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This is a textbook question:

Suppose you are using chromatography to separate a mixture of two substances. Can you propose a means of quantifying how good or how poor the separation is?

So I got the first part, which was to describe the properties of a good and bad separation (i.e., distinct bands in a good separation but not in a bad separation). I'm stuck on the "quantifying" part.

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Curt F's link to the Wikipedia article gives the idea.

$R = (t_B – t_A)/(w_A + w_B)$

Where

$R$ = resolution

$t_A, t_b$ are the rention times for A and B

$w_a, w_b$ are the peak widths.

For analytical chemistry the peak widths are generally measured at half-height (full width at half maximum, FWHM).

This is basically sort of like a T-Test in statistics where the FWHM values are the standard deviations. Since the peaks are close together you assume that they have "about" the same FWHM. In statistics the $\sqrt{w_a^2 + w_b^2}$ would be used.

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I believe when it comes to separation (column)the only assessment that can be done would be qualitative. The resolution of a elution is a quantitative measure of how well two elution peaks can be differentiated in a chromatographic separation. It is defined as the difference in retention times between the two peaks, divided by the combined widths of the elution peaks. And resolution only comes into picture when one is doing HPLC or GC.

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