含义Meaning
A ⇌ B 体系向平衡的趋近速率由正、逆速率常数之和决定。温度跳跃、压力跳跃等弛豫方法（艾根）据此测量极快反应。
An A ⇌ B system approaches equilibrium at a rate set by the sum of forward and reverse rate constants. Relaxation methods (temperature or pressure jump, Eigen) use this to measure very fast reactions.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\tau\) | 弛豫时间relaxation time | s |
| \(K\) | 平衡常数equilibrium constant | 1 |
推导Derivation
\(-d[\mathrm A]/dt = k_1[\mathrm A] - k_{-1}[\mathrm B]\)，\([\mathrm B] = [\mathrm A]_0 - [\mathrm A]\)。
Write the net rate with mass balance.
令 \(x = [\mathrm A] - [\mathrm A]_\text{eq}\)，平衡时净速率为零，得 \(dx/dt = -(k_1 + k_{-1})x\)。
With x the deviation from equilibrium, \(dx/dt = -(k_1 + k_{-1})x\).
测得 τ 和 K 即可分别求 k₁、k₋₁。
τ and K together give both rate constants.
适用条件与局限Assumptions & limitations
二级对峙反应在小扰动下也可线性化，τ 表达式不同（如 \(1/\tau = k_1([\mathrm A] + [\mathrm B])_\text{eq} + k_{-1}\)）。
Second-order equilibria linearise for small perturbations with different τ.
例题Worked example
H⁺ + OH⁻ ⇌ H₂O 的复合速率常数（1.4×10¹¹ L·mol⁻¹·s⁻¹）由温度跳跃法测得，是已知最快的溶液反应之一。
H⁺ + OH⁻ recombination (1.4×10¹¹ L mol⁻¹ s⁻¹) was measured by temperature jump.