How to Find the Molar Mass of Methanol?

Hydrogen has the lightest molar mass, at 1.008 g/mol. On the other hand, some large molecules like DNA can have molar masses as high as thousands of grams per mole.

Substances can exist in various forms, like elements, compounds, ion complexes, and so on. Each of these forms contain different number of particles. For example, the number of particles in 1 gram of common salt (sodium chloride) is different from that in 1 gram of baking soda (sodium bicarbonate).

Moreover, because atoms and molecules are so small, they cannot be spotted by the naked eye, as even a small amount can contain billions of them. But, the knowledge of the number of particles is essential to understand the correct proportion of chemicals used in industrial processes. To make this easier, the concept of a mole was introduced.

A mole is an amount of a substance which contains the same number of particles as the number of atoms in 12 grams of the C-12 isotope of carbon. This number, called the Avogadro Constant, is 6.022 × 10²³. Therefore, 1 mole of any substance, whether salt or baking soda, contains an equal number, of 6.022 × 10²³ molecules.

So, the concept of a mole relates the amount of a substance with the number of particles it will contain. But, this only gives the number of particles, not the weight. In this context, the concept of molar mass finds relevance. It is the weight of one mole of a substance.

Let us understand what the steps are to find the molar mass of methanol (CH₃OH), considering that it is a common solvent used in chemical manufacture, and an alternative fuel.

The subscripts indicate the number of atoms of each element which is present in one molecule of the compound. In the formula CH₃OH, the subscript 3 indicates 3 hydrogen atoms. Since carbon, oxygen, and the other hydrogen don't have subscripts, this means that they are present as single atoms.

Look up these elements in the periodic table, and find their relative atomic masses. The relative atomic mass of an element is the mass of one atom of that element compared with 1/12 the mass of a single carbon atom of the C-12 isotope.

Since it is a 'relative' term, it does not have units, and is expressed in atomic mass units (amu). The relative atomic weights of the elements of methanol are:

Carbon (C) = 12.01 amu

Hydrogen (H) = 1.008 amu

Oxygen (O) = 15.999 amu

Calculate the total number of atoms present in one molecule of methanol. Since the molecular formula is CH₃OH, this means:

Carbon = 1 atom

Hydrogen = 4 atoms

Oxygen = 1 atom

Now, add the relative atomic weights of each element, keeping in mind the number of atoms of that element in the molecule. This is the molecular weight of methanol.

Molecular Weight = (1 × C) + (4 × H) + (1 × O)

= (1 × 12.01) + (4 × 1.008) + (1 × 15.999)

= 32.041 amu

Since the relative atomic masses are dimensionless quantities, their sum also has no units, and is expressed in amu. To convert it into molar mass, we have to multiply this sum by the Molar Mass Constant (M_u), which has a value of 1 g/mol.

Molar Mass = 32.041 amu × M_u

= 32.041 amu × 1 g/mol

= 32.041 g/mol

Hence, the molar mass of methanol is nothing but the sum of the relative atomic weights of its elements (molecular weight), expressed in grams per mole. It can be obtained by just adding 'g/mol' after its molecular weight.

This value of molar mass expressed in grams per mole is the commonly used unit. However, when used in equations, where other values are expressed in their SI units, the molar mass of methanol has to be expressed in kilograms per mole (kg/mol).

To calculate it in SI units, the value of the molar mass constant used in calculation of the molar mass is taken as 1 × 10^-3 kg/mol.

Molar Mass = 32.041 amu × 1 × 10^-3 kg/mol

= 0.032 kg/mol

There is often a lot of confusion between molecular mass and molar mass. Since molecular mass deals with the weight of one molecule of a substance, it remains constant and has no units. Molar mass, on the other hand, changes with the number of moles, and is expressed in g/mol or kg/mol. So, the molar mass of 1 mole of methanol is 32.04 g/mol, that of 2 moles is 62.04 g/mol, and so on. However, the molar mass of 1 mole and the molecular mass are numerically similar.