Chemistry Van Der Waals Noble Gas Bp Increases Ne Ar

The noble gas boiling point theorem

In chemistry, the noble gases helium, neon, argon, krypton, xenon, and radon show a clear trend: their boiling points rise steadily as you move down the group. Helium boils at 4.22 kelvin, neon at 27.07, argon at 87.30, krypton at 119.93, xenon at 165.05, and radon at 211.4. The standard explanation is that larger atoms have more electrons and a larger, more polarizable electron cloud, which strengthens the weak attractions between atoms. Those attractions, the van der Waals forces, must be overcome to separate the atoms into a gas, so stronger forces mean a higher boiling point.

The formal statement named noble_gas_bp_increases_ne_ar says, in the machine-checked library of formal statements, that the boiling point of neon is less than the boiling point of argon. It verifies the inequality 27.07 < 87.30 by direct computation from the table of boiling points defined in the same file. This is a narrow result: it does not derive the boiling points from first principles, nor does it prove the trend for any other pair of noble gases. It simply checks one numerical comparison that the table already contains.

The statement sits in a broader formal development of van der Waals forces. That development defines a proxy for polarizability, the tendency of an atom's electron cloud to distort in an electric field, as the period number of the element. It also defines a London dispersion force proxy that scales with the product of two atoms' polarizabilities and inversely with the sixth power of their separation, matching the classical 1/r⁶ dependence. The framework's own account, described in the file's docstring, ties these to an eight-tick ledger of recognition events, but the boiling point statement itself does not depend on that mechanism.

What the declaration does not claim is just as important. It does not prove that the boiling point trend causes or is caused by van der Waals forces; it only records the numerical fact. It does not establish the trend for any pair other than neon and argon, although companion statements cover the other adjacent pairs. And it does not derive the boiling point values from atomic properties, polarizability, or any physical law. The values are entered as definitions, and the statement merely checks the ordering.

For a reader, the practical takeaway is that the formal library has verified one small piece of standard chemistry: neon boils below argon. The statement is a check on the data table, not a derivation of the data. It is a building block in a larger formalization that aims to connect van der Waals forces to the framework's recognition-based account of physical structure, but that connection remains a program, not a proved result.

theorem noble_gas_bp_increases_ne_ar : nobleGasBoilingPoint 10 < nobleGasBoilingPoint 18 := by
  simp only [nobleGasBoilingPoint]
  norm_num

theorem noble_gas_bp_increases_ne_ar : nobleGasBoilingPoint 10 < nobleGasBoilingPoint 18 := by
  simp only [nobleGasBoilingPoint]
  norm_num

/-- Boiling points of noble gases (Kelvin). -/
def nobleGasBoilingPoint : ℕ → ℝ
| 2  => 4.22    -- He
| 10 => 27.07   -- Ne
| 18 => 87.30   -- Ar
| 36 => 119.93  -- Kr
| 54 => 165.05  -- Xe
| 86 => 211.4   -- Rn
| _  => 0

What this page does not claim

The statement does not derive the boiling point trend from van der Waals forces or polarizability. The statement does not prove the boiling point ordering for any pair other than neon and argon. The statement does not establish that the framework's recognition ledger causes the observed boiling points.

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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