# How to retrieve Dalton value from m/z value?

As I understand, Dalton (Da) is the standard way for representing mass unit. As for $m/z$, which is a specific notation for mass spectrometry, quoting for wikipedia:

This notation eases data interpretation since it is numerically more related to the unified atomic mass unit

Considering this, could I say that the $m$ in $m/z$ is a $\mathrm{Da}$ unity? If so, given an $m/z$ value, can I retrieve the original mass of the atomic mass by multiplying it by the ions charge, if I have that information?

I ask this because I have a spectrum analysis file with $m/z$ in the $x$ axis and I'm asked to compare masses in $\mathrm{Da}$.

• – Curt F. Jul 22 '16 at 5:43

## IUPAC is wrong

Martin's answer is useful for its pointer to the IUPAC Gold Book, which is one of the most authoritative sources for chemical nomenclature around.

However, on this particular question, the Gold Book is laughably wrong.

The abbreviation $m/z$ is used to denote the dimensionless quantity formed by dividing the mass number of an ion by its charge number.

This sentence is wrong. The $m$ in $m/z$, as used by nearly every practicing chemist in the world (except IUPAC), is the ion mass, not the mass number. The mass number is the sum of protons and neutrons in a nucleus. Therefore it is always an integer. Thus, according to IUPAC, ions with a charge of $\pm 2$ would always have $m/z$ values that are either integers (if $m$ is even) or half-integers. Thus, according to their definition, saying the $m/z$ value of $\ce{C7H7^2+}$ is 45.52683903 would be wrong. However that is exactly what most mass spectrometrists would say it is.

Here is some evidence:

• A lipid maps database entry for $\ce{C7H7}$ lists $m/z$ values for a hypothetical $\ce{C7H8+}$ ion that have four decimal places.
• I happen to have the latest print edition of the Journal of The American Society for Mass Spectrometry in front of me, and paging through the contents I see things such as:

...an intense signal for the $\ce{Cu^2+ - His_3}$ complex at $m/z$ 245.6, instead of the $\ce{[His_3 + 2H]+}$ at $m/z$ 215.1...

...MS spectra of standard solutions containing (a) lactose ($m/z$ 365.11, $\ce{[M + Na]+}$; $m/z$ 381.309, $\ce{[M + K]+}$), (b) cytidine ($m/z$ 266.218, $\ce{[M + Na]+}$, ...

These excerpts are not using the (integer) mass number in their calculation of $m/z$, they are using the ion mass, measured in Daltons. (If they were, the only numbers after the decimal point would be .0 or .5). That means that $m/z$ values are not really dimensionless, which makes the sentence wrong again. In fact a unit called the Thomson has been proposed for $m/z$ values in honor of JJ Thomson. However this nomenclature has not really caught on widely. Nonetheless, $m/z$ values are not dimensionless.

The Gold Book goes on...

It has long been called the mass-to-charge ratio although $m$ is not the ionic mass nor is $z$ a multiple or the elementary (electronic) charge, $e$.

This sentence is wrong because $m$ is the ionic mass (in Daltons) as explained above. It is additionally misleading because $z$ is always a multiple of the elementary electronic charge, with the understanding that charge must be measured in multiples of $e$, not in Coulombs.

The abbreviation $m/e$ is, therefore, not recommended.

Finally something I agree with IUPAC on!

Thus, for example, for the ion $\ce{C7H7^2+}$, $m/z$ equals 45.5.

Most folks would find that to be an OK approximation to the true $m/z$, which as I said above should be 45.52683903.

For the purposes of your question, Martin was right when he said

For all intents and purposes the mass number may be seen as the mass of the ion in u or Da...

One thing to keep in mind is that this definition of "mass number" is at odds with IUPAC and nearly every other chemical text, which restricts "mass number" to be integers.

It's a bit unclear in your question if you want to determine the mass of an ion or the mass of the parent (usually neutral) molecule that gave rise to that ion. If you want to determine the mass of an ion, then the other answer is right and you can just multiply the $m/z$ by $z$, the (absolute value of the) reduced electric charge.

If you want the mass of the parent neutral molecule, you will (a) need more information, and (b) have to do a bit more work. The extra information you need is the ionization mechanism. In electron ionization mass spectrometry, ionization is usually by electron gain or loss. So to get the neutral molecule mass, you will have to add back the missing electrons (or substract the gained electrons) from the calculated ion mass to get the molecule mass. For example, if $\ce{C7H7^2+}$ arose by the loss of two electrons, the $m/z$ would be 45.52683903, the ion mass would be 91.05367806, and the molecule mass would be 91.05477522.

Other types of mass spectrometry involve ionization by gaining or losing protons, not electrons, and so the difference between ion mass and neutral molecule mass is much more significant.

• How can the mass number be different from the mass of it just omitted the unit? If z was always a multiple of the charge, then it would be allowed to be negative. Claiming IUPAC is wrong is quite far reaching, I find none of your arguments compelling. – Martin - マーチン Jul 1 '16 at 19:22
• The mass number as defined by IUPAC & by Wikipedia is the sum of the number of protons and neutrons in a nucleus. Therefore it is always an integer. Thus, according the IUPAC the $m/z$ values of ions with $z=1$ must be integers. This is laughable. I can see how I missed a few points in my explication above and will edit to improve. – Curt F. Jul 1 '16 at 19:37
• I suspect that IUPAC drafted this statement before "high resolution" mass spectrometers were available to many users. If all you have is unit mass resolution, then the worst of IUPAC's errors ceases to matter. However, high-mass instruments have been available for some decades now. – Curt F. Jul 1 '16 at 21:30

As a mass spectrometrist, I agree with Curt. IUPAC is wrong, and you can convince yourself of this by going back to SI units.

Mass is in kilograms, charge is in coulombs (technically Amp*seconds), so the SI unit for mass/charge should be kilograms/coulomb. Mass/charge is not, and should not be defined as, 'dimensionless'.

So, there is a unit problem at the heart of mass spectrometry. We 'fudge' the issue by stating 'm/z 45.52683903', but it's a cop-out. Until IUPAC fixes their error, we won't have consensus on what units to actually use.

Given that the mass will be in u or Da, and the charge must be n*e (where n is an integer and e is the (absolute value of the) charge on an electron, then the obvious unit should be Da/e or u/e. The 'Thompson' or 'th' has been proposed, and is sometimes used, but unless IUPAC adopts it and properly defines it, it won't become the mainstream unit. Until then, we are in limbo.

That said, it is easy to calculate the mass if you know the m/z and the charge, z. m/z can be measured off the spectrum, and z can be determined by the isotopic spacing which would be about 1.0034/z for carbon isotopes. Thus the mass of the neutral molecule will be the m/z multiplied by z, and removing any adduct masses (such as protons, electrons, sodium ions, etc) which were added to turn the neutral molecule into an ion.

• Interesting comment and +1. Welcome to chem.se! I myself don't see a "fudge" in the absence of a IUPAC ruling, except maybe for whether "Th" will catch on. But I don't think many mass spectrometrists feel stuck in limbo when they say "$m/z$ of 45.52683903"; they know the units are really Da / $e$. – Curt F. Jul 5 '16 at 13:29

From the IUPAC gold book:

mass-to-charge ratio, $\frac{m}{z}$
in mass spectrometry
The abbreviation $\frac{m}{z}$ is used to denote the dimensionless quantity formed by dividing the mass number of an ion by its charge number. It has long been called the mass-to-charge ratio although $m$ is not the ionic mass nor is $z$ a multiple or the elementary (electronic) charge, $e$. The abbreviation $\frac{m}{e}$ is, therefore, not recommended. Thus, for example, for the ion ($\ce{C7H7^2+}$), $\frac{m}{z}$ equals $45.5$.

The mass-to-charge ration $m/z$ is an abbreviation. It should not been taken literal.
For all intents and purposes the mass number may be seen as the mass of the ion in $\mathrm{u}$ or $\mathrm{Da}$ without its unit. The charge number represents the "count" of the charges, without specifying what charge it is. In general you can multiply the signal value by the ions charge (and mass unit) to obtain the ions mass.

• @user2018675 you should never apologise for changing your accepting vote - it is your choice to pick the answer that helped you the most. – Martin - マーチン Jul 1 '16 at 19:24