含义Meaning
平衡常数随温度的变化由反应焓决定（1884）：吸热反应升温 K 增大，放热反应升温 K 减小——勒夏特列原理的定量形式。ln K 对 1/T 作图，斜率 −ΔH°/R。
How K changes with temperature, set by the reaction enthalpy (1884): heating raises K for endothermic and lowers it for exothermic reactions — Le Chatelier made quantitative. ln K versus 1/T has slope −ΔH°/R.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\Delta_rH^\circ\) | 标准反应焓standard reaction enthalpy | kJ·mol⁻¹ |
推导Derivation
\(\ln K = -\Delta_rG^\circ/RT\)，对 T 求导。
Differentiate ln K = −ΔG°/RT.
由吉布斯–亥姆霍兹方程 \(d(\Delta G^\circ/T)/dT = -\Delta H^\circ/T^2\) 得上式。
Gibbs–Helmholtz gives the result.
若 ΔH° 在区间内近似不变，积分得两温度式；也可写成 \(\ln K = -\frac{\Delta H^\circ}{RT} + \frac{\Delta S^\circ}{R}\)。
For constant ΔH°, integrate; equivalently ln K = −ΔH°/RT + ΔS°/R.
适用条件与局限Assumptions & limitations
温度范围大时 ΔH° 随温度变化（基尔霍夫定律），需考虑 ΔCp。
Over wide ranges include ΔCp (Kirchhoff).
例题Worked example
N₂ + 3H₂ ⇌ 2NH₃（ΔH° = −92 kJ/mol）：K(298 K) ≈ 6×10⁵，K(700 K) ≈ 10⁻⁴ ——高温不利于平衡产率，所以哈伯法需权衡速率与平衡。
Ammonia synthesis: K falls from ~6×10⁵ at 298 K to ~10⁻⁴ at 700 K — the Haber trade-off between rate and yield.