含义Meaning
单色光通过稀溶液时，吸光度与吸光物质浓度和光程成正比。分光光度法定量分析的基础。
For monochromatic light through a dilute solution, absorbance is proportional to concentration and path length — the basis of spectrophotometric analysis.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(A\) | 吸光度absorbance | 1 |
| \(T\) | 透射率transmittance | 1 |
| \(\varepsilon\) | 摩尔吸光系数molar absorption coefficient | L·mol⁻¹·cm⁻¹ |
| \(b\) | 光程path length | cm |
| \(c\) | 浓度concentration | mol·L⁻¹ |
推导Derivation
厚 dx 的薄层吸收的光强与入射光强和吸光分子数成正比：\(-dI = k\,c\,I\,dx\)。
A thin layer dx absorbs in proportion to intensity and absorber concentration: \(-dI = kcI\,dx\).
分离变量积分：\(\ln(I_0/I) = kcb\)。
Integrate: \(\ln(I_0/I) = kcb\).
改用常用对数并令 \(\varepsilon = k/2.303\)：\(A = \lg(I_0/I) = \varepsilon bc\)。
Switch to log₁₀ with \(\varepsilon = k/2.303\).
微观上 ε 与分子吸收截面 σ 成正比：\(\sigma/\mathrm{cm^2} = 3.82\times10^{-21}\,\varepsilon/(\mathrm{L\,mol^{-1}\,cm^{-1}})\)。
Microscopically ε is proportional to the absorption cross-section: \(\sigma/\mathrm{cm^2} = 3.82\times10^{-21}\,\varepsilon/(\mathrm{L\,mol^{-1}\,cm^{-1}})\).
适用条件与局限Assumptions & limitations
适用于稀溶液（通常 c < 0.01 mol/L）；高浓度时分子相互作用、折射率改变导致偏离。
Dilute solutions (usually < 0.01 M); high concentration causes deviations.
要求单色光；多色光、杂散光使校准曲线在高吸光度时弯曲（A 一般控制在 0.2–0.8 误差最小）。
Requires monochromatic light; polychromatic or stray light bends curves at high A (best range 0.2–0.8).
化学偏离：缔合、解离、酸碱平衡随浓度改变吸光物种。散射（浑浊样品）也会造成假吸收。
Chemical deviations: association, dissociation, pH equilibria; scattering adds false absorbance.
例题Worked example
KMnO₄ 在 525 nm ε = 2.4×10³ L/(mol·cm)，1 cm 比色皿测得 A = 0.48：c = 0.48/2400 = 2.0×10⁻⁴ mol/L。
KMnO₄ at 525 nm (ε = 2400): A = 0.48 in 1 cm gives c = 2.0×10⁻⁴ M.