\[\alpha_{\mathrm{HA}} = \frac{[\mathrm H^+]}{[\mathrm H^+] + K_a},\quad \alpha_{\mathrm A^-} = \frac{K_a}{[\mathrm H^+] + K_a};\qquad \alpha_j(\mathrm H_n\mathrm A) = \frac{[\mathrm H^+]^{n-j}\prod_{i\le j}K_{ai}}{\sum_{k=0}^n[\mathrm H^+]^{n-k}\prod_{i\le k}K_{ai}}\]
含义Meaning
各型体占总浓度的分数只取决于 pH 与 pKa，与总浓度无关。pH = pKa 时相邻两型体各占 50%。
Fractions of each species depend only on pH and the pKa values, not on total concentration; adjacent species are 50:50 at pH = pKa.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\alpha_j\) | 失去 j 个质子的型体分数fraction of the species that has lost j protons | 1 |
推导Derivation
写出总浓度 \(c = [\mathrm H_n\mathrm A] + [\mathrm H_{n-1}\mathrm A^-] + \cdots\)，用逐级 Ka 把各型体都表示为 [HₙA] 的倍数。
Express every species through the stepwise Ka values and [HₙA].
除以总和即得各分数。
Divide by the sum.
适用条件与局限Assumptions & limitations
忽略活度与其他配位副反应。
Ignores activity and other side reactions.