Chromatography Forum

I was going through some old HPLC course notes and came across the following equation:

Wm = 1000 MW (k + 1) (S/N) N' L dc^2 / E N^1/2 Lc

where

MW = mol. wt (Daltons)
k = retention factor
S/N = signal to noise for required CV
N' = baseline noise in absorbance units
L = column length (cm)
dc = column internal diameter (cm)
E = analyte molar absorptivity
N = plate number
Lc = flowcell path length (cm)

A few things:

Q/ What does Wm stand for?

Q/ Is this equation correct for instance if you increase Lc in this equation then Wm goes down. Is it written correctly in my notes?

Q/ Also there is no occurence of flow rate.... and as we should know, increasing flow rate reduces residence time in the flow cell... which reduces peak height.

Any comments, thoughts on anything here... PS. thanks for considering this post...

1- I'll take a guess from the context that Wm is the minimum weight of analyte on column that can be detected. I haven't yet deduced the units, but I think it is milligrams. That makes it independent of injection volume, and also does not include dilution factors and recovery.

2- That would be correct. If you have a longer optical path, the detectable weight will decrease in proportion (assuming everything else stays the same). In practice, changing the flowcell geometry can affect both N and N' so you may or may not see any actual improvement. Keep in mind that N' must be measured with a control sample under your analytical conditions, and is likely to exceed the detector's noise spec.

3- Flow rate does not affect peak height directly, except in its effect on N. Rather it is the peak area (expressed as AU*min) that is inversely proportional to flow rate (for the reasons you cited). In fact if you multiply by the flow rate to express area in AU*mL the result is the same at any flow rate (assuming that you have enough data points for good integration). Here is some data from some recent work I did: Cheers,

That equation was in the first edition of the Snyder, Glajch, & Kirkland Practical HPLC Method Development book. I can't find it in the second edition.

Mark has it right:

• Wm is mass on column in milligrams
  1000 is required to convert molecular weight (grams) to milligrams
  MW is the analyte molecular weight
  k (or k', if you prefer) is the retention factor (capacity factor)
  S/N is the target signal/noise ratio (usually taken as = 3 for LOD and =10 for LLOQ)
  N' is detector baseline noise (peak-to-peak)
  L is column length (cm)
  dc is column internal diameter (also in cm)
  ε is the molar extinction coefficient
  N is the column plate number
  Lc is the flow cell path length

This is, of course, a "back-of-the-envelope" approximation; it is useful primarily at the beginning of method development (plug in some "typical" numbers and see if you are close to what you need in terms of sensitivity) and as a troubleshooting mnemonic (it serves as a reminder of all the things that can affect sensitivity).

Many thanks for your replies chaps, much appreciated as per usual. Now that I see that Wm stands for "minimum weight detectable on column" the whole equation makes more sense to me.

As a further note is there a similar fundamental equation that relates minimum detectable peak height to all the various chromatographic parameters. This would be useful from a pharma. perspective looking at peaks at the 0.05% level compared to the main peak.

As a side note I was considering the whole flow rate versus peak height perspective again. Is it true that peak height only strictly stays approximately constant against flow rate for isocratic spearations?

The reason I ask is that I was reviewing some old gradient separations data from a while back, and it does seem that at a flow of 1.5 mL/min I'm getting a much larger peak height (at least 2/3 as large) signal than at 3.0 ml/min. (I can't access the numbers right now but I can endeavour to try if anyone is really interested!).

This flow rate vs peak area thing was discussed extensively, probably even exhaustively, not long ago. This morning I was on the verge of saying something about this "residence time in the detector" which one could consider formally correct, but conceptually it can be misleading. So instead of saying what I had intended, I think its best to do another hypothetical exercise (actually should be a simple experiment): If one were to fill a tube (small enough inner diameter to prevent laminar flow) connected to the detector with a UV absorbing solution and then pushed this through the detector slowly one would get a peak of area x and hight y (peak width at baseline would be the time it takes to push this column of liquid through). Now one does the same (same concentration, same volume in the same tube) again, but pushes it through at twice the rate (half the time). Your area obviously has to be x/2 while the peak hight has to be still y (width at basline must be half of that above). See it? (I think we concurred before that the response time of UV detectors is way to fast to cause a deviation from this).

Rob, I think your gradient observation parallels Mark's: a dependence of peak height on flow rate is a secondary effect of the change in plate number.

Higher flow -> lower plate number -> wider peak -> shorter peak (for the same mass).

The effect is masked a bit in gradients because all peaks on a chromatogram have approximately the same width.

In the case of a gradient separation, raising the flow rate will result in shorter peaks. In a gradient the retention time is dominated by the composition curve more than the flow rate. In consequence, the peaks elute only slightly earlier, but in a greater volume of mobile phase. If you scale the gradient slope proportionally to the flow rate, then the peaks will be about the same height, and the retention times will be roughly proportional to flow rate. (Again, flow rate affects N, which affects peak height.)