calculation of no. of Theoretical plates (units??)

[miro2009]

I have a question regarding how to calculate the no. of theoretical plates for a certain peak, the questions is a little primitive... but what units should be used when substituting in the equation N= 5.5 (tR/wH)2, or 16 (tR/wB)2 ? in cm, mm, min, sec? ie. in units of time or distance, because with each I get different results. The same also for resolution factor calculation.. 2(tRB-tRA/ wA+wB)

[Don_Hilton]

Are you taking the formulae from a text book? I would start with the discussion that would be in the source of the equations.

Also, I would be quite surprised if the calcuation of resolution factor would change based on the time units you are using. I've been known to measure retention times and peak widths with a ruler (back in the days of strip chart recorders) and use the measurements from the ruler for calculating resolution factor. (And the answer was correct.)

[tom jupille]

Don is right.

To amplify a bit on his post: retention factor and plates are both "dimensionless" quantities; the units used should cancel out. That means that you need to use the same units for retention and for width. It doesn't matter what they are, so long as they are the same: time (as measured by a data system), distance (as measured with a ruler on a printout), or even volume (time multiplied by flow rate).

[miro2009]

Thank you for ur replies, but may I give you an example to help me realize this practically? I need to calculate the no. of theor. plates for peak B.
I have the chrom with 2 peaks with ret. times 28.9(A) and 33.1(B) min respectively, the width of both peaks at their base is 0.3 cm (but this is acc. to my printout, wouldn't this differ from one print out to another with different x-axis scales? Should I use their widths in terms of time (~0.1 min) which should be constant whatever the scale?
The retention "distance" for peak B is 9.3 cm
So substituting using all "min" units: 16 (33.1/0.1)2 = 1752976
in "cm" unit: 16 (9.3/0.3)2= 15376

There must be something I'm completely messing up here, but can you please tell me how you would calculate the no. of theor. plates and the resolution factor for the above example?

[Don_Hilton]

Check your measurements. If you have measured the retention of the peak and the peak width correctly, the ratio of time to peak width would be the same no matter what units you used to measure them. The time scale on your chroamtographic plot should be linear and there will be some scale factor of centemeters per minute. And the time and distance measurements will be interconvertable with that scale factor. Is there a chance you have the 0.1 and 0.3 measurements switched?

[tom jupille]

I think you may have slipped a decimal place. Using peak B, you have 33.1 min retention = 9.3 cm. That's a scale factor of 3.6 min/cm. At that scale factor, your width of 0.3 cm = 1.1 min, (3.6 x 0.3), not 0.1 min. And 15,000 plates is a "reasonable" number.

One final note: all of the above calculations assume *isocratic* conditions.

[miro2009]

thank you all for ur feedback. Tom, ur right I did skip a decimal, width is 1.1 min.
So I assume the same rule applies to calculating resolution factor? I use all units either in cm or min?

[tom jupille]

I use all units either in cm or min?

Correct. As long as you use the same units, they will cancel and the result will be appropriately "dimensionless".