双语化学辞典Chem Lexicon
本科Undergraduate 化学平衡 Chemical equilibrium

勒夏特列原理的定量形式Le Chatelier's principle, quantitatively

\[\left(\frac{\partial\ln K_x}{\partial p}\right)_T = -\frac{\Delta n_g}{p},\qquad \left(\frac{\partial\ln K}{\partial T}\right)_p = \frac{\Delta_rH^\circ}{RT^2}\]

含义Meaning

改变浓度、压强或温度时,平衡向减弱这种改变的方向移动。定量判断:浓度、压强的改变使 Q ≠ K;温度的改变则直接改变 K。

An equilibrium shifts to counteract an imposed change. Quantitatively, changing concentration or pressure makes Q ≠ K, whereas changing temperature changes K itself.

符号说明Symbols

符号Symbol含义 Meaning单位 Unit
\(K_x\)以摩尔分数表示的平衡常数mole-fraction equilibrium constant1
\(\Delta n_g\)气体分子数变化change in moles of gas1

推导Derivation

  1. 理想气体 \(K_p = K_xp^{\Delta n_g}\),Kp 只与 T 有关,所以 \(K_x \propto p^{-\Delta n_g}\):加压使平衡向气体分子数减少的方向移动。

    Since Kp depends only on T, \(K_x \propto p^{-\Delta n_g}\).

  2. 恒容加入惰性气体:分压不变,平衡不移动;恒压加入惰性气体:相当于减压。

    Inert gas at constant volume: no shift; at constant pressure: like lowering p.

  3. 温度:由范特霍夫方程,吸热方向随升温而有利。

    Temperature: van ’t Hoff.

适用条件与局限Assumptions & limitations

  • 原理只给方向,不给移动程度;某些情况(如在恒压下向 N₂ + 3H₂ ⇌ 2NH₃ 加 N₂)定性判断会出错,需用 Q 与 K 比较。

    Gives direction only; some cases (adding N₂ at constant pressure in certain compositions) need a Q-vs-K check.

例题Worked example

N₂O₄ ⇌ 2NO₂(298 K,Kp = 0.148):1 bar 时解离度 18.9%,10 bar 时 6.1%。

N₂O₄ ⇌ 2NO₂: dissociation 18.9 % at 1 bar, 6.1 % at 10 bar.