In spectroscopy, an isosbestic point is a specific wavelength, wavenumber or frequency at which the total absorbance of a sample does not change during a chemical reaction or a physical change of the sample. The word is derived from two Greek words: "iso", meaning "equal", and "sbestos", meaning "extinguishable".
Interpretation An isosbestic point corresponds to an absorbance A λ {\displaystyle A_{\lambda }} at a fixed wavelength λ {\displaystyle \lambda } that remains fixed. The absorbance can be written as sum of absorbances of each species (Beer–Lambert law)
A λ = ℓ ∑ i = 1 n ϵ i ( λ ) c i , {\displaystyle A_{\lambda }=\ell \sum _{i=1}^{n}\epsilon _{i}(\lambda )c_{i}\,,}
where c i {\displaystyle c_{i}} the concentration of species i, ℓ {\displaystyle \ell } the optical path length. By definition, an isosbestic point can be interpreted as a fixed linear combination of species concentrations,
L = ∑ i n b i c i , d L d t = 0 , {\displaystyle L=\sum _{i}^{n}b_{i}c_{i},\ \ \ {\frac {dL}{dt}}=0\,,}
i.e. an isobestic point is a conservation law. The IUPAC gold book provides as an example the reaction
A + B → c C + d D + e E , {\displaystyle A+B\rightarrow cC+dD+eE\,,}
which will lead to an isosbestic point if
ϵ A ( λ ) + ϵ B ( λ ) = c ϵ C ( λ ) + d ϵ D ( λ ) + e ϵ E ( λ ) , {\displaystyle \epsilon _{A}(\lambda )+\epsilon _{B}(\lambda )=c\ \epsilon _{C}(\lambda )+d\ \epsilon _{D}(\lambda )+e\ \epsilon _{E}(\lambda )\,,}
Isosbestic points can be observed in a variety of techniques (for instance UV-VIS, IR, NMR). In UV-VIS, an isosbestic point is often interpreted as implying the occurrence of a single linearly independent reaction. The simplest examples of isosbestic points involve only two species, but isosbestic points do not imply the participation of only two species (e.g. the IUPAC example involves 5 species), which is a common misconception.
Isosbestic plot When an isosbestic plot is constructed by the superposition of the absorption spectra of two species (whether by using molar absorptivity for the representation, or by using absorbance and keeping the same molar concentration for both species), the isosbestic point corresponds to a wavelength at which these spectra cross each other. A pair of substances can have several isosbestic points in their spectra. When a 1-to-1 (one mole of reactant gives one mole of product) chemical reaction (including equilibria) involves a pair of substances with an isosbestic point, the absorbance of the reaction mixture at this wavelength remains invariant, regardless of the extent of reaction (or the position of the chemical equilibrium). This occurs because the two substances absorb light of that specific wavelength to the same extent, and the analytical concentration remains constant. For the reaction:
X → Y {\displaystyle X\rightarrow Y}
the analytical concentration is the same at any point in the reaction:
c X + c Y = c {\displaystyle c_{X}+c_{Y}=c\,} . The absorbance of the reaction mixture (assuming it depends only on X and Y) is:
A = l ⋅ ( ϵ X c X + ϵ Y c Y ) {\displaystyle A=l\cdot (\epsilon _{X}c_{X}+\epsilon _{Y}c_{Y})} . But at the isosbestic point, both molar absorptivities are the same:
ϵ X = ϵ Y = ϵ {\displaystyle \epsilon _{X}=\epsilon _{Y}=\epsilon \,} . Hence, the absorbance
… excerpt ends here. Continue reading the full article.
