Isosbestic point

In spectroscopy, an isosbestic point is a specific wavelength at which two chemical species have the same molar absorptivity (ε) or -more generally- are linearly related. The word derives from two Greek words: isos: equal, and sbestos: extinguishable.^[1]

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:

$X \rightarrow Y$

the analytical concentration is the same at any point in the reaction:

$c_X %2B c_Y = c \,$ .

The absorbance of the reaction mixture (assuming it depends only on X and Y) is:

$A = l\cdot (\epsilon_{X} c_{X} %2B \epsilon_{Y} c_{Y} )$ .

But at the isosbestic point both molar absorptivities are the same:

$\epsilon_X = \epsilon_Y = \epsilon \,$ .

Hence, the absorbance

$A = l\cdot (\epsilon_{X} c_{X} %2B \epsilon_{Y} c_{Y} )=l\cdot\epsilon \cdot (c_{X} %2B c_{Y} )=l\cdot\epsilon\cdot c$

does not depend on the extent of reaction (i.e. in the particular concentrations of X and Y)

The requirement for an isosbestic point to occur is that the two species involved are related linearly by stoichiometry, such that the absorbance is invariant for one particular wavelength. Thus other ratios than one to one are possible. The presence of an isosbestic point typically does indicate that only two species that vary in concentration contribute to the absorption around the isosbestic point. If a third one is partaking in the process the spectra typically intersect at varying wavelengths as concentrations change, creating the impression that the isosbestic point is 'out of focus', or that it will shift as conditions change.^[2] The reason for this is that it would be very unlikely for three compounds to have extinction coefficients linked in a linear relationship by chance for one particular wavelength.

Applications

In chemical kinetics, isosbestic points are used as reference points in the study of reaction rates, as the absorbance at those wavelengths remains constant throughout the whole reaction.

Isosbestic points are used in medicine in a laboratory technique called oximetry to determine hemoglobin concentration, regardless of its saturation. Oxyhaemoglobin and deoxyhaemoglobin have isosbestic points at 590 nm and near 800 nm.

Isosbestic points are also used in clinical chemistry, as a quality assurance method, to verify the accuracy in the wavelength of a spectrophotometer. This is done by measuring the spectra of a standard substance at two different pH conditions (above and below the pKa of the substance). The standards used include potassium dichromate (isosbestic points at 339 and 445 nm), bromothymol blue (325 and 498 nm) and congo red (541 nm). The wavelength of the isosbestic point determined does not depend on the concentration of the substance used, and so, it becomes a very reliable reference.

References

^ IUPAC Gold Book (International Union of Pure and Applied Chemistry)
^ page 49 of Kinetics and Mechanism By John W. Moore, Ralph G. Pearson and Arthur Atwater Frost (3rd Edition, John Wiley and Sons, 1981) ISBN 0471035580, 9780471035589