Fundamental resolution equation

The fundamental resolution equation is used in chromatography to help relate adjustable chromatographic parameters to resolution. a

Equation

where,
= Number of theoretical plates
= Selectivity Term =
The term is the column factor, the term is the thermodynamic factor, and the term is the retention factor. The 3 factors are not completely independent, but can be treated as such.

Intervention

To increase resolution of two peaks on a chromatogram, one of the three terms of the equation need to be modified.

N can be increased by lengthening the column.
Increasing also helps. This can be done by lowering the column temperature in G.C., or by choosing a weaker mobile phase in L.C.
Changing α is the most effective way of increasing resolution. This can be done by choosing a stationary phase that has a greater difference between and. It can also be done in L.C. by using pH to invoke secondary equilibria.

Resolution

The fundamental resolution equation is derived as follows:
For two closely spaced peaks, , and,
so,
Where and are the retention times of two separate peaks.
Since, then
Using substitution,.
Now using the following equations and solving for and
Substituting again and you get:
And finally substituting once more and you get the Fundamental Resolution Equation: