The fundamental resolution equation or Purnell equation is used in chromatography to help relate adjustable chromatographic parameters to resolution.
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 (least effective, as doubling the column will get a or 1.44x increase in resolution). 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. (moderately effective) 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 (if applicable).
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:
References
Bibliography Spring 2009 Class Notes, CHM 5154, Chemical Separations taught by Dr. John Dorsey, Ph.D, Florida State University