## How to calculate the molar mass of a molecule?

The molar mass is the mass of one mole of a substance (a simple body, a chemical compound). It is expressed in grams per mole (g · mol-1 or g / mol).

This is accomplished by:

$M = \frac{m}{n}$

with:

• n: the quantity of substance in moles (symbol "mol", as IF);
• m: mass in grams ("g" symbol, according to SI);
• M: molecular weight in grams per mole (or "g / mol" or "g · mol-1," according to SI)

## Determination of molar masses

### Case of simple body

For each chemical element, the mass of one mole of atoms is in the periodic table of elements. It is in fact the average molar mass for all isotopes of an element based on the proportion of each isotope. The value of the molar mass also corresponds to the average number of nucleons per atom of the element to which we must subtract the binding energy of the nucleons inside the nucleus.

Example: one mole of chlorine atoms 35Cl has a mass of 35 g. One mole of atoms of chlorine 37Cl has a mass of 37 g which must be subtracted from the mass corresponding to the binding energy of the nucleons. The element chlorine exists in its natural state with the proportions 75.77% / 24.23% in 35Cl/37Cl. So, its molecular weight is 35, 5 g ⋅ mol-1:

$\frac{75,77 \times 35 + 24,23 \times 37}{100} = 35,485$

to which one must subtract a mass of 0.032 g corresponding to the binding energy to regain ground (35.453) given in the table element. The molar mass of a single body is simply the product of the number of atoms in the molecules of the body by the molar mass elementary. Example: O2 oxygen has a molar mass de31, 9988 ⋅ g mol-1, which is the oxygen mass multiplied by two.

### Case of compound body

#### Molecular compounds

The molar mass of a molecular compound is calculated by summing the molecular weights of all the elements that constitute the molecules in part by multiplying the coefficients of the empirical formula of this compound.

#### Examples

We read in the periodic table of elements:

• MH = 1.0 g ⋅ mol-1;
• MC = 12.0 g ⋅ mol-1;
• MW = 16.0 g ⋅ mol-1.

Water has the formula H2O gross or

Meau = 2 ⋅ MH + MW = 2 × 1 + 16 = 18 g ⋅ mol-1

Glucose has the formula (C6H12O6), we find from the information below:

Mglucose = 6 × 12 × MC + MH + 6 = MO × 6 × 12.0 + 12 × 6 × 1.0 + 16.0 = 180.0 g ⋅ mol-1.

The molar mass is numerically identical to the average molecular mass is the mass of a single molecule and is expressed in atomic unit (u).

#### Ionic solids

As for molecular compounds, one must first know the empirical formula of the ionic solid. Again, we add all the molar masses for all elements of the solid taking into account the proportions of each element, and adding water molecules in the case of solid hydrates.

#### Example

copper sulphate (II) pentahydrate CuSO4 5H2O:
M = M (Cu) + M (S) + 4 M (O) + 5 x [2 M (H) + M (O)] = 63.5 + 32.1 + 4 x 16 + 5 (2 + 16 ) = 249.6 g mol-1

Content licensed under the CC-BY-SA. Source: Article molar mass of the French Wikipedia (authors)