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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 *M*_{u}.

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 ^{12}C is the molar mass of carbon-12.

The approximate value of *M*_{u} 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 *M*_{u} ≈ 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 (*N*_{A}).

Using the above two equations , we get,

From the definition of the unified mass unit (u) and the atomic mass constant (*m*_{u}), we have the below relationship.

From the above two equations, we have

Using *M*_{u} ≈ 1 g mol^{−1},

Relative atomic weight is a dimensionless quantity and it is denoted as *A*_{r}. The relative atomic weight of carbon-12 is 12.

We can replace the numeral 12 in the equation *M*_{u} = ^{1}∕_{12} *M*_{(12C)} by *A*_{r(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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