= Isosbestic point
An isosbestic point is a <wavelength>, <wavenumber> or <frequency> at which a sample's total <absorbance> remains unchanged during a specified chemical or physical transformation. It is a property of the observed spectra and transformation, rather than proof of a particular reaction mechanism.<IUPAC Compendium of Chemical Terminology, fifth edition (Gold Book) by International Union of Pure and Applied Chemistry>[isosbestic point, I03310, definition and stoichiometric qualifications]{ref}
For a simple conversion between two species $A$ and $B$, assume additive <Beer-Lambert law> response, fixed optical path length $\ell$ and constant total concentration $C=c_A+c_B$. Then
$$
\mathcal A(\lambda)=\ell\left(\varepsilon_A(\lambda)c_A+\varepsilon_B(\lambda)c_B\right).
$$
At a wavelength $\lambda_*$ where $\varepsilon_A(\lambda_*)=\varepsilon_B(\lambda_*)=\varepsilon_*$,
$$
\mathcal A(\lambda_*)=\ell\varepsilon_*C,
$$
independent of the conversion fraction. For example, stipulated values $\ell=1\,\mathrm{cm}$, $C=10^{-4}\,\mathrm{mol\,L^{-1}}$ and $\varepsilon_*=5000\,\mathrm{L\,mol^{-1}\,cm^{-1}}$ give constant absorbance $0.50$.
\Image[/isosbestic-mixtures-and-species-count.png]
{title=<Isosbestic point> in two- and three-species model mixtures}
{description=Original analytic spectra with a shared value at $550\,\mathrm{nm}$. Left: fractions $1-f,f$. Right: fractions $1-f,f/2,f/2$ of three components, all of which agree at the marked wavelength. Path length and total concentration are held fixed. No chemical identities, measured spectra or fitted experimental parameters are assigned.}
An isosbestic point does not establish that exactly two species exist. Three species could all have the same absorption coefficient at $\lambda_*$; every mixture with the same total concentration would then give the same absorbance there. More generally, constant stoichiometric combinations of coefficients can produce an invariant signal. Conversely, dilution, changing path length, background absorption or changing spectra can remove a crossing without demonstrating a new reaction intermediate.
In an experimental test, record multiple full spectra while controlling total concentration, path length and background. Inspect the stability of the common intersection relative to measurement uncertainty, rather than selecting one pair of curves that happens to cross. The invariant wavelength alone cannot determine composition in the two-species model: its response has deliberately lost sensitivity to the conversion fraction. Measurements away from that wavelength carry the separating information, a distinction also useful in <co-oximetry>.
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