双语化学辞典Chem Lexicon
本科Undergraduate 结构、立体化学与物理有机 Structure, stereochemistry & physical organic chemistry

对映体过量Enantiomeric excess

\[ee = \frac{|n_R - n_S|}{n_R + n_S}\times 100\% \approx \frac{[\alpha]_{\text{观测}}}{[\alpha]_{\text{纯}}}\times 100\%\]\[ee = \frac{|n_R - n_S|}{n_R + n_S}\times 100\% \approx \frac{[\alpha]_{\text{obs}}}{[\alpha]_{\text{pure}}}\times 100\%\]
对映体比enantiomeric ratio
\[er = \frac{n_R}{n_S},\qquad ee = \frac{er - 1}{er + 1}\]
不对称催化中两条路径的活化能差difference in activation energies in asymmetric catalysis
\[\Delta\Delta G^\ddagger = RT\ln er\]

含义Meaning

主要对映体超过次要对映体的摩尔分数。外消旋体 ee = 0，纯对映体 ee = 100%。

Excess of the major over the minor enantiomer as a mole fraction: racemate 0 %, pure enantiomer 100 %.

符号说明Symbols

符号Symbol含义 Meaning单位 Unit
\(n_R, n_S\)两对映体的量amounts of each enantiomermol
\(er\)对映体比enantiomeric ratio1
\(\Delta\Delta G^\ddagger\)非对映过渡态能量差energy gap between diastereomeric transition stateskJ·mol⁻¹

推导Derivation

  1. 按定义；旋光度对两对映体线性叠加且大小相等符号相反，所以光学纯度 \(= [\alpha]/[\alpha]_{\max} = (n_R - n_S)/(n_R + n_S)\)。

    By definition; rotations add linearly with equal and opposite contributions, so optical purity equals ee.

  2. 动力学控制下产物比等于速率常数比 \(k_R/k_S = \exp(\Delta\Delta G^\ddagger/RT)\)。

    Under kinetic control the product ratio equals \(k_R/k_S = \exp(\Delta\Delta G^\ddagger/RT)\).

  3. 因此 90% ee（er = 19）在 25 °C 只需 \(\Delta\Delta G^\ddagger = 7.3\ \mathrm{kJ/mol}\)。

    So 90 % ee (er = 19) at 25 °C needs only 7.3 kJ/mol.

适用条件与局限Assumptions & limitations

  • 光学纯度法受杂质、非线性效应（Horeau 效应）影响；现代测定用手性 HPLC/GC 或手性位移试剂 NMR。

    Optical-purity methods suffer from impurities and non-linear effects; use chiral HPLC/GC or NMR with chiral shift reagents.