\[\text{链长 } \nu = \frac{\text{链传递速率}}{\text{链引发速率}},\qquad \mathrm{H_2 + Br_2}:\ v = \frac{k[\mathrm H_2][\mathrm{Br_2}]^{1/2}}{1 + k'[\mathrm{HBr}]/[\mathrm{Br_2}]}\]\[\text{chain length} \nu = \frac{\text{propagation rate}}{\text{initiation rate}},\qquad \mathrm{H_2 + Br_2}:\ v = \frac{k[\mathrm H_2][\mathrm{Br_2}]^{1/2}}{1 + k'[\mathrm{HBr}]/[\mathrm{Br_2}]}\]
含义Meaning
链反应由引发、传递和终止步骤组成，一次引发可产生许多产物分子。支链反应（如 H₂ + O₂）中自由基数目指数增长，可导致爆炸。
Chain reactions have initiation, propagation and termination; one initiation yields many product molecules. In branching chains (H₂ + O₂) radicals multiply exponentially and can explode.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\nu\) | 动力学链长kinetic chain length | 1 |
推导Derivation
H₂–Br₂：引发 Br₂ → 2Br；传递 Br + H₂ → HBr + H，H + Br₂ → HBr + Br；抑制 H + HBr → H₂ + Br；终止 2Br → Br₂。
H₂–Br₂: initiation, two propagation steps, inhibition by HBr, termination.
对 Br 和 H 用稳态近似，联立解出 [Br] ∝ [Br₂]^{1/2}，代入得博登斯坦–林德方程。
Steady state for Br and H gives [Br] ∝ [Br₂]^{1/2} and the rate law.
支链：每个自由基产生 α > 1 个新自由基，若支化速率超过终止速率，自由基浓度发散 → 爆炸（存在爆炸极限）。
Branching with net growth leads to explosion limits.
适用条件与局限Assumptions & limitations
稳态近似在爆炸条件下失效。
The steady-state approximation fails in explosive regimes.