Chemistry Van Der Waals Noble Gas Bp Increases Ar Kr

Noble gas boiling points

Noble gases are the elements in group 18 of the periodic table: helium, neon, argon, krypton, xenon, and radon. Their boiling points rise steadily down the group, from 4.22 K for helium to 211.4 K for radon. The trend is a textbook consequence of van der Waals forces, the weak attractions between uncharged atoms that grow stronger as atoms get larger and more easily distorted.

The specific step from argon to krypton is a small but concrete instance. Argon, with 18 electrons, boils at 87.30 K. Krypton, with 36 electrons, boils at 119.93 K. The difference, 32.63 K, reflects krypton's greater polarizability: its electron cloud is larger, so temporary fluctuations in charge distribution create stronger instantaneous dipoles, and those dipoles bind the atoms more firmly in the liquid state.

In Recognition Science, the framework models this trend with a discrete ledger of electron distribution events. The ledger's eight-tick cycle creates temporary asymmetries that act as instantaneous dipoles; polarizability rises with the number of electron shells. The framework's machine-checked library of formal theorems contains a proof, named noble_gas_bp_increases_ar_kr, that the boiling point of argon is less than the boiling point of krypton. The proof is a direct numerical check on the framework's own table of boiling points, not a measurement or a new physical law.

The theorem does not claim that van der Waals forces are the only factor in boiling point, nor that the framework's polarizability proxy is a complete physical model. It certifies an ordering within a defined list of numbers. The physical explanation, that larger atoms have stronger dispersion forces, remains a standard chemistry account, not a result of the framework's proof.

theorem noble_gas_bp_increases_ar_kr : nobleGasBoilingPoint 18 < nobleGasBoilingPoint 36 := by
  simp only [nobleGasBoilingPoint]
  norm_num

What this page does not claim

The theorem does not prove that van der Waals forces are the sole cause of the boiling point ordering. The theorem does not establish the framework's polarizability proxy as a physically accurate model. The theorem does not derive the numerical boiling point values from first principles.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Chemistry/VanDerWaals.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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