finding concentration in a nonlinear solvent gradient

[Phillip260785]

All the peristaltic pumps my lab has that are capable of automated solvent mixing are bust. As a result I recently I recently set-up an anion-exchange column to be eluted with a gradient as follows.

Two 1 L conical flasks are connected at the bottom by a short hose with a tap in the middle. Solvent is being pumped out of the flask containing the more dilute buffer causing more concentrated buffer to be drawn into said flask at half the speed the pump is operating at.

Can anyone help me with an equation to find the concentration being used to elute the column at any given time? There are only three variables, the volume in each flask (which will always be equal) and the concentration in the initially more dilute flask.

If anyone has the maths skills to help me out with this I would be extremely grateful.

cheers,
Phill the ozzie chemist

[Noser222]

This sounds like a calculus problem or differential equations problem that I haven't done in a few years...maybe I'll take a stab at it at lunch.

[HW Mueller]

I didn´t really understand what you are doing, but normally one calibrates something like this with a standard, then runs the samples under exactly the same conditions.

[unmgvar]

where is the mixing done? something fells fishy in your set up.

i can't see how you certify that what goes to the pump from the first flask is an homegenous solution at all times and that further more the composition is actually changing over time since you mention that in both flasks the solution level are always equal. if they are being pump at equal rates doesn't it means that you are in isocratic mode?

maybe i missed something?

[tom jupille]

It would be a lot easier if the "A" flask were closed, so that its volume stayed constant. In that case, you would have a simple "exponential dilution" (actually, "exponential addition), where:

• C%(t) = 100*[1-exp(-F*t/V)] where
  C%(t) is the percentage of B in A at time=t
  F is the flow rate
  t is elapsed time
  V is the volume of the "A" flask

The fact that the "A" flask volume is decreasing complicates matters. I'm too lazy to do the math; it's easier to simply set up an Excel spreadsheet and approximate it. If anyone wants to play with it, you can get it here:
http://spreadsheets.google.com/pub?key= ... gU51sEvbGA

This is a "quick-and-dirty", so I make no claims to correctness (i.e., use at your own risk )