3.2 Mass-Volume Relationship

  Stoichiometry

It relates the mass of a species (reactant or product) and the volume of a gaseous species (reactant or product) involved in a chemical reaction. Suppose we are provided with ‘$a’$ grams of $NaHC{O_3}$ in a vessel of capacity $V\ litre$ and the vessel is heated, so that $NaHC{O_3}$ decomposes as,

\[2NaHC{O_3}\xrightarrow{\Delta }N{a_2}C{O_3} + {\text{ }}{H_2}O{\text{ }} + {\text{ }}C{O_2}\]

Now, we want to calculate the volume of $C{O_2}$ gas being produced.

Moles of $NaHC{O_3}$ taken = $\frac{a}{{84}}$

Now, since $2$ moles of $NaHC{O_3}$ gives $1$ mole of $C{O_2}$ at STP. Thus

Moles of $C{O_2}$ produced = $\frac{1}{2} \times \frac{a}{{84}}$

As we know that $1$ mole of any gas at STP occupies a volume of $22.4{\text{ }}L.$

So, volume of $C{O_2}$ produced is $$\left( {\frac{1}{2} \times \frac{a}{{84}} \times 22.4} \right)L$$