Calculate Molar Mass

Molecular mass can be calculated for any molecule. As in the previous post, the conversion factor for carbon-12 is shown. With molecules, one must calculate the molecular mass.  Thus, the molecular mass is the summation of the resulting product of a component atom and its respective molecular mass of that atom over all atoms in the molecule (see Equation 1 below). For example, the molecular mass of methane can be calculated by this:

4*(atomic mass of hydrogen) + (1)*atomic mass of carbon= molecular mass of methane

4*(1.008) + 12.01 = 16.042 amu 

With the conversion factor from the previous post, we can easily convert 16.042 amu to g/mol so that molar mass of methane is 16.042 g in one mole.

${\displaystyle \sum _{i=A_r}^n{A}_{r_i}\cdot X_{n_i}=(A_r\cdot X_n)}$
Equation 1: The summation equation of calculating Molecular Mass of a substance

Calculate Molecular Mass

The molecular mass of a compound is the relative mass of some number of moles of a substance. The SI (International System or Système Internationale d'Unités) unit for relative mass of a atom/molecule is the mole (mol). The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.022 × 10²³ elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in mol⁻¹ , and is called the Avogadro number (IUPAC definition). One mole can also be defined as exactly the same number of atoms that are contained in 12 grams (one mole) of the carbon-12 isotope. In addition, the mass of one atom of carbon is stated as 12 amu (atomic mass units).

One can find the mass of one mole of any atom by looking at the periodic table, and this number is found usually below the atomic symbol, and this value is reported as the average molar mass (M_r). For example, the average molar mass of carbon is reported as 12.011 g/mol. This means that a mole of carbon has a weight contribution from some heavy isotopes of carbon, such as C-13 (stated as "carbon thirteen" and expressed commonly as ¹³C or carbon-13) and C-14 (¹⁴C). Similarly, the average molar mass of one mole of Nitrogen is 14.007 grams with nitrogen-14 being the most abundant isotope. As well, the average molar mass of one mole of Boron is 10.81 with boron-11 contributing the most to mass of one mole (while 20 percent of the molar mass being contributed by boron-10). 

Conversion factors can be made from any isotope or atom from the periodic table as such:

${\displaystyle \left(\frac{\text{12 grams of carbon-12}}{\text{1 mole of carbon-12}}\right)}$
${\displaystyle }$

Equation 1: A conversion factor for the carbon-12 isotope so that one can convert from grams to mole and vice versa

${\displaystyle \frac{\text{(10.81 grams of boron)}}{\text{(1 mole of boron)}}}$

 

Equation 2: A conversion factor for the average molecular mass of boron and a mole of boron


${\displaystyle \frac{\text{(1 mole of X)}}{\text{(molar mass of X)}}}$ 

Equation 3: The general conversion factor of 1 mole of any compound or element and its molar mass


${\displaystyle \frac{\text{1 mole of X}}{6.023\cdot {10}^{23}\text{of X atoms}}}$  

Equation 4: A conversion factor from 1 mole of any molecule/atom and the number of atoms in that mole of substance