\[\Delta_rG = \Delta_rG^\circ + RT\ln Q = RT\ln\frac QK\]
含义Meaning
任意组成下反应的吉布斯能变化。Q < K 时 ΔG < 0，正向自发；Q > K 时逆向自发；Q = K 时平衡。
The reaction Gibbs energy at any composition: Q < K means forward is spontaneous, Q > K reverse, Q = K equilibrium.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(Q\) | 反应商（形式同 K，但用任意时刻的活度）reaction quotient (like K but at current activities) | 1 |
推导Derivation
\(\Delta_rG = \sum\nu_\mathrm J\mu_\mathrm J = \sum\nu_\mathrm J(\mu_\mathrm J^\circ + RT\ln a_\mathrm J)\)。
Sum chemical potentials with stoichiometric numbers.
\(= \Delta_rG^\circ + RT\ln\prod a_\mathrm J^{\nu_\mathrm J} = \Delta_rG^\circ + RT\ln Q\)。
Collect the logarithms into ln Q.
代入 \(\Delta_rG^\circ = -RT\ln K\) 得 \(RT\ln(Q/K)\)。
Use ΔrG° = −RT ln K.
适用条件与局限Assumptions & limitations
ΔrG 是反应进度的微分量（\(\partial G/\partial\xi\)），描述此刻的趋势，而非整个反应的总变化。
ΔrG is ∂G/∂ξ — the current tendency, not a total change.