Hydrogen bonds are formed in many compounds e.g., H2O, HF, NH3. The boiling point of such compounds depends to

NCERT Exemplar · Q4

Q. Hydrogen bonds are formed in many compounds e.g., H2O, HF, NH3. The boiling point of such compounds depends to a large extent on the strength of hydrogen bond and the number of hydrogen bonds. The correct decreasing order of the boiling points of above compounds is :

(i) HF > H2O > NH3

(ii) H2O > HF > NH3

(iii) NH3 > HF > H2O

(iv) NH3 > H2O > HF

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Concept understanding — Hydrogen Bonding

Hydrogen Bonding: From Intuition to Precision

Imagine you're holding two magnets. If you bring the north pole of one close to the south pole of another, they snap together. Now imagine a much weaker version of that — a tiny tug, not a full lock. That's the spirit of hydrogen bonding.

In chemistry, atoms in a molecule share electrons through covalent bonds. But electrons aren't shared equally in all cases. Some atoms are greedy — they pull the shared electrons closer to themselves. Oxygen, nitrogen, and fluorine are the biggest electron-hoarders. When one of these atoms bonds with hydrogen, the hydrogen ends up with a slight positive charge (because its electron has been pulled away), and the other atom gets a slight negative charge.

Now here's the key: that slightly positive hydrogen is attracted to any nearby slightly negative atom (like oxygen, nitrogen, or fluorine) on another molecule. This attraction is a hydrogen bond.

Note

A hydrogen bond is not a true chemical bond like a covalent or ionic bond. It's an intermolecular force — a strong dipole-dipole attraction — but weaker than covalent bonds (about 1/10th to 1/20th the strength).

The Precise Definition

A hydrogen bond is an attractive interaction between a hydrogen atom covalently bonded to a highly electronegative atom (N, O, or F) and another electronegative atom (N, O, or F) that has a lone pair of electrons.

We can write it as:

\text{X—H} \cdots \text{Y}

where X and Y are N, O, or F. The dotted line ( $\cdots$ ) represents the hydrogen bond. X—H is the donor (the molecule that provides the hydrogen), and Y is the acceptor (the molecule that provides the lone pair).

Why Only N, O, and F?

Three things make these three elements special:

High electronegativity — They pull electrons hard, creating a large partial positive charge on hydrogen.
Small size — The lone pair on Y is compact, allowing the hydrogen to get very close. Closer distance means stronger attraction.
Lone pairs — They have unshared electron pairs that can act as the acceptor.

Chlorine is electronegative, but it's too large — the hydrogen can't get close enough for a strong bond. Carbon is not electronegative enough.

What Makes Hydrogen Bonding Special?

Unlike other dipole-dipole interactions, hydrogen bonds are directional and stronger. They're about 5–30 kJ/mol, compared to 0.5–2 kJ/mol for ordinary van der Waals forces. This strength has dramatic consequences.

Real-World Consequences

Water's high boiling point — Water ( $H_2O$ ) boils at $100^\circ C$ , while hydrogen sulfide ( $H_2S$ ) boils at $-60^\circ C$ . Both are similar molecules, but water forms hydrogen bonds; $H_2S$ does not (sulfur is not electronegative enough). Those bonds must be broken to boil water, requiring much more energy.

Ice floats — In liquid water, molecules jostle and form temporary hydrogen bonds. When water freezes, the molecules arrange into a hexagonal lattice held open by hydrogen bonds. This structure is less dense than liquid water — hence ice floats. Without hydrogen bonding, ice would sink, and lakes would freeze from the bottom up, killing aquatic life.

DNA double helix — The two strands of DNA are held together by hydrogen bonds between base pairs (adenine-thymine and guanine-cytosine). These bonds are strong enough to keep the strands together, but weak enough to be unzipped during replication. …

Why this formula?

Hydrogen Bonding: Why It Happens — The Reasoning, Not Just the Rule

Hydrogen bonding is not a full covalent bond — it's a special type of intermolecular attraction. To understand why it occurs, we must look at the electronic structure of the atoms involved.

1. The Core Requirement: A "Naked" Proton

A hydrogen bond forms when a hydrogen atom is covalently bonded to a highly electronegative atom (like F, O, or N). Why?

Electronegativity difference pulls the bonding electron pair strongly toward the electronegative atom.
The hydrogen atom is left with almost no electron cloud — it becomes a partially positive proton ( $\delta^+$ ).

Key idea: The hydrogen is now a small, dense positive charge — it can get very close to a lone pair on another electronegative atom.

2. The Electrostatic Attraction (The "Why")

The partially positive hydrogen ( $\delta^+$ ) is attracted to a lone pair of electrons on another electronegative atom (the acceptor).

This is electrostatic — Coulomb's law governs it:

F = \frac{1}{4\pi\varepsilon_0} \cdot \frac{q_1 q_2}{r^2}

$q_1$ = partial positive charge on H
$q_2$ = partial negative charge on lone pair
$r$ = distance between them

Because the hydrogen is so small, $r$ is very small → force is strong (stronger than van der Waals, weaker than covalent).

3. Why Only F, O, N?

Not all electronegative atoms work. The atom must have:

Property	Why it matters
High electronegativity	Pulls electron density away from H, creating $\delta^+$
Small atomic size	Allows close approach of the H to the lone pair
At least one lone pair	Provides the negative site for attraction

F, O, and N satisfy all three. Cl is electronegative but too large — the H cannot get close enough for a strong bond.

4. The "Formula" for Hydrogen Bond Strength

There is no single formula for hydrogen bond energy, but the strength depends on:

E_{\text{H-bond}} \propto \frac{\delta^+ \cdot \delta^-}{r^2}

Where:

$\delta^+$ = partial charge on H (depends on electronegativity of donor atom)
$\delta^-$ = partial charge on acceptor lone pair
$r$ = distance between H and acceptor atom

Typical strengths (for context):

Covalent bond: ~400 kJ/mol
Hydrogen bond: 10–40 kJ/mol
van der Waals: ~1–5 kJ/mol

5. Directionality — The "Linear" Preference

Hydrogen bonds are directional: the strongest interaction occurs when the donor H–X bond and the acceptor lone pair are collinear (180° angle).

Why? Because:

The positive charge on H is concentrated along the bond axis …

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Boiling point depends on the total number of hydrogen bonds per molecule and their strength. Water forms the most extensive network (two H-bonds per molecule), followed by HF (one strong H-bond per molecule), then NH₃ (one weaker H-bond per molecule). The correct order is H₂O > HF > NH₃, option (B).

Why boiling point trends for hydrogen-bonded compounds are not trivial

You might think: "HF has the strongest hydrogen bond because F is the most electronegative — so HF should boil highest." That's a common trap. Boiling point is not about the strength of a single bond alone; it's about the total intermolecular energy that must be overcome to turn the liquid into gas. That depends on how many hydrogen bonds each molecule can form and how they link together.

Water, with two O–H bonds and two lone pairs, can form four hydrogen bonds per molecule in a 3D network. HF, despite the strongest single H-bond, can only form two per molecule (one donor, one acceptor) in zigzag chains. NH₃ has three N–H bonds but only one lone pair, so it forms at most two per molecule — and those bonds are weaker because N is less electronegative than O or F.

Let's break it down step by step.

1. Count the hydrogen bonds each molecule can form

A molecule can act as a donor through its H atoms (bonded to N, O, or F) and as an acceptor through its lone pairs.

Compound	Donor H atoms	Lone pairs	Max H-bonds per molecule
H₂O	2	2	4 (but effectively 2 per molecule in bulk, each shared)
HF	1	3	2 (one donor, one acceptor)
NH₃	3	1	2 (one acceptor, up to three donors but steric limits)

Watch out

Don't confuse "maximum possible" with "actual in the liquid." In bulk water, each molecule forms about 3.4 hydrogen bonds on average at room temperature — but the key point is that water's network is far more extensive than HF's or NH₃'s.

2. Compare the strength of a single hydrogen bond

Electronegativity difference drives H-bond strength: F > O > N. So a single O–H···O bond is weaker than F–H···F, but stronger than N–H···N.

E_{\text{HF}} \approx 40\text{–}50 \quad E_{\text{H}_2\text{O}} \approx 20\text{–}25 \quad E_{\text{NH}_3} \approx 10\text{–}15

3. Combine number × strength to get total intermolecular energy

This is the decisive step. Water's many moderately strong H-bonds per molecule create a 3D network that requires a lot of energy to break. HF's fewer but stronger bonds form only 1D chains — easier to disrupt. NH₃ has both fewer and weaker bonds. …

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Q.Hydrogen bonds are formed in many compounds e.g., H2O, HF, NH3. The boiling point of such compounds depends to a large extent on the strength of hydrogen bond and the number of hydrogen bonds. The correct decreasing order of the boiling points of above compounds is :

Why boiling point trends for hydrogen-bonded compounds are not trivial

1. Count the hydrogen bonds each molecule can form

2. Compare the strength of a single hydrogen bond

3. Combine number × strength to get total intermolecular energy

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