Q.Arrange the following compounds in the increasing order of their densities.

Concept: Density depends on molecular mass and packing. For similar-sized aromatic rings, density increases with the mass of substituents (heavier halogens raise density more).

Reasoning:

1. Benzene (a) has the smallest molecular mass ($78$) and no heavy atoms — lowest density.
2. Chlorobenzene (b) has one Cl ($M \approx 112.5$) — density higher than benzene.
3. 1,3-Dichlorobenzene (c) has two Cl atoms ($M \approx 147$) — denser than monochlorobenzene. …

The question asks for increasing order of density. For organic liquids at room temperature, density depends on two main factors: molecular mass (heavier molecules generally pack more mass per unit volume) and intermolecular forces (which affect how tightly molecules pack). Halogen atoms are heavy and also polar, so adding them increases density significantly.

Let’s examine each compound.

1. Benzene (C₆H₆) — molecular mass = 78 g/mol. It is a light hydrocarbon with no heavy atoms. Density ≈ 0.88 g/mL. This will be the lowest.

2. Chlorobenzene (C₆H₅Cl) — one chlorine atom (atomic mass 35.5) replaces a hydrogen. Molecular mass = 112.5 g/mol. The chlorine adds significant mass and also introduces polarity, leading to better packing. Density ≈ 1.11 g/mL. Clearly denser than benzene.

3. 1,3-Dichlorobenzene (C₆H₄Cl₂) — two chlorine atoms. Molecular mass = 147 g/mol. More mass than chlorobenzene, and the two chlorines increase polarity further. Density ≈ 1.29 g/mL. So it is denser than chlorobenzene. …

Concept: Density Trends in Haloarenes

Density of organic compounds depends primarily on molecular mass and packing efficiency. For substituted benzenes, heavier halogen atoms (Br > Cl) increase density. More halogen atoms also increase density.

Method: Molecular Mass Comparison

Step 1: Calculate molecular masses

• Benzene ($C_6H_6$): $6 \times 12 + 6 \times 1 = 78$ g/mol
• Chlorobenzene ($C_6H_5Cl$): replace one H of benzene with Cl: $78 - 1 + 35.5 = 112.5$ g/mol
• 1,3-dichlorobenzene ($C_6H_4Cl_2$): replace two H with two Cl: $78 - 2 + 2 \times 35.5 = 147$ g/mol
• 1-bromo-3-chlorobenzene ($C_6H_4BrCl$): replace two H with one Br and one Cl: $78 - 2 + 80 + 35.5 = 191.5$ g/mol

Step 2: Arrange in increasing order of molecular mass

$78 < 112.5 < 147 < 191.5$ …

Common Mistakes & How to Avoid Them

Mistake 1: Assuming meta-substitution reduces packing enough to reorder the trend

The error: Students reason that since 1,3-dichlorobenzene is asymmetric (meta-substituted), its molecules must pack less efficiently than chlorobenzene's, and conclude chlorobenzene should therefore be denser than 1,3-dichlorobenzene — reordering the list to (a)< (c)< (b)< (d).

Why it's wrong: Real densities don't support this: benzene ≈ 0.877 g/mL, chlorobenzene ≈ 1.106 g/mL, 1,3-dichlorobenzene ≈ 1.288 g/mL, 1-bromo-3-chlorobenzene ≈ 1.667 g/mL. Adding a second heavy halogen atom increases mass more than any packing-efficiency loss from losing symmetry can offset — 1,3-dichlorobenzene is genuinely denser than chlorobenzene, not less dense.

How to avoid:

• For this class of comparison (aromatic ring + halogen substituents, no big shape change), substituent mass is the dominant factor, not packing symmetry. Don't invent a symmetry-based reversal without checking real values.
• Order by cumulative substituent mass: no halogen (78) < one Cl (112.5) < two Cl (147) < one Br + one Cl (191.5).

Mistake 2: Confusing density with molecular weight alone (without checking it actually holds)

The error: Students arrange purely by molar mass without double-checking whether any packing effect could plausibly reverse the order.

Why this is actually fine here: Density = mass/volume, and packing DOES matter in general — but for this specific set of closely related aromatic halides (same ring, no big shape distortion), the extra halogen mass dominates and molar-mass ordering happens to match the real density ordering exactly.

How to avoid:

• Use molar mass as your first estimate, then sanity-check: is there a reason (major shape change, hydrogen bonding, drastically different symmetry) the order might flip? Here there isn't — the ordering by mass is correct.

Mistake 3: Forgetting that bromine is much heavier than chlorine

The error: Students treat Br and Cl as similar "heavy atoms" and guess 1-bromo-3-chlorobenzene might be similar in density to 1,3-dichlorobenzene.

Why it's wrong:

• Atomic mass: Br ≈ 80, Cl ≈ 35.5. …