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In Lehninger's Principle of Biochemistry Pg. $14$, this is the definition for molecular weight (relative molecular mass):

The molecular weight of a substance is defined as the ratio of the mass of a molecule of that substance to one-twelfth the mass of carbon- $12$ ($12$C). Since $M_r$ is a ratio, it is dimensionless—it has no associated units.

What I do not understand is how we find the mass of the molecule in the beginning. What unit would we use?

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  • $\begingroup$ @user1136 The phrase "molecular weight" may be frowned on, but I doubt it's ever going to go away unless all the reagent makers get on board. I don't think I've ever seen a protein standard marketed as a "molecular mass marker"... $\endgroup$ – MattDMo Oct 16 '20 at 18:44
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    $\begingroup$ @user1136 I agree with you that the most precise term should be used, I just wanted to make the point that there is a lot of historical weight (so to speak) on the term "molecular weight", and I don't think its usage will decrease until reagent makers get on board. $\endgroup$ – MattDMo Oct 16 '20 at 18:57
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    $\begingroup$ I voted to close this question as off-topic as it is a general chemistry question. $\endgroup$ – David Nov 5 '20 at 12:04
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The mass of a biological molecule is evaluated by the process of Mass Spectrometry (specifically MS/MS or MALDI-TOF). These are an improved version of Mass Spectrometry(MS) and results from the works of physical chemists.In a nutshell, you can ionize the molecule. It dissociates into several ionized particles. Then subject them to a magnetic field and an electrical field at the same time. The ionized particles take a curved route while moving , and the amount of curve depends on m/q of molecule ( mass of particle (in kg) and charge of it)

see https://en.wikipedia.org/wiki/Mass_spectrometry

Molecular weight is dimensionless indeed. However one may add Dalton/amu/u "False" physical units for better understanding. The best other example in physics is radians. Angles are defined in radians in physics. But they are dimensionless.

In Circular motion , we have these formula :

$ v = \omega \times r$

$\theta = \omega \times t$

see: this

unit of $v$ is (meter per second) and unit of $r$ is (meter). therefore the unit of $\omega$ is $s^{-1}$ . unit of $\omega$ is $s^{-1} $ while the unit of $t$ is $s$.

So $\theta$ is dimensionless although we describe it as radians for better understanding

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