How to calculate peak width in Gas Chromatography

[beruniy]

During separation of the mixture of alcanes and unknown matter (X) the following data were obtained:
Retention  time:
ethane - 4 minutes
propane - 8 minutes
Corrected retention time for X = 5,2 min
Kovats index I = 246
Separation factor (X and propane) = 1.
Henry coefficients for X and pentane 20.1 and 2.8, respectively.

But the peak was damaged by sulfuric acid
I need to recover it. I know only its intensity = 75. I need to know its width and 1/2 of width.

From Kovats index I can calculate retention time for X, it is 5,5 minutes. Then I calculate the "dead" time.
t = 5,5 - 5,2 = 0,3 min.
Knowing that intensity is the function of time (I = f(t)) I can suppose that the peak is symmetric and I can consider it as isosceles triangle.

Tell me please, how is it possible to associate Henry coefficients with retention times?

[Don_Hilton]

Is this, by chance, a school assignment? You have the value for H for an unknown compound and the corrected retention time and Kovats Index for that same compund, but not the peak width? (Sounds like a compund that is pretty well known, except to the student.) Normally I get the peak width by examining the chromatographic trace. (It seems to me that there is a relationship between peak width, retention time, and separation factor...)

And a GC peak was damaged by sulphuric acid, but you have the intensity? I am missing something here?

Relationship between Henry's law and retention times - you have some data, but no temperature information. Henry's constants are temperature dependant. Note: http://en.wikipedia.org/wiki/Henry's_law . I assume this answer would relate to some class notes?

[Peter Apps]

Is this, by chance, a school assignment? You have the value for H for an unknown compound and the corrected retention time and Kovats Index for that same compund, but not the peak width? (Sounds like a compund that is pretty well known, except to the student.) Normally I get the peak width by examining the chromatographic trace. (It seems to me that there is a relationship between peak width, retention time, and separation factor...)

And a GC peak was damaged by sulphuric acid, but you have the intensity? I am missing something here? Hi Don, the phrase " you couldn't make this up" springs to mind. I suspect that a careless person dripped sulfuric acid onto a paper chromatogram - maybe they thought that they were developing a TLC plate -- Peter

Relationship between Henry's law and retention times - you have some data, but no temperature information. Henry's constants are temperature dependant. Note: http://en.wikipedia.org/wiki/Henry's_law . I assume this answer would relate to some class notes?

[beruniy]

Yes, it's school assignement for olympiads. I'm preparing for olympiads using different books because chromatography is not included in school program. So I have some questions and looking for advice of specialists.

Relationship between Henry's law and retention times - you have some data, but no temperature information

But T = const in GC. Probably we can use relation of Henry's coefficients:
G1/G2 = t'1/t'2 where
t'1 and t'2 are corrected retention times for each compound. Or not?

It seems to me that there is a relationship between peak width, retention time, and separation factor...

Yes, I've found this relationship but I don't know how to calculate peak width:
R = 2(t1 - t2) / (w1 + w2) where

R is separation factor = 1, t1 and t2 are retention times which are 8 for propane and 5.5 for X.
w1 and w2 are peak width for propane and X.
How can I find w1 and w2?

And a GC peak was damaged by sulphuric acid, but you have the intensity?

Yes, problem says that only maximal point of peak was saved.

I suspect that a careless person dripped sulfuric acid onto a paper chromatogram - maybe they thought that they were developing a TLC plate

No, it was just careless person which occasionally spilled sulfuric acid onto a paper chromatogram...

Altogether: I used Kovats index for retention time (X) identification. I've found the "dead time" using corrected retention time. How can I use Henry's coefficients? I guess that I haven't to use temperature if it const?

[Don_Hilton]

I need to go see if I can get my GC text back (I'd loaned it - I lose them this way...) to be sure I have equations right.

If we deal with ideal peak shapes, the number of theoretical plates is the same for each peak, so the relationship between peak widths can be estimated based on retention times - but that may be the long way round for what you are doing. I don't know the level of text you are using, so the authors may handle peak broadening in the run differently. Using Henry constants looks like chromatography for a physical chemist - and a lot of us on the more "practical" side (as opposed to theoretical) tend to talk in terms of parition coefficients, which comes down to about the same thing. Or partition coeffients vs. Henry constants may depend on which part of the world one is from... )

For relationship between Henry constant and retention time. The elution time of a compund is the sum of the time spent in the vapor phase - (which takes the dead time to elute from the column) - and the time spent in the stationary phase - (which is the corrected retention time). And the time spent in each phase is proportional to the concentration in each phase -- and this is where the partition coefficient or Henry constant comes in.

Actually T is not always constant in GC. Many GC methods use a temperature ramp during the chroamtographic analysis to change the partition constant (or partition coefficient to facilitate separation between compunds). But, as a teaching construct, this does not have to be introduced at the start of exploring plate theory or dynamic theory of separations. With no consideration for T being mentioned in the problem, then it should be safe to assume that T is constant for the problem.

[beruniy]

I need to go see if I can get my GC text back (I'd loaned it - I lose them this way...) to be sure I have equations right.

Okay, please see equations...

If we deal with ideal peak shapes, the number of theoretical plates is the same for each peak, so the relationship between peak widths can be estimated based on retention times

I think that we are entitled to consider peak shapes to be ideal because problem says "consider that peak is symmetric". That's why we can imagine it as isoscales triangle in which height is known. We are asked to calculate the base of a triangle (peak width) and 1/2 of its base. So we can estimate it proceeding from retention times.

Using Henry constants looks like chromatography for a physical chemist - and a lot of us on the more "practical" side (as opposed to theoretical) tend to talk in terms of parition coefficients, which comes down to about the same thing

Partition coefficients are not known, Henry coefficients are only known. One of them corresponds to X and another to pentane (I don't know - what for is pentane? If initially we had only ethane and propane).

The elution time of a compund is the sum of the time spent in the vapor phase - (which takes the dead time to elute from the column) - and the time spent in the stationary phase - (which is the corrected retention time). And the time spent in each phase is proportional to the concentration in each phase -- and this is where the partition coefficient or Henry constant comes in.

Well then we can write G1/G2 = t'1/t'2?
t' - corrected retention time.

With no consideration for T being mentioned in the problem, then it should be safe to assume that T is constant for the problem

I'm fully sure that T = const in this problem.

[Don_Hilton]

On Henry constants being known and partition coefficients: The henry constant is the ratio of the parital pressure of the gas to the concentration of the gas in the liquid phase. A partition coefficient is the ratio of the gas concentration in the vapor phase to the gas concentration in the liquid phase. Pressure and concentration are related, particulalry for an ideal gas, by the ideal gas law: PV=NRT, where the presure (P) is related the concentration (number of particles (N) divided by volume(V)), a constant (R) and the temperature (T).

So, it would appear to me that the math that works with partion coeffients should work with henry constants, differing between handling pressure as opposed to concentration.

I still need to track down my book. Others with the formulas at hand are welcome to jump in.

Don

[lmh]

not a useful reply, but on the subject of dripping acid on printouts:
Years ago, a technician came into the lab holding a piece of paper carrying the results of a complete night of scintillation counting on many samples. Unfortunately the dot-matrix printer paper feed had jammed, and moved shorter and shorter distances between lines as each sample ran, ending up with the results compressed into about two inches of ever denser text. Technician was distraught.

"That's all right!" declared professor. "Just put it in the paper chromatography tank and run them all back out again..."