双语化学辞典Chem Lexicon
高中Senior high 化学动力学 Chemical kinetics

速率方程与反应级数Rate law and reaction order

\[v = k[\mathrm A]^m[\mathrm B]^n,\qquad \text{总级数} = m + n\]\[v = k[\mathrm A]^m[\mathrm B]^n,\qquad \text{overall order} = m + n\]
初速率法确定级数method of initial rates
\[\frac{v_2}{v_1} = \left(\frac{[\mathrm A]_2}{[\mathrm A]_1}\right)^m\]

含义Meaning

速率与各反应物浓度幂次之积成正比。级数 m、n 必须由实验确定,一般不等于计量数;只有基元反应的级数等于其分子数(质量作用定律)。

Rate is proportional to a product of concentration powers. Orders must be found by experiment and generally differ from coefficients; only for elementary steps do they equal molecularity (law of mass action).

符号说明Symbols

符号Symbol含义 Meaning单位 Unit
\(k\)速率常数rate constant(随级数而异)
\(m, n\)对 A、B 的反应级数orders in A and B1

推导Derivation

  1. 基元反应 A + B → 产物:碰撞频率 ∝ [A][B],所以 v = k[A][B](质量作用定律,古德贝格–瓦格,1864)。

    For an elementary A + B step collision frequency ∝ [A][B] (law of mass action).

  2. 总反应的速率方程由机理决定(决速步、预平衡等),可出现分数或零级。

    Overall rate laws follow from mechanisms and can have fractional or zero order.

  3. 初速率法:保持其他浓度不变,改变 [A] 观察速率倍数,取对数得 m。

    Initial rates: vary [A] alone and compare.

适用条件与局限Assumptions & limitations

  • 速率方程只在一定浓度、温度范围内有效;产物抑制、催化等可使形式更复杂。

    Valid over limited ranges; inhibition or catalysis complicates it.

  • k 的单位随总级数变化:(mol/L)^{1−n}·s⁻¹。

    k has units (mol/L)^{1−n} s⁻¹.

例题Worked example

H₂ + Br₂ 的速率方程 v = k[H₂][Br₂]^{1/2}/(1 + k′[HBr]/[Br₂]),说明它是链反应而非基元反应。

H₂ + Br₂ has a complex rate law revealing a chain mechanism.