含义Meaning
理想气体反应的平衡常数可完全由分子性质（质量、转动常数、振动频率、键能）计算，无需测量。
For ideal-gas reactions the equilibrium constant follows entirely from molecular properties — masses, rotational constants, vibrational frequencies and bond energies.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(q_{\mathrm{J},m}^\circ\) | 标准摩尔配分函数（p° 下）standard molar partition function | 1 |
| \(\Delta_rE_0\) | 0 K 反应能（含零点能之差）reaction energy at 0 K (zero-point corrected) | J·mol⁻¹ |
| \(\nu_\mathrm{J}\) | 计量数（产物为正）stoichiometric number (+ for products) | 1 |
推导Derivation
理想气体 \(G_m^\circ(\mathrm J) = G_m(0) - RT\ln(q_m^\circ/N_A)\)。
\(G_m^\circ = G_m(0) - RT\ln(q_m^\circ/N_A)\) for each ideal gas.
\(\Delta_rG^\circ = \sum\nu_\mathrm JG_m^\circ = \Delta_rE_0 - RT\sum\nu_\mathrm J\ln(q_m^\circ/N_A)\)。
Sum with stoichiometric numbers.
由 \(\Delta_rG^\circ = -RT\ln K\) 即得。
Use \(\Delta_rG^\circ = -RT\ln K\).
适用条件与局限Assumptions & limitations
限理想气体；溶液反应需溶剂化模型。对 ΔE₀ 极其敏感（误差 4 kJ/mol → K 误差约 5 倍）。
Ideal gases only; extremely sensitive to ΔE₀ (4 kJ/mol error ≈ factor 5 in K).
例题Worked example
同位素交换 H₂ + D₂ ⇌ 2HD：高温极限 K → 4（对称数比），实际 298 K 约 3.3（零点能差）。
H₂ + D₂ ⇌ 2HD: K → 4 at high T (symmetry numbers), ≈ 3.3 at 298 K (ZPE).