双语化学辞典Chem Lexicon
本科Undergraduate 电化学 Electrochemistry

离子迁移数Transport (transference) number

\[t_+ = \frac{I_+}{I} = \frac{u_+}{u_+ + u_-} = \frac{\nu_+\lambda_+}{\Lambda_m},\qquad t_+ + t_- = 1\]

含义Meaning

某种离子所迁移的电量占总电量的分数,取决于离子迁移率。用希托夫法或界面移动法测定,可把电导率分解为各离子的贡献。

The fraction of current carried by an ion, set by its mobility; measured by the Hittorf or moving-boundary method, it splits conductance into ionic contributions.

符号说明Symbols

符号Symbol含义 Meaning单位 Unit
\(u_\pm\)离子电迁移率ionic mobilitym²·V⁻¹·s⁻¹
\(\lambda_\pm\)离子摩尔电导率ionic molar conductivityS·m²·mol⁻¹

推导Derivation

  1. 离子漂移速度 \(v = uE\),所以各离子承载的电流 ∝ 浓度 × 电荷 × 迁移率。

    Drift velocity v = uE, so current ∝ c z u.

  2. 对 1:1 电解质,\(t_+ = u_+/(u_+ + u_-)\)。

    For a 1:1 salt t₊ = u₊/(u₊ + u₋).

  3. 离子摩尔电导 \(\lambda = zFu\)。

    λ = zFu.

适用条件与局限Assumptions & limitations

  • 迁移数随浓度略变;溶剂化离子的有效大小影响迁移率。

    Varies slightly with concentration.

例题Worked example

KCl 中 t(K⁺) ≈ 0.49,接近 0.5,所以 KCl 盐桥可减小液接电势;HCl 中 t(H⁺) ≈ 0.82。

In KCl t(K⁺) ≈ 0.49, hence its use in salt bridges; in HCl t(H⁺) ≈ 0.82.