pKa 与取代基：酸性的定量比较 pKa and substituent effects — 公式推导、符号与局限

\[\Delta G^\circ_{\text{电离}} = 2.303\,RT\,\mathrm{p}K_a,\qquad \Delta\mathrm{p}K_a = \frac{\delta\Delta G^\circ}{5.71\ \mathrm{kJ\,mol^{-1}}}\ (25\,{}^\circ\mathrm{C})\]\[\Delta G^\circ_{\text{ionisation}} = 2.303\,RT\,\mathrm{p}K_a,\qquad \Delta\mathrm{p}K_a = \frac{\delta\Delta G^\circ}{5.71\ \mathrm{kJ\,mol^{-1}}}\ (25\,{}^\circ\mathrm{C})\]

含义Meaning

每 1 个 pKa 单位对应 5.71 kJ/mol 的电离自由能差。吸电子基稳定共轭碱、降低 pKa；诱导效应随距离迅速衰减（约每隔一个 CH₂ 减弱一半）。

Each pKa unit corresponds to 5.71 kJ/mol of ionisation free energy at 25 °C. Electron-withdrawing groups stabilise the conjugate base and lower pKa; inductive effects roughly halve per CH₂.

符号说明Symbols

符号Symbol	含义 Meaning	单位 Unit
\(\mathrm{p}K_a\)	酸解离常数的负对数negative log of Ka	1

推导Derivation

\(\Delta G^\circ = -RT\ln K_a = 2.303RT\,\mathrm{p}K_a\)。
\(\Delta G^\circ = -RT\ln K_a = 2.303RT\,\mathrm{p}K_a\).
25 °C 时 \(2.303RT = 5.71\ \mathrm{kJ/mol}\)。
At 25 °C, \(2.303RT = 5.71\) kJ/mol.

适用条件与局限Assumptions & limitations

pKa 依赖溶剂：气相、DMSO、水中的酸性顺序可以不同（如醇在气相中酸性随烷基增大而增强）。
pKa is solvent-dependent; gas-phase, DMSO and water orders can differ.

例题Worked example

乙酸 4.76、氯乙酸 2.86、二氯乙酸 1.29、三氯乙酸 0.65；4-氯丁酸 4.52，说明诱导效应随距离衰减。

Acetic 4.76, chloroacetic 2.86, dichloroacetic 1.29, trichloroacetic 0.65; 4-chlorobutanoic 4.52 shows decay with distance.