Is there an equation or mathematical model which links retention (k') with the pH of your mobile phase in RPLC?
I have used such methods to link retention with %organic.

Yes:

k = (k0+k1*d)/(1+d)

where k0 is the retention factor of the deprotonated form, k1 the retention factor of the protonated form and

d = 10^(pH - pKa)

pKa is the negative logarithm of the dissoziation constant.
This equation applies to things with a single protonation step; for compounds with multiple steps one just adds other terms to this.

Uwe's right, but the catch to the above is that you have to know the pKa of your analyte in your mobile phase. In principle, you can determine the effective pKa and the limiting k's from three measurements cascade out into big predictive errors.

We've been through this with our DryLab software; in the last major revision we moved away from the "correct" model and are now using a cubic spline fit. The empirical fit is just as good, it's less prone to "blowing up" when you try to extrapolate, and it's easier to extend it to multiply ionized species (especially if you're not sure!).

By way of commercial, you can download an evaluation copy of DryLab at http://www.lcresources.com

-- Tom Jupille / LC Resources

The short answer is no- as Tom has noted, not for
nonaqueous systems. Acid-base equilibria in a
nonaqueous solvent is determined by the acid/base
properties of the solvent as well as the
autoprotolysis and dielectric constants.Equations
abound for relating these to dissociation
constants unfortunately these equations dont
really provide values which match those
experimentally determined.

I don't know about the "no". The equation that I gave above holds, no matter what the mobile phase is. While there are some departures of the pKa of the analyte and the buffer from the values determined in water, there is no reason whatsoever that the actual relationship will depart from the equation above. There are also a bunch of publications that show how the pKa's are shifting with the addition of the organic solvent, so one can deal at least with a few rules of thumb that help in an understanding how this works as well.

Actually, I think that both of you are right, but approaching the problem from different angles. Unfortunately, I mis-typed the first paragraph of my earlier post; that may have contributed to the misunderstanding. Here's what I *meant* to say:

"In principle, you can determine the effective pKa and the limiting k's from three measurements; in practice, however, the steepness of the retention/pH curve in the vicinity of the pKa makes small errors in measuring either mobile phase pH or retention cascade out into big predictive errors."

For those of you just tuning in, you might also want to check out the post on "Alcohols and pH" that appeared a month or so ago.

-- Tom Jupille / LC Resources

Tom, Uwe and Alex- I have assumed that Alex wants
to predict a capacity factor using a calculation
having the complexity of a k’ /%organic
determination: plug pH and dissociation constants
into an equation such as that provided by U.Neue.
My point is simply that the values needed will, in
all likelihood, have to be experimentally
determined. For example the pH is not the actual
pH of the mobile phase -it’s the pH of the aqueous
component of the mobile phase. The pKa in the
mobile phase is similarly unknown.

In summary then
(1) yes the calculation can be made
(2) it is not a trivial exercise and depending on
the Alex’s application may not be a practical use
of his time.

Well, we'll see what Alex wants to do, if he is getting back to us. The retention factors of the non-ionized and the ionized species are about as unknown as the pKa or the pH in the presence of an organic solvent. However, some things nay be much easier than we think. The pK shifts with the addition of organic solvents may be sufficiently similar for compounds with similar ionic functional groups and for buffers of the same type. The publications of the Barcelona groups show common factors at least for similar buffers (actually, if I remember correctly, the common factors have been shown only for carboxylic acid buffers).
Anyway, I understood the question as being directed towards the principle of the thing, and this is trivial indeed. The devil is in the detail, especially once one is looking at the real properties of real packings.
BTW: I am glad that at least for the moment we got some discussion going. Usually, this board follows the pattern: question - answers - dead...

hi everyone - I would like to thank you for all your ideas!
The reason I needed the information is that I am evaluating the Drylab package in some detail, and I wanted to see if its predictions were accurate. In most cases, they werent, which could be due to many factors:
the organic solvent relationship as uwe mentioned,
the version of drylab I am using uses a polynomial fit instead of cubic spline which makes it less reliable

I am not going into too much detail in my research - I just wanted to provide a bit of background to the project & to be able to 'manually' test the software by using the equations to see if I get the same results as it does.
The separation I am using to test it is the parabens, with a methanol/water mobile phase acidified with formic acid but not buffered and a phenyl column (as a bit of a twist!)
so thanks again for all your ideas!
PS Alex is a girl!

I am surprised that you are getting any effect. Parabens have a pK around 8. With unbuffered formic acid you are 50 miles (5 pH units) away from the pKa. If you are getting effects from the pH or the acid concentration, they are probably not due to the ionization of the samples.

Hi, Alex. Which version of DryLab are you using?

The current version (DryLab 2000) *does* use a cubic spline (of course, if you use fewer than 5 calibration points, a cubic spline reduces to a polynomial anyway). Earlier versions used a "titration curve" fit (basically the same equation that Uwe described earlier in the thread). We switched to the cubic spline based on feedback from users. If you're getting "funny" predictions, could you get me more details so that we improve the situation?

You can contact me directly by e-mail (tom.jupille@lcresources.com) or give me a call at 800-379-5221 (assuming you're in North America).

Hi Alex,

you wrote: "The reason I needed the information is that I am evaluating the Drylab package in some detail, and I wanted to see if its predictions were accurate. In most cases, they werent..."
Did you repeated your runs at least twice at each pH of the eluent? Silica is kind of a week polycondensed form of the buffer (silicic acid:silicate), and if you don't wait enough, you will still have changes in retention time. Therefore wait about 30 min at each pH, until the last two runs have identical retention times. You certainly know the saying: "Junk in, junk out". It is not DryLabs fault, if predictions are not accurate, but the accuracy of the input data. DryLab can only calculate, what we have measured.
BTW: The direct measurement of the retention time as a function of the pH and the consequent use of DryLab is the only way to establish robust methods in HPLC. Than: with complex samples - bases and acids in mixture - a pH-change of only 0.05 is already large enough to ruin your separation (s.also as an example under
www.molnar-institut.com, look for DryLab and go to the bottom of the page and click on Animation)

As long as we are revisiting this topic there is a
typo in the equation above: d=10^pKa –pH not
10^pH- pKa.

pH adjustment for amiloride hydrochloride and its impurities as per BP monograph would be very intersting.

Regarding the accuracy of drylab predictions, I can't speak for pH predictions, but I can speak for the gradient and temperature predictions. I used the 3D resolution mapping capabilities of drylab to solve a development problem that had persisted for months. I modeled the separation using data acquired with different temperatures and gradient times. I was able to predict optimal separation using a certain temp combined with a segmented gradient. I was suspicious, especially of predictions made using a segmented gradient. The prediction ended up amazingly accuracte and brought an abrupt end to my headaches.