User:Kehrli/mz misconception

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When J.J. Thomson measured the charge-to-mass ratio of the electron in 1897 it was clear that the mass-to-charge ratio would have a dimension of mass/charge, just as the name suggests.[1].

Only much later a small group within the scientific community, the mass spectrometrists, started to replace the mass-to-charge ratio by the dimensionless entity m/z. Unfortunately this m/z was never clearly defined. Until these days it is not clear if the m/z designates a physiscal quantity, the numerical value of a physical quantity or the unit of a physical quantity. The only attempt for a definition was made by the Analytical Chemistry Division of the IUPAC. It reads [2]:

mass-to-charge ratio (in mass spectrometry), m/z
The abbreviation 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 m/e is, therefore, not recommended. Thus, for example, for the ion C7H72+, m/z equals 45.5.

This definition, however, confuses more than it reveals. It explicity states that m/z is a dimensionless (physical) quantity. It also states that m/z is a abbreviation. An abbreviation for what? An abbreviation for the mass-to-charge ratio? Probably not, because the It has long been called ... although ... seems to indicate that m/z has mistakenly been called mass-to-charge ratio. Also, the physical quantity mass-to-charge ratio is not dimensionless, it has the dimension mass/charge.

Today, many that use m/z say that m stands for the mass number. The mass number is defined as the number of nucleons in a particle. However, the official IUPAC symbol for the mass number is A, not m which is reserved for mass. Also it is evident that mass spectrometers measure the mass-to-charge ratio of an ion and they do not count nucleons in an ion. This is a big difference since counting nucleons would always reveal a whole number, whereas some mass spectrometers are able and do separate ions with same mass number and same charge number.

The large majority of the scientific community is not using the m/z. From the subgroup of scientists that deal with charged particles and that therefore use the mass-to-charge ratio do not use the m/z except the mass spectrometrists where m/z is widely used.

The following is a collection of arguments explaining why the concept of the dimensionless mass-to-charge ratio m/z is a misconception and should no longer be used. Use the dimensioned m/q instead. (Some people even use a dimensioned m/z, which is also ok, though against any IUPAC recommendations.)


Contents

[edit] Physical quantities

The IUPAC green book about Quantities, Units and Symbols in Physical Chemistry explains:

Any value of a physical quantity Q can be expressed as the product of a numerical value {Q} and a unit [Q].
Q = {Q} x [Q]
Neither the name of a physical quantity nor the symbol used to denote it, implies a particular choice of unit.

some examples:

  • l = 3 m (the physical quantity length is three meters)
  • m = 5 kg (the physical quantity mass is 5 kilograms)
  • m = 5 u ( the physical quantity is 5 unified atomic mass units)
  • q = 3.5 C ( three and a half coulombs)
  • q = 2 e (two elementary charge units)

In the following it will be demonstarted that the m/z used by so many mass spectrometrists does not comply to above fundamental instruction about the measurement of physical quantities.

In this article symbols for a physical quantity are written in italics (e.g. q), units are written in bold (e.g. kg). n represents a numerical value that is a real number and z represents a numerical value that is a whole number.

[edit] What the IUPAC says

Current IUPAC definition

The abbreviation 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 m/e is, therefore, not recommended. Thus, for example, for the ion C7H72+, m/z equals 45.5.

Critique
  • why should dividing a mass quantity by a dimensionless quantity yield a dimensionless quantity?
  • why is m not a mass and what is it then?
  • if z is not a multiple of the elementary charge what is it then?
  • the quantity mass number has the official symbol A - why is it not used?
  • everyone knows that mass spectrometers measure the mass to charge ratio - so why the fuss about mass numbers and charge numbers instead of just using plain mass and charge?
  • how can you conclude from m is not the ionic mass nor is z a multiple or the elementary (electronic) charge, e that therefore m/e is not recomended? Where is the logic?
  • why should anyone substitute z (a physical quantity) with e (a unit)?
  • why does IUPAC issue a definition that completly contradicts its own green book?

[edit] Three reasons why m/z is wrong

1) Mass spectrometers measure the physical quantity mass to charge ratio which is not dimensionless. This is a simple fact.

2) There are some dimensionless physical properties. The most famous one is the Reynolds Number Re and the most common in mass spectrometry is the mass resolving power R = m/dm. The characteristic of such dimensionless properties is that it does not matter what system of units you use: whether you use kg or Da, m/dm will be the same. This is not the case for the mass-to-charge ratio: whether you use kg or Da makes a big difference.

3) If a non-dimensionless physical quantity is measured we should use units. This is exactly what units were invented for. Units are a cultural achievement like the wheel or the language and they should be used.

[edit] What went wrong

Let us investigate where the z is coming from: start with Q = n x [Q] and use it for a charge:

q = n x [q]

Now, if [q] is the elementary charge, n will always be a whole number. Whole numbers are often indicated with z. Therefore in this special case we could write:

q = z x e

This means z is not the symbol of charge as it is used by mass spectrometrists (m/z), it is only the numerical factor belonging to the unit to form a quantity. Hence z is the number that you read from the x-axis and should not appear in the label. Compare this with a charge measurement:

q = n [l] or, when measuring in coulombs: q = n C, and when measuring in elementary charge units: q = z e.

Now, if you label a x-axis that represents a charge, do you label it with “z” ? No! It is labeled with q (C) or q (e). Consequently we should eliminate the z because it is the source of the whole confusion.

[edit] A correct approach

[edit] What symbol to use?

Here are the basic facts:

  1. mass spectrometers measure the physical quantity mass/charge
  2. the symbol for mass is m
  3. the symbol for charge is q (it is actually Q, but q is also often used).
  4. we need to choose a symbol for the mass to charge ratio. Possible choices are m/q, m/z, and it would actually be even more correct to have a single symbol like μ or mQ but this is to far ahead of the mass spec community.

Note: as stated above, the symbol m/q is completely independent on the units [m/q] that are being used. Analogously it is common to use the symbol for mass m with kg as well as with lb:

m = 3 kg
m = 6 lb

[edit] what units to use

Now we have settled the question of the symbol. Let’s turn to the second part, the units to be used. Obviously, everyone in MS wants to measure the mass in u and the charge in elementary charge units. Therefore

m = n [m]
q = n [q]

becomes:

m = n u
q = n e

Hence, the unit mass spectrometrists use is [m/q] = u/e. That is by the way what everyone uses, even when they claim to a dimensionless m/z.

m/q = n u/e

Note how clumsy it is to say: "the ion C7H72+ has a mass-to-charge ratio of 45.5 atomic mass units per elementary charge units".

[edit] A better approach

The problems with above approach are:

(A) e is not an official unit and therefore cannot be used
(B) "atomic mass unit" is a very clumsy name and is gradually replaced by dalton (Da)

(A) is a severe problem: everyone uses a unit that does not exist officially. There are four ways out:

  1. we make e official (in which case we should not call it e, but for example millikan (Mi).
  2. we create the Th (which de facto creates e through the back door)
  3. we use kg/C

(3) is unpractical, (2) requires (1), therefore there is no way around (1)!

Problem (B) is best solved by adopting the dalton Da

So we end up with:

m = n Da
q = n Mi
m/q = n Da/Mi

[edit] An even better approach

m/q = n Th

where 1 Th (thomson) = 1 Da/Mi

[edit] The correct approach

mQ = n Th

but this is too far ahead for the mass spec community

[edit] Conclusion

Say:

the ion C7H72+ has a mass-to-charge ratio of 45.5 Th
the peak at 45.5 Th is probably C7H72+

[edit] See also

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