The correct decreasing order of densities of the following compounds is
(a) (D) (C) (B) (A)
(b

Q: Why do we assume the volume is constant?

While the volume isn't perfectly constant, the benzene ring makes up the bulk of the molecule's volume. The difference in volume added by a Cl or Br atom is relatively small compared to the massive increase in atomic weight they bring. Thus, mass dominates the density trend.

Q: Does the position of the substituents (ortho, meta, para) affect density?

Yes, slightly. The packing efficiency in the solid or liquid state can vary between isomers, leading to small differences in density. However, the difference in mass between different halogens (like Cl vs Br) is a much larger effect and dictates the overall trend.

Q: What if we compare benzene with an aliphatic chain of the same mass?

Then volume becomes a major factor. Aromatic rings pack differently than straight chains. You can only safely use the 'mass dominates' rule when comparing structurally very similar molecules.

Q: Is bromine always denser than chlorine?

As an element, yes. Bromine is a dense liquid, while chlorine is a gas at room temperature. When attached to a molecule, substituting a heavier atom like Br for a lighter one like Cl almost always increases the density.

Q: Why is density important in organic chemistry?

Density is a crucial physical property used for identifying compounds and separating mixtures. For example, in a separatory funnel, knowing which layer (organic or aqueous) is denser tells you which one is on the bottom. Halogenated organics are typically denser than water!

Question

The correct decreasing order of densities of the following compounds is

Options:

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

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

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

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

Sigma Percentile · Accepted Answer

### Analyzing the Setup

Imagine you are given four different liquids in identical flasks: Benzene, Chlorobenzene, 1,3-dichlorobenzene, and 1-bromo-3-chlorobenzene. If you were to weigh these identical flasks, which one would be the heaviest? That is exactly what this question is asking us to figure out by finding the decreasing order of their densities.

We are dealing with four aromatic compounds that share the exact same foundational structure: a benzene ring. The only difference lies in the atoms attached to this ring.

### The Master Equation: Density vs Mass

To solve this, we need to go back to the fundamental definition of density. Density ($ho$) is defined as mass ($M$) per unit volume ($V$):

$$ ho = \frac{M}{V} $$

Here is the crucial insight: because all these molecules are built on the same rigid, planar benzene ring, they take up roughly the same amount of space. Their molar volumes ($V$) are approximately constant.

When the denominator ($V$) is constant, the fraction is entirely controlled by the numerator ($M$). Therefore, the density becomes directly proportional to the molar mass:

$$ ho \propto M $$

This simplifies our problem immensely. We don't need to worry about complex packing fractions or intermolecular forces; we just need to find out which molecule is the heaviest!

### Comparing the Substituents

Let's break down the masses by looking at the substituents attached to the benzene ring. 
- **Compound (A)** is pure Benzene. It only has light Hydrogen atoms attached.
- **Compound (B)** is Chlorobenzene. One Hydrogen has been replaced by a Chlorine atom. Chlorine has an atomic mass of about $35.5$, which is significantly heavier than Hydrogen ($1$).
- **Compound (C)** is 1,3-dichlorobenzene. Now we have *two* heavy Chlorine atoms.
- **Compound (D)** is 1-bromo-3-chlorobenzene. Here, we have one Chlorine and one Bromine. Bromine is a massive atom with an atomic weight of about $80$.

If we calculate the approximate molar masses:
- $M_A \approx 78 	ext{ g/mol}$
- $M_B \approx 112.5 	ext{ g/mol}$
- $M_C \approx 147 	ext{ g/mol}$
- $M_D \approx 191.5 	ext{ g/mol}$

### Final Calculation and Conclusion

The order of their molar masses is crystal clear:

$$ M_D > M_C > M_B > M_A $$

Since we established that density is directly proportional to mass for these structurally similar compounds, the density will follow the exact same trend. The heavier the molecule, the denser the substance.

Therefore, the correct decreasing order of density is:

$$ 	ext{(D)} > 	ext{(C)} > 	ext{(B)} > 	ext{(A)} $$

This is a classic example of how a seemingly complex physical chemistry question can be elegantly solved by identifying the dominant variable—in this case, the atomic mass of the substituents!

Animated Solution for Chemistry - Organic Chemistry: The correct decreasing order of densities of the following compounds is

Select Answer:

Visualized Solution

$Analyzing the Compounds$

$Density Formula$

$Comparing Molar Masses$

$Calculating Approximate Masses$

$Final Density Order$

$The Way Forward$

The Sigma Insight: Haloalkanes & Haloarenes

Analyzing the Setup

The Master Equation

Comparing the Substituents

Final Calculation and Conclusion

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