Energy Scale and the Nature of Boiling

General Chemistry I – Week 1

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First-Class Question

When water boils at 100 °C (1 atm), why are the O–H covalent bonds not broken? Answer this question using energy arguments.

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1. Start from Kinetic Theory

From last semester, we learned that the average translational kinetic energy of a molecule is:

E ≈ (3/2) kT

At the boiling point of water:

T = 373 K

Boltzmann constant:

k = 1.38 × 10⁻²³ J/K

Therefore:

kT ≈ 5.1 × 10⁻²¹ J ≈ 0.032 eV

3kT ≈ 1.5 × 10⁻²⁰ J per molecule ≈ 0.1 eV

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2. Convert to Energy per Mole

Multiply by Avogadro's number (6.02 × 10²³):

3kT ≈ 9 kJ/mol (order of magnitude)

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3. Compare Energy Scales

Covalent O–H bond energy:

≈ 460 kJ/mol ≈ 4.8 eV

Hydrogen bond (intermolecular):

≈ 10–25 kJ/mol ~0.1–0.25 eV

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4. What Does This Tell Us?

The average thermal energy at 373 K:

• Is far smaller than covalent bond energy.
• Is comparable to intermolecular interaction energies.

Therefore:

• Molecules do not break apart.
• Hydrogen bonds between molecules can be overcome.
• Molecules separate → phase transition occurs.

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5. The Deeper Point

Boiling is not about breaking molecules. It is about overcoming intermolecular potential energy.

Chemistry often depends on comparing energy scales.

If the available thermal energy is:

• Much smaller than bond energy → no chemical reaction.
• Comparable to intermolecular forces → phase change possible.

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6. A Question for This Semester

Why does boiling occur sharply at 100 °C (1 atm)?

In this semester, we will learn that at the boiling point:

ΔG = 0

Liquid and vapor phases have equal chemical potential (molar Gibbs energy).

Today we just compared energy scales. In this semester we will minimize Gibbs free energy.

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Chemistry begins when we learn to think in energy scales.