含义Meaning
单层、均匀表面、吸附分子间无作用时的吸附覆盖度与压强的关系（1916）。低压时与压强成正比，高压时趋于饱和单层。多相催化动力学（朗缪尔–欣谢尔伍德机理）的基础。
Coverage versus pressure for monolayer adsorption on a uniform surface with no lateral interactions (1916): proportional to p at low pressure, saturating at a monolayer at high pressure. The basis of Langmuir–Hinshelwood kinetics in heterogeneous catalysis.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\theta\) | 表面覆盖度 V/V_mfractional coverage V/V_m | 1 |
| \(K\) | 吸附平衡常数 k_a/k_dadsorption equilibrium constant | Pa⁻¹ |
| \(V_m\) | 单层饱和吸附量monolayer capacity | cm³·g⁻¹ |
推导Derivation
吸附速率 \(\propto p(1 - \theta)\)（只有空位能吸附），脱附速率 \(\propto \theta\)。
Adsorption rate ∝ p(1 − θ) on empty sites; desorption ∝ θ.
平衡时 \(k_ap(1-\theta) = k_d\theta\)，解出 \(\theta = Kp/(1 + Kp)\)。
At equilibrium \(k_ap(1-\theta) = k_d\theta\).
线性化：以 p/V 对 p 作图，斜率 1/V_m、截距 1/(KV_m)。
Linear form: p/V versus p gives V_m and K.
K 随温度按 \(K = K_0e^{-\Delta H_\text{ads}/RT}\) 变化（吸附放热，升温 K 减小）。
K follows \(K_0e^{-\Delta H_\text{ads}/RT}\); exothermic adsorption weakens with heating.
适用条件与局限Assumptions & limitations
真实表面不均匀、吸附热随覆盖度下降、存在侧向作用和多层吸附，此时用弗罗因德利希、捷姆金或 BET 等温式。
Real surfaces are heterogeneous, with coverage-dependent heats, lateral interactions and multilayers — use Freundlich, Temkin or BET.