Gas chromatography/mass spectrometry: Can I use peak ratios and molecular mass to derive quantity?

Question

Can derive the quantity of a substance from a GC/MS report if I know:

• the ratio to another substance in the data,

• the quantity of that second substance, and

• the molecular mass of both substances.

The site was very dense and vague regarding how GC/MS test work, but fairly upfront regarding how they derive their ratios.

Here are the numbers (slightly tweaked, but more or less in proportion):

Substance A:

• Quantity: $300 \:\pu{mg}$ (Know already, not part of GC/MS report)
• Mol. Mass: $500 \:\pu{g/mol}$ (found in external source)
• Peak Proportion: 3

Substance X:

• Quantity: Unknown
• Mol. Mass: $425 \:\pu{g/mol}$ (again, external source)
• Peak Proportion: 1

To be clear, the ratio of 1:3 means that substance X has a horizontal peak $\frac13$ of substance A. I'm not clear on what the x-axis is actually a measurement of, which is part of why I'm at a loss. The site does make it very explicit that the ratios are not directly proportional to mass ratio (so if it found a ratio of 3:1 of glucose to arsenic, this doesn't mean the substance is 75% glucose and 25% arsenic, only that the glucose "peaks" 3 times higher, which I've taken to mean "3 times the oomph", but that may be incorrect, as well).

So, if I know that the molecular mass($\rm M$) of substance X is 0.85 of substance Y, can I derive the actual mass of substance X using the formula:

\begin{equation}\mathrm{qty}_X=\frac{\mathrm{qty}_A\times(M_X/M_A)}{\mathrm{peak}_A/\mathrm{peak}_X}\end{equation}

with data being:

\begin{equation}\rm qty_X=\frac{300\:\pu{mg}\times(425/500)}{3/1}\end{equation}

Which simplifies to:

\begin{equation}\rm qty_X=(300\:\pu{mg}\times 0.85)/3\end{equation}

and finally the result of $85 \:\mathrm{mg}$.

So I guess in the end there are 3 questions:

1. Is this even how GC/MS results work?
2. If so, is my assumption to derive the mystery quantity using the molecular mass correct?
3. Is the math itself in order? (I'm specifically worried that I should invert either the mass ratio or the peak ratio or both).

Of course, if the answer to the first questions is no, then my true question is: can I derive the quantity of substance X with the given data, and if so, what would be the right approach?

If anyone is curious for some context, I need to know the actual quantity of substance X as I know that, by mass, it has a threshold between harmless and toxic, so just knowing substance X is $\frac13$ "peak" of substance A doesn't let me know if I should let my dog/child/self ingest it.

Answer 1

Is this even how GC/MS results work?

As cbeleites said the method you described is a proper technique but not likely to be appropriate given the information you cited.

In GC/MS you should have two sets of information. The first is the GC Total Ion Chromatograph (TIC) which will have time as the x-axis and response (abundance) as the y-axis. For each retention time on the TIC there will be a corresponding Mass Spectra (MS). In the MS the x-axis is m/z (ion) and y-axis is also response (abundance).

Different compounds have different responses so if you inject the exact same amount of two different compounds you could get a much larger response from one compared to the other. For example tramadol gives much higher response compared to hydrocodone. This is why you want your internal standard to be structurally similar to your analyte.

Quantification of a compound is often done by running 3 - 5 calibrators at known concentrations in order to make a calibration curve. Once an acceptable calibration curve is made the sample along with controls can be fit onto the curve to calculate the amount of the compound of interest in the sample and controls. If the controls are correct then the sample value can be used.

To make a calibration curve you need an internal standard in each calibrator, control and sample. You can then make the curve either with ion ratios between paired internal standard and analyte ions OR if your internal standard response is consistent in all the calibrators, controls and sample you can use the GC peak response.

In conclusion if you only have one GC/MS run with the two dissimilar compounds in it you will not be able to easily calculate the quantity of the second compound based on the GC response of the first unless you have additional information that was not listed in this question.

Answer 2

This sounds like A being an internal standard for the determination of B.

Internal standards are used to get rid of (small) multiplicative variation due to certain influences, e.g.

• in GC, the injected volume
• in optical spectroscopy, the optical path length or the illuminated volume.

Sometimes the calculation part of the idea is called normalization.

The English Wiki page for the Response factor explains the internal standard (and calculations).

The important part is:

One of the main reasons to use response factors is to compensate for the irreproducibility of manual injections into a gas chromatograph (GC). Injection volumes for GC's can be 1 microliter (µL) or less and are difficult to reproduce. Differences in the volume of injected analyte leads to differences in the areas of the peaks in the chromatogram and any quantitative results are suspect.

So you switch your whole calibration to response normalized to the response of the internal standard (= signal analyte / signal internal standard) and the result is concentration analyte / concentration of internal standard = molar amount analyte / molar amount internal standard. With the known amount/concentration of internal standard you can calculate back to the analyte amount/concentration.

If you can read German, here's another explanation and HPLC example calculation.

Skoog & Leary's Instrumental Analysis says that with a suitable internal standard, accuracy of < 1 % is possible.

So, if your A is an internal standard, then, yes, that is a proper technique. Note, however, that arsenic does not sound like an internal standard for glucose (nor vice versa): the internal standard should be

• as similar as possible to the analyte

• but the signal should not overlap with other substances

• for GC/MS that could even be an isotope labeled version of the analyte for maximum chemical similarity.