含义Meaning
艾林、埃文斯和波拉尼（1935）假设反应物与活化络合物（过渡态）处于准平衡，过渡态以频率 kT/h 越过势垒。由此可从速率常数的温度依赖得到活化焓和活化熵。
Eyring, Evans and Polanyi (1935) assumed quasi-equilibrium between reactants and the activated complex, which crosses the barrier at frequency kT/h. Temperature dependence then yields activation enthalpy and entropy.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\Delta^\ddagger G^\circ\) | 活化吉布斯能Gibbs energy of activation | kJ·mol⁻¹ |
| \(\Delta^\ddagger H^\circ, \Delta^\ddagger S^\circ\) | 活化焓、活化熵enthalpy and entropy of activation | kJ·mol⁻¹, J·mol⁻¹·K⁻¹ |
| \(\kappa\) | 透射系数（通常取 1）transmission coefficient (usually 1) | 1 |
| \(k_\mathrm BT/h\) | 普适频率（298 K 时 6.2×10¹² s⁻¹）universal frequency (6.2×10¹² s⁻¹ at 298 K) | s⁻¹ |
推导Derivation
A + B ⇌ [AB]‡ → P，\(K^\ddagger = [\mathrm{AB}^\ddagger]/([\mathrm A][\mathrm B])\)。
Assume A + B ⇌ [AB]‡ in quasi-equilibrium.
沿反应坐标的那个振动频率 ν 很低，把它从 \(K^\ddagger\) 的配分函数中分离出来得 \(k_\mathrm BT/h\nu\)。
Factor the low reaction-coordinate vibration out of the partition function, giving \(k_\mathrm BT/h\nu\).
速率 = ν[AB‡]，ν 相消：\(k = (k_\mathrm BT/h)\bar K^\ddagger\)。
Rate = ν[AB‡]; ν cancels.
用 \(\Delta^\ddagger G^\circ = -RT\ln\bar K^\ddagger\) 得艾林方程。
Use \(\Delta^\ddagger G^\circ = -RT\ln\bar K^\ddagger\).
适用条件与局限Assumptions & limitations
假设越过过渡态后不返回（κ ≈ 1）；隧穿（轻原子转移）和溶剂动力学效应需修正。
Assumes no recrossing; tunnelling and solvent dynamics need corrections.
活化熵符号可提示机理：缔合型 ΔS‡ < 0，解离型 ΔS‡ > 0。
The sign of ΔS‡ hints at associative (<0) or dissociative (>0) mechanisms.
例题Worked example
室温下 ΔG‡ = 80 kJ/mol 对应 k = 6.2×10¹²×e^(−80000/2478) ≈ 0.06 s⁻¹（t½ ≈ 11 s）；每增加 5.7 kJ/mol 速率降为 1/10。
At room temperature ΔG‡ = 80 kJ/mol gives k ≈ 0.06 s⁻¹; each 5.7 kJ/mol slows it tenfold.