In 2.5 Isotopes and Relative Abundance, we introduced the Dalton (Da) and the atomic mass unit (amu). These tell us the mass of individual atoms – which is roughly equal to the number of protons and neutrons.

Naturally, their small size makes it impractical for us to measure by the individual atom. As such, Avogadro's number was constructed with the mass of carbon-12 in mind (the same element used in the definition of Da and amu), allowing us to determine the amount of moles present in a material by weight. As such, practicing chemists hardly work with amu, but with Molar mass; the amount of grams required for 1 mole ([latex]gmol^{-1}[/latex]) of a substance. It is defined in such a way that it is equivalent in number to Daltons.

In the case of carbon-12, with an atomic mass of 12.01 Da, we can also read this as 12.01 grams needed to have 1 mole of carbon-12. For determining chemical equations with molar coefficients, this is extremely useful. We can now read our periodic table and determine the molar mass of any element (see Figure 5.2.1 and Table 5.2.1).

Molar Mass of Compounds

To calculate the molar mass of a compound or molecule, we must add the molar masses of each atom found within it.

In sodium carbonate, 3 atoms of oxygen are needed to form only 1 molecule. We can directly relate this to the 3 moles of oxygen needed to form 1 mole of sodium carbonate.

The definition of molar mass creates an important relationship between the amount of substance (moles) and the mass of the substance (m): \[
n=\frac{m}{M}
\]

Where, [latex]M[/latex] is molar mass [latex]\left(\textrm{g}\textrm{mol}^{-1}\right)[/latex]
[latex]m[/latex] is the mass of the substance [latex]\left(\textrm{g}\right)[/latex]
[latex]n=[/latex] is the number of moles [latex]\left(\textrm{mol}\right)[/latex]

This is one of the most important formulas in chemistry! It allows us to determine the amount of moles of a substance present within a reaction through its mass.

The Mole and Chemical Formulas

As we have learnt, chemical formulas indicate the number of atoms of each element present in a compound. For instance, in [latex]\ce{Na}_{2}\ce{CO}_{3}[/latex], one molecule of sodium carbonate contains two atoms of sodium, one atom of carbon and three atoms of oxygen. Similarly, chemical formulas can also indicate the number of moles of atoms of each type of element present in one mole of a compound. Let’s take the same example [latex]\ce{Na}_{2}\ce{CO}_{3}[/latex] again; this time, the chemical formula of sodium carbonate indicates that 2 moles of sodium, one mole of carbon and three moles of oxygen are present in one mole of sodium carbonate.

Stoichiometric Coefficient

In chemical equations, the stoichiometric coefficient is the number written immediately before the atoms, ions and molecules in a balanced chemical equation. These numbers indicate the ratio of any reactant or product that reacts or forms in a reaction.

For example, let’s consider the reaction between hydrogen gas and nitrogen gas to form ammonia. The balanced chemical equation can be written as follows: \[
3\ce{H}_{2}\left(g\right)+\ce{N}_{2}\left(g\right)\rightarrow2\ce{NH}_{3}\left(g\right)
\]

Stoichiometric coefficients are the numbers found in front of the reactants and products of our chemical equation. 3 and 2 are written in front of [latex]\ce{H_2}[/latex], and [latex]\ce{NH}_{3}[/latex] and are our coefficients. For components without a number, such as [latex]\ce{N_2}[/latex], we can treat this as a 1. Stoichiometric coefficients in this reaction show that three molecules of hydrogen gas react with one molecule of nitrogen gas to form two ammonia molecules.

The Molar Ratio and Chemical Equations

The stoichiometric coefficients in a balanced chemical equation can also be interpreted on the molar scale. For a general reaction such as:

[latex]\ce{aA + bB {\rightarrow} cC + dD}[/latex] 

the number of moles of A divided by its stoichiometric coefficient a is equal to the number of moles of B divided by its stoichiometric coefficient b, etc., as shown in below equation:

[latex]{{\frac{Amol}{a}} = {\frac{Bmol}{b}} = {\frac{Cmol}{c}} = {\frac{Dmol}{d}}}[/latex]

Let’s consider the same example again: \[
3\ce{H}_{2}\left(g\right)+\ce{N}_{2}\left(g\right)\rightarrow2\ce{NH}_{3}\left(g\right)
\]

Based on the molar scale, we can say that three moles of hydrogen gas react with one mole of nitrogen gas to form two moles of ammonia gas. Molar scale interpretation relates to the quantities of substances involved in the reaction. Therefore, if we know the amount of one substance involved in the reaction, we can use the molar ratio to determine the amounts of others involved in the reaction.