# Calculating Sensitivity in Mass Spectrometry

My mass spectrometry textbook gives the following example:

Calculating sensitivity Magnetic sector instruments are specified to have a sensitivity of about $$4 \times 10^{-7} C \ \mu g^{-1}$$ for the molecular ion of methylstearate, $$m/z \ 298$$, at $$R = 1000$$ in $$70 \ eV$$ EI mode. One microgram of methylstearate is equivalent to $$3.4 \times 10^{-9} mol$$ or $$2.0 \times 10^{15}$$ molecules. The charge of $$4 \times 10^{-7} C$$ corresponds to $$2.5 \times 10^{12}$$ electron charges of $$1.6 \times 10^{-19} C$$ each. Vice versa, in dividing the number of molecules per microgram by the number of charges at the detector we may conclude that only one out of $$800$$ molecules is finally detected.

I have three questions:

1. What is $$R = 1000$$ supposed to be? The author never mentioned such a quantity at any previous point in the textbook.

2. How did the author calculate that the charge of $$4 \times 10^{-7} C$$ corresponds to $$2.5 \times 10^{12}$$ electron charges of $$1.6 \times 10^{-19} C$$ each? Or is this just a fact that he has knowledge of?

3. How did the author calculate the last part:

Vice versa, in dividing the number of molecules per microgram by the number of charges at the detector we may conclude that only one out of $$800$$ molecules is finally detected.

?

I would greatly appreciate it if people could please take the time to clarify this.

• For your second question, the total charge is the product of the number of electrons times the charge per electron. So just multiply the numbers: 2.5 times 1.6 = 4 and $\ce {10^{12}}$ times $\ce {10^{-19}}$ = $\ce {10^{-7}}$. – Ed V Jun 20 '19 at 16:46
• @EdV Yes, but I'm referring to the converse of the calculation; that's the point of the author's statement in the second question. We start with the information that the instruments are specified to have a sensitivity of about $4 \times 10^{-7} C \ \mu g^{-1}$. The author then decomposes this into $2.5 \times 10^{12}$ electron charges of $1.6 \times 10^{-19} C$ each. The point of question 2 is, starting with the value of $4 \times 10^{-7} C \ \mu g^{-1}$, how did the author induce that this is $2.5 \times 10^{12}$ electron charges of $1.6 \times 10^{-19} C$ each? ... – The Pointer Jun 20 '19 at 16:54
• ... After all, we could have used any other combination of $x$ and $y$ such that $x + y = 4 \times 10^{-7} C$ - not necessarily $2.5 \times 10^{12}$ and $1.6 \times 10^{-19} C$. So, the question becomes, how did the author get the specific values $2.5 \times 10^{12}$ and $1.6 \times 10^{-19} C$? – The Pointer Jun 20 '19 at 17:01
• One electron has the stated charge and the sensitivity is given as $\ce {4 x 10^{-7}}$ C, so dividing the sensitivity by one electron charge tells you how many electrons it would take to have that charge. That gives $\ce {2.5 x 10^{-7}}$ electrons. Then if 1 microgram of methylstearate contains $\ce {2.0 x 10^{15}}$ molecules, the number of molecules is 800 times larger than the number of electrons, so 1 molecule in 800, assuming unity charge, could be detected. The other 799 (average, right) cannot get charges because molecules outnumber electrons 800 to 1. – Ed V Jun 20 '19 at 17:05
• Charges have to be in integer multiples of the charge on one electron. But the molecular charge of the methylstearate ion is unity: it does not have two or more charges, under the stated operational conditions. (This can be confirmed by looking at the molar mass of methyl stearate.) If the molecular ions were multiply charged, then the m/z ratios would be smaller. If the ions were doubly charged, for example,then the m/z ratio would be 149. – Ed V Jun 20 '19 at 17:16