but is not permitted to be used in scientific writing according to the SI system (use $\pu{cm^3}$ instead). $\endgroup$ – andselisk♦ Sep 27 '20 at 8:07
  • $\begingroup$ @andselisk You're right, cc would need to be defined or changed to $\text{cm}^3$, so I did the latter. Often when I post I'll use convenient abbreviations (b/c having to type out the cumbersome syntax [e.g., $\text{cm}^3$] interferes with my flow of thoughts), and add the syntax later. So I don't mind the reminder :). Also, note that SI units are not uniformly required in scientific publications. For instance, "u" (unified atomic mass) is not an SI unit (goldbook.iupac.org/terms/view/U06554) [Though "cc" would not be permitted—but because it's too casual, not because it's not SI] $\endgroup$ – theorist Sep 27 '20 at 19:36
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    $\begingroup$ Both the astronomical and unified atomic mass units are non-SI units accepted for use with the SI. The issue with amu is that it was used for oxygen-based units and is now obsolete. I agree there is no need to run with SI units only, but since Chemistry.SE is a multi-national community, using up-to-date and standardized notations would be a tremendous help in scientific communication. We happen to live in a rapid era of changes and globalization, and we need to adapt no matter whether we like it or not. $\endgroup$ – andselisk♦ Sep 27 '20 at 19:50
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Density is a macroscopic measurement so we should look for average properties spread over several molecules.

The average density of a liquid is not that much smaller than that of its solid ($\approx 0.9$, there are a v. few exceptions, water/ice, silicon, gallium, germanium, bismuth where it is greater) which means that the distance between molecules is only slighter larger than that in the solid. Just enough to allow one molecule to squeeze past another and make the liquid mobile. This means that the average distance between two molecules is not that much larger than the average distance between its atoms. Even though intermolecular forces are weak (between neutral atoms) there are many such atoms in a molecule and so the total interaction is enough to maintain the liquid. Consequently individual molecular size is not that important in determining density, it is the average mass / volume that counts, where volume means that occupied by numerous molecules.

An example is the very similar density of alcohols of differing mass and size

\begin{array}{lcc} \hline & \text{mass} & \mathrm{density\, (kg/m^3)} \\ \hline \text{methanol} & 32 & 791\\ \text{butanol} & 74 & 810\\ \text{octanol} & 130 & 827\\ \hline \end{array}

which shows that it is the average mass over several molecules that is important.

For thio- alcohols the density is greater than for alcohols reflecting the increased mass but this falls slightly as the alcohol gets larger,

\begin{array}{cc}\\ \hline & \mathrm{density \,(kg/m^3)} \\ \hline \ce{CH3SH} & 900 \\ \ce{CH2H5SH} & 860 \\ \ce{C4H9SH} & 836 \\ \hline \end{array}

and this is because more lower mass $\ce{C-H}$ is present on average for larger molecules vs the increased mass of $\ce{S}$ over $\ce{O}$ atoms. The increase in size of $\ce{S}$ appears to have a smaller effect in reducing the density than the mass has in increasing it.

In the case of small molecules similarly the average mass is v. important, for example the density of $\ce{H2O}$ is $\pu{1000 kg m-3}$ but that of $\ce{D2O}$ is $\pu{1105 kg/m^3}$ and in the case of chloroform there is a large in mass in a relatively small molecule so the average mass is far greater than for water taken over many molecules even when the increase in size of $\ce{Cl}$ atoms is accounted for; the densities are $\pu{1492 kg m-3}$ and $\pu{1000 kg/m^3}$

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  • $\begingroup$ Yes, density is a macroscopic measurement, but the central point of my answer wasn't to average over many molecules, but to do an average over all the atoms within each molecule. Indeed, by attempting to construct a model purely based on u/atom, I was explicitly ignoring the attribute that can only be seen macroscopically (the packing fraction), and instead attempting to see if we could see explain trends in density purely from a microscopic attribute (average atomic mass of the atoms). Thus your characterization of what I was doing is the opposite of what I was actually doing. $\endgroup$ – theorist Sep 27 '20 at 18:53
  • $\begingroup$ @theorist, clearly I misunderstood, I will edit my answer to remove a reference to your answer. $\endgroup$ – porphyrin Sep 28 '20 at 6:57

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