定义Definition
平衡常数 K 是可逆反应达到平衡时,生成物浓度(或分压)幂之积与反应物浓度(或分压)幂之积的比值,各浓度的指数等于化学方程式中的计量数。对给定反应,K 只随温度改变。
The equilibrium constant K is, for a reversible reaction at equilibrium, the product of the product concentrations (or partial pressures) divided by the product of the reactant concentrations (or partial pressures), each raised to the power of its coefficient in the balanced equation. For a given reaction K changes only with temperature.
表达式Writing the expression
对 aA + bB ⇌ cC + dD,Kc = [C]ᶜ[D]ᵈ / ([A]ᵃ[B]ᵇ),方括号表示平衡浓度(mol dm⁻³)。气相反应也可用分压表示:Kp = p(C)ᶜp(D)ᵈ / (p(A)ᵃp(B)ᵇ)。纯固体和纯液体(包括稀溶液中的溶剂水)不写入表达式。K 的单位由表达式中的浓度单位决定,指数相互抵消时 K 无单位。
For aA + bB ⇌ cC + dD, Kc = [C]ᶜ[D]ᵈ / ([A]ᵃ[B]ᵇ), where square brackets are equilibrium concentrations in mol dm⁻³. For gases partial pressures can be used: Kp = p(C)ᶜp(D)ᵈ / (p(A)ᵃp(B)ᵇ). Pure solids and pure liquids (including water as solvent in dilute solution) are left out. The units of K follow from the expression; when the powers cancel, K has no units.
K 的意义What K tells you
K 很大(如 > 10¹⁰)说明平衡时几乎全部为生成物,反应进行得很完全;K 很小说明平衡时主要是反应物。K 只反映反应能进行到什么程度,不反映反应快慢。把任意时刻的浓度代入同一表达式得到浓度商 Q:Q < K 时反应正向进行,Q > K 时逆向进行,Q = K 时处于平衡。
A very large K (say > 10¹⁰) means the equilibrium mixture is almost all products and the reaction goes essentially to completion; a very small K means mostly reactants remain. K shows how far a reaction goes, not how fast. Putting the concentrations at any moment into the same expression gives the reaction quotient Q: if Q < K the reaction moves forward, if Q > K it moves backward, and if Q = K it is at equilibrium.
温度与其他条件Temperature and other conditions
改变浓度、压强或加入催化剂都不改变 K,只改变到达平衡的位置或快慢。只有温度能改变 K:对放热反应,升温使 K 减小;对吸热反应,升温使 K 增大。这与勒夏特列原理的预测一致。
Changing concentration or pressure, or adding a catalyst, does not change K; they change only the position reached or the time taken. Only temperature changes K: for an exothermic reaction K decreases as temperature rises; for an endothermic reaction it increases. This agrees with Le Chatelier's principle.
与吉布斯自由能的关系Link to Gibbs energy
标准吉布斯自由能变与标准平衡常数的关系为 ΔG° = −RT ln K。ΔG° 为负时 K > 1;ΔG° 每变化约 5.7 kJ mol⁻¹,298 K 下 K 改变 10 倍。K 随温度的变化由范特霍夫方程描述。
The standard Gibbs energy change is related to the standard equilibrium constant by ΔG° = −RT ln K. A negative ΔG° gives K > 1; at 298 K, each change of about 5.7 kJ mol⁻¹ in ΔG° changes K tenfold. The temperature dependence of K is described by the van 't Hoff equation.
反应Reactions
仅随温度变化
depends only on temperature
指数相互抵消,Kc 无单位
the powers cancel, so Kc has no units
Kc 的单位为 mol⁻² dm⁶
Kc has units of mol⁻² dm⁶
固体不写入表达式
solids are left out of the expression
年表Timeline
- 1864
古德贝格与瓦格提出质量作用定律
Guldberg and Waage state the law of mass action
- 1884
范特霍夫给出平衡常数随温度变化的关系
van 't Hoff gives the temperature dependence of the equilibrium constant
- 1884
勒夏特列提出平衡移动原理
Le Chatelier states his principle of equilibrium shift
- 1876–1878
吉布斯建立化学平衡的热力学基础
Gibbs lays the thermodynamic foundations of chemical equilibrium
相关公式Formulas
例题Worked example
H₂ + I₂ ⇌ 2HI,698 K 时 K = 54:若起始 [H₂] = [I₂] = 1.00 mol/L,平衡时 [HI] = 1.57 mol/L。
H₂ + I₂ ⇌ 2HI at 698 K (K = 54): from 1.00 M each, [HI] = 1.57 M at equilibrium.
例题Worked example
N₂O₄ ⇌ 2NO₂,298 K,Kc = 5.9×10⁻³ mol/L:Kp = 5.9×10⁻³×0.08314×298 = 0.146(bar)。
N₂O₄ ⇌ 2NO₂ at 298 K: Kp = 0.146 bar.
例题Worked example
Ag⁺ + e⁻ → Ag(0.799 V)与 AgCl + e⁻ → Ag + Cl⁻(0.222 V):lg Ksp = (0.222 − 0.799)/0.05916 = −9.75,Ksp(AgCl) = 1.8×10⁻¹⁰。
From the Ag⁺/Ag and AgCl/Ag potentials: Ksp(AgCl) = 1.8×10⁻¹⁰.