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26th Jun 2019 @ 2 min read
The molar mass constant is a quantity similar to the atomic mass constant. The constant, as from the name, is related to the molar mass of carbon-12.
It is defined as the one-twelfth of the molar mass of carbon-12.
The molar mass constant is denoted by Mu.
The unit of the molar mass constant is g mol−1.
According to the above definition, the formula of the constant is as follows:
where 12C is the molar mass of carbon-12.
The approximate value of Mu is 1 g mol−1. The more precise value, as per Committee on Data for Science and Technology (CODATA), is given below.
As we can see the above-mentioned value is very close to one. Thus, we can say for practical purposes Mu ≈ 1.
The molar mass constant, as mention earlier, is given as:
Here, M(12C) is the molar mass of carbon-12, or in other words, the mass of carbon-12 in one mole.
The molar mass of carbon-12 can be expressed as the mass of one carbon-12 atom (m(12C)) multiplied by the Avogadro’s constant (NA).
Using the above two equations , we get,
From the definition of the unified mass unit (u) and the atomic mass constant (mu), we have the below relationship.
From the above two equations, we have
Using Mu ≈ 1 g mol−1,
Relative atomic weight is a dimensionless quantity and it is denoted as Ar. The relative atomic weight of carbon-12 is 12.
We can replace the numeral 12 in the equation Mu = 1∕12 M(12C) by Ar(12C). Thus, we have
From the above equation, the molar mass constant is the ratio of the molar mass of carbon-12 to the relative atomic weight of carbon-12.
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