含义Meaning
只有一种离子能透过膜时，膜两侧达到平衡的电位差（平衡电位、反转电位）。
The equilibrium (reversal) potential across a membrane permeable to only one ion.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(E_{\text{ion}}\) | 平衡电位（内相对外）equilibrium potential (inside relative to outside) | V |
| \(z\) | 离子电荷数charge number | 1 |
| \(F\) | 法拉第常数Faraday constant | 96485 C·mol⁻¹ |
推导Derivation
离子在膜内外的电化学势：\(\tilde\mu = \mu^\circ + RT\ln c + zF\phi\)。
Electrochemical potential: \(\tilde\mu = \mu^\circ + RT\ln c + zF\phi\).
平衡时 \(\tilde\mu_{\text{内}} = \tilde\mu_{\text{外}}\)：\(RT\ln c_{\text{内}} + zF\phi_{\text{内}} = RT\ln c_{\text{外}} + zF\phi_{\text{外}}\)。
At equilibrium the two are equal.
整理得 \(\phi_{\text{内}} - \phi_{\text{外}} = \frac{RT}{zF}\ln\frac{c_{\text{外}}}{c_{\text{内}}}\)。
Rearrange for \(\phi_{\text{in}} - \phi_{\text{out}}\).
适用条件与局限Assumptions & limitations
只描述单一离子的平衡；静息膜电位由多种离子共同决定，需用戈德曼方程。
Single-ion equilibrium only; the resting potential involves several ions (Goldman equation).
用浓度代替活度。
Uses concentrations for activities.
例题Worked example
神经元 [K⁺]外 = 5 mmol/L、[K⁺]内 = 140 mmol/L：E_K = 61.5×lg(5/140) = −89 mV。
Neuron K⁺ 5 mM out, 140 mM in: E_K = −89 mV.