Compare density of halogen substituted benzene rings

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


[![enter image description here](https://i.stack.imgur.com/1sQGy.png)](https://i.stack.imgur.com/1sQGy.png)


(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


Official Answer: (1)


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](https://chemistry.stackexchange.com/q/32399/108386) may be helpful but is irrelevant here because we are comparing densities in between cyclic compounds only.




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.


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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](https://chemistry.stackexchange.com/questions/152150/relationship-between-molar-mass-and-density-in-solids/152153#152153))


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](https://en.wikipedia.org/wiki/Close-packing_of_equal_spheres).


**Reference Hofmann table**


Hofmann, D. W. M., *Fast estimation of crystal densities* in *Acta. Cryst.* **B**58, 2002, 489-493; [doi: 10.1107/S0108768101021814](https://doi.org/10.1107/S0108768101021814).


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