Molar Mass Constant

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.

Definition of Molar Mass Constant

It is defined as the one-twelfth of the molar mass of carbon-12.

Symbol

The molar mass constant is denoted by M_u.

Unit

The unit of the molar mass constant is g mol⁻¹.

Formula

According to the above definition, the formula of the constant is as follows:

$M_\text{u} =\frac{1}{12} M_{(^{12}\text{C})}$

where ¹²C is the molar mass of carbon-12.

Value of Molar Mass Constant

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.

$M_\text{u} =0.999\,999\,999\,65(30) \, \text{g} \, \text{mol}^{-1}$

As we can see the above-mentioned value is very close to one. Thus, we can say for practical purposes M_u ≈ 1.

Molar Mass Constant, Atomic Mass Constant, and Avogadro Constant

The molar mass constant, as mention earlier, is given as:

$M_\text{u} =\frac{1}{12} M_{(^{12}\text{C})}$

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).

$M_{(^{12}\text{C})} = m_{(^{12}\text{C})} \times N_\text{A}$

Using the above two equations , we get,

$M_\text{u} =\frac{1}{12} m_{(^{12}\text{C})} \times N_\text{A}$

From the definition of the unified mass unit (u) and the atomic mass constant (m_u), we have the below relationship.

$1\,\text{u} = m_\text{u} =\frac{1}{12} m_{(^{12}\text{C})}$

From the above two equations, we have

$M_\text{u} &=\frac{1}{12} 12\,\text{u} \times N_\text{A} = 1\,\text{u} \times N_\text{A} \\ &=\frac{1}{12} 12\, m_\text{u} \times N_\text{A} = m_\text{u} \times N_\text{A}$

$\therefore M_\text{u} = 1\,\text{u} \times N_\text{A} = m_\text{u} \times N_\text{A}$

Using M_u ≈ 1 g mol⁻¹,

$1\,\text{u} \times N_\text{A} = m_\text{u} \times N_\text{A} \approx 1\,\text{g}\,\text{mol}^{-1}$

Relation with Relative Atomic Weight

Relative atomic weight is a dimensionless quantity and it is denoted as A_r. The relative atomic weight of carbon-12 is 12.

$A_{\text{r}(^{12}\text{C})} =12$

We can replace the numeral 12 in the equation M_u = ¹∕₁₂ M_(¹²C) by A_r(¹²C). Thus, we have

$M_\text{u} =\frac{1}{ A_{\text{r}(^{12}\text{C})}} M_{(^{12}\text{C})} =\frac{ M_{(^{12}\text{C})}}{ A_{\text{r}(^{12}\text{C})}}$

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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