Internal Standard Calculation Question

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Hi all. I'm fairly new to chromatography, so just wanted to check that the following equation is correct.

I'm doing gas chromatography and using an internal standard (IS) to calculate the concentration of an unknown based on that.

The equation I have found is:

Conc. of Unknown Analyte = (Peak Area of Analyte / Peak Area of IS) x Concentration of IS

Is this the correct equation to use? Furthermore, should the concentration of the internal standard be its actual concentration (eg 0.1mg/mL) or should it be the amount I put in (eg 0.05mg).

Many thanks in advance.
Almost correct. You need to include the relative response factor (RF) which is the ratio of the slopes of the lines generated when you plot response vs. concentration for the internal standard and the analyte.

The RF comes from the following - assuming a linear detector response with concentration for both the internal standard and the analyte, k's are the conversion factors between measurable signal on the instrument and the concentration in the sample):

Ai = ki*Ci (for the analyte i)

Ais = kis*Cis (for the internal standard)

Divide the equations by each other:

Ai/Ais = (ki/kis)*(Ci/Cis)

A's are peak areas (or heights) for the analyte (i) and the internal standard (is). ki/kis = RF.

Solve for Ci (the unknown concentration of analyte and you get:

(Ai/Ais)*Cis/RF = Ci

RF is the "response factor" (ratio of the slopes of the lines - response vs. concentration) for analyte and internal standard.

Generally, I will make different solutions of different but known concentrations of both IS and analyte and run them. Plot the data as:

Ai/Ais = RF*(Ci/Cis)

It won't work well if you don't have linear responses for both. RF is the slope of this line. You also want your ratios to be as different as possible (explore the dynamic range of your detector). I'll throw out some numbers like when IS is 100 ppm, have the analyte concentration be 1-10 ppm and vice versa. You don't want your ratios to cluster in one place.

How you report your numbers is up to you. For condensed-phase analysis, generally you're going to want your answer to be in some type of concentration unit anyway so I would recommend that for most cases.

If you do mass only, you need to make sure that the sample volume is the same all of the time. Sometimes I do this when I'm looking for something in the lining of an empty beverage can. In that case, I'm always sampling a fixed volume (say 12 oz. can, nominally 378 mL when seamed). If I know the mass of the analyte I detect, I can translate it to the concentration that would have ended up in the beverage if it all leached out into the 355 mL of fluid.

Have fun! Good luck.
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