Compare density of halogen substituted benzene rings

The correct decreasing order of densities of the following compounds is :

(1) (D) > (C) > (B) > (A)

(2) (C) > (D) > (A) > (B)

(3) (C) > (B) > (A) > (D)

(4) (A) > (B) > (C) > (D)

Question Source: JEE Mains 2021

How to solve this question practically in exam? Can we compare density assuming packing efficiency approximately similar for given compounds in option and $$\rho \propto$$ Molar Mass?

This may be helpful but is irrelevant here because we are comparing densities in between cyclic compounds only.

• You have completely change the question. Actually this is a new question. I did what I have to do. Aug 19, 2021 at 14:51
• I have a feeling this has something to do with dipole moment Aug 20, 2021 at 15:53
• @Buraian if $(\rho)^{-1} \propto$ dipole moment then density of C should be greater than D. Assuming your guess to be correct.
– Jay
Aug 21, 2021 at 6:43
• I remember reading somewhere that density of phenol was related to packing efficiency and that was related to dipole moment. I spent like few hours searching where I read it yesterday but I couldn't find it :( . Maybe I guess I learned some wrong information. Aug 21, 2021 at 6:44
• @Buraian The thing of packing efficiency and dipole moment is about alkenes in cis or trans form and packing efficiency can be determined there in alkene but here there is no easy way to determine packing efficiency; you might have read that in isomerism chapter.
– Jay
Aug 21, 2021 at 6:47

Examining the compounds from a distance suggests these conclusions, with little or no extensive knowledge of chemistry:

1. B is more dense than A and C is more dense than B, because you know that hydrogen is the lightest element (the least dense, because it is used in blimps) and chlorine is denser (it sinks and was used as a poison gas because it hugs the ground).

2. D is more dense than C, because bromine is farther down the periodic table than chlorine, and is likely to be denser.

3. Therefore D is the densest compound. Only one choice puts D as the densest: #1.

It seems to me that the intricacy of the question, and/or the difficulty, lies in the wording: what is decreasing order of densities?

At the very least, it should be obvious that D is the extreme compound, but a confusion between the meaning of increasing and decreasing could suggest that #4 is the correct choice. A little reflection rules that out: the density of D cannot be less than that of A!

The density of 1-bromo 3-chlorobenzene was not available in my search, but for the others, benzene has 0.876, chlorobenzene 1.11, m-dichlorobenzene 1.228, and bromobenzene 1.5. Bromochlorobenzene would probably come in at about 1.75. The actual densities are not at all similar, so the question must have been going after something else.

The effect of packing efficiency, due to dipole moment - in liquids - is probably much, much smaller. One challenging possibility would be that one of the compounds, perhaps C or D, could be a solid - but, no, they are all liquids.

Maybe it was a freebie: you have to work at it to get it wrong.

• The bonded radius is moer complicated... but nice that this method gives the answer @Jay Aug 22, 2021 at 10:19

The wanted densities are the ratio of the mass of the molecule by the volume of the molecule.

You may borrow an approximation used in crystallography for an estimate of the trend of the densities and substitute the former

• the mass of the molecule is the sum of the atomic masses (tabulated or/and memorized as an approximate)

• the volume of the molecule is approximated as the sum of the atomic volumes (tabulated, e.g., Hofmann table mentioned in an earlier answer here)

Thus, using the relevant entries from the Hofmann table

|------------------------------+-------+------+-------+------+------+------|
| element                      |     C |    H |     F |   Br |   Cl |    I |
| average atomic volume [A**3] | 13.87 | 5.08 | 11.17 | 32.7 | 25.8 | 46.2 |
|------------------------------+-------+------+-------+------+------+------|


you obtain

|--------------------+--------+--------+---------+----------|
| compound           |      A |      B |       C |        D |
|--------------------+--------+--------+---------+----------|
| formula            |   C6H6 | C6H5Cl | C6H4Cl4 | C6H4BrCl |
| mass [amu]         |  78.11 | 112.56 |  147.00 |   191.45 |
| volume [A**3]      | 113.70 | 134.42 |  155.14 |   162.04 |
| density [amu/A**3] |   0.69 |   0.84 |    0.95 |     1.18 |
|--------------------+--------+--------+---------+----------|


As stated earlier, this provides a coarse estimate of the trend for the density, which however is not the density of the liquid. This approximation (if you compare to, e.g. packing of apples in crate) does not consider the gaps between molecules packed which, given the shape of molecules and conformational flexibility of e.g., alkyl chains may be more complex than just close packing of spheres of one diameter/hcp.

Reference Hofmann table

Hofmann, D. W. M., Fast estimation of crystal densities in Acta. Cryst. B58, 2002, 489-493; doi: 10.1107/S0108768101021814.