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HI,

If anyone can explain to me a good way to grasp the concept of plate height and theoretical plates I would be greatly appreciative. A web address would be fine too. I am taking Analytical right now and stumbled across this website and figured I would post my question. Thanks.

Rebecca

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Have you taken PChem yet and done distillation calculations? In distillation, the plate number is the number of discrete equilibrations between two phases (gas and liquid in distilation, mobile and stationary in chromatography) that gives the observed profile. The name comes from classical distillation columns, which actually have (had?) "plates" where vapor equilibrates with pools of consensate liquid.

In chromatography, there are no discrete plates, but the process can be modeled as though it did, so the "theoretical" plate number is the number of discrete equilibrations that would generate approximately the observed peak profile. It is defined as the ratio of the square of the first statistical moment to the second statistical moment. The first statistical moment equals the retention time, the second statistical moment equals the variance. The square root of the variance is 1/4 the baseline width of a symmetrical, gaussian peak, so we get the standard textbook equation for plate number:

N = 16(tR/w)^2

This is a handy way of talking about peak width, because it's a linear function of column length.

The "plate model" is not used any more, but the parameter has stayed.

Hope this helps.

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I forgot to add, the plate height is simply the column length divided by the plate number. It's simply a way of normalizing of different length to see how well they perform. In practice, you will see plates/meter quoted more often as a specification (this is simply the reciprocal of plate height), but plate height lends itself a little better to theoretical calculations.

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Rebecca:

Try this concept. Your sample molecules are floating down the tubing that makes up your column being swept along by the carrier gas. While doing so, they encounter the liquid stationary phase, either "painted" on the walls of an open tubular column, or coated on the solid support of a packed column. In either case, the molecules dissolve in the liquid phase. Some time later, as "clean" carrier gas comes sweeping by, the molecules vaporize out of the liquid phase and again move down the column. Every time your sample molecules make this transition from mobile gas phase to liquid stationary phase and back again that's one theoretical plate. You can see the similarity to distillation.

Depending on the thickness of the phase, diameter of the column, effectiveness of coating, length, carrier velocity, etc., etc. your column will have more or less theoretical plates. Interestingly, all (or most) types of vapor components in your sample, if they tend to dissolve in the stationary phase at all, will make roughly the same number of transitions, and your column will have the roughly the same number of theoretical plates when measured with a wide variety of different components. Since all components spend the same amount of time in the mobile gas phase, the reason you can separate different components is that different components spend different amounts of time dissolved in the liquid phase.

With that concept of gas chromatography, most of the mathematics comes easier to me, being just a way of quantifying and predicting the behavior of GC systems. The number of theoretical plates is calculated as "anonymous" described. The significance of that calculation is the skinnier your peaks (small width, "w") and the greater their retention time ("Tr")for a given width, the greater the number of theoretical plates. A 60m, 0.25mm ID, 0.25 micron film methyl silicone capillary column might have 500,000 theoretical plates (0.012 cm/plate = HETP). A 1m, 1/8" OD packed column of methyl silicone phase would be proud to have 2000 theoretical plates (0.05 cm/plate = HETP). So, theory predicts and experience confirms that capillary columns give nice tall skinny peaks and packed columns give shorter, squattier peaks generally.

An oversimplification for sure, but I hope that helps convey the concept of theoretical plates as used in GC.

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Further the shorter the plate height, higher the plant count will be.

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