双语化学辞典Chem Lexicon
本科Undergraduate 化学动力学 Chemical kinetics

稳态近似Steady-state approximation

\[\frac{d[\mathrm I]}{dt} \approx 0\]

含义Meaning

对于高活性、浓度很低的中间体(自由基、碳正离子、酶–底物复合物),其生成速率与消耗速率近似相等,浓度保持近似恒定。是从机理推导速率方程的最重要工具(博登斯坦,1913)。

For highly reactive, low-concentration intermediates (radicals, carbocations, enzyme–substrate complexes) formation and consumption nearly balance, so their concentration is roughly constant — the key tool for deriving rate laws from mechanisms (Bodenstein, 1913).

符号说明Symbols

符号Symbol含义 Meaning单位 Unit
\([\mathrm I]\)中间体浓度intermediate concentrationmol·L⁻¹

推导Derivation

  1. 以 A → I(k₁),I → P(k₂)为例:\(d[\mathrm I]/dt = k_1[\mathrm A] - k_2[\mathrm I]\)。

    Example A → I → P.

  2. 若 \(k_2 \gg k_1\),I 一生成就被消耗,经过短暂诱导期后 \(d[\mathrm I]/dt \approx 0\)。

    If k₂ ≫ k₁, after a brief induction period d[I]/dt ≈ 0.

  3. 于是 \([\mathrm I] = k_1[\mathrm A]/k_2\),产物生成速率 \(k_2[\mathrm I] = k_1[\mathrm A]\):总速率由第一步决定。

    Then [I] = k₁[A]/k₂ and the product rate equals k₁[A].

适用条件与局限Assumptions & limitations

  • 只有中间体浓度远小于反应物、且消耗远快于生成时才成立;不能用于反应初期的诱导期。

    Valid only when the intermediate stays scarce and reacts fast; not during the induction period.