Converting Volume of Reactant to Volume of Product — Examples

Converting Volume of a Reactant to Volume of a Product

Stoichiometry applies dimensional analysis to convert between quantities of reactants and products. An aha moment should go off in your head when you see volume. It usually indicates we need to use density in our stoichiometric calculations.

The density is unique for each specific substance. It's an intensive property. But remember, the density is influenced by various conditions. So it changes with temperature and varies between the phases of matter. For example, let's consider the density of water. Liquid water has a density of $1.0\frac{g}{ml}$. What if we freeze it? The density of solid water is $0.917\frac{g}{ml}$. If we boil it, the density becomes $5.98\times$ $10^{-4}$ $\frac{g}{ml}$!

Note: If we are at standard temperature and pressure (STP), one mole of any gas equals 22.4 L. While this is not a density, it is extremely important for the interconversion of gas volume to moles of product or vice versa.

So, just like in converting between mass of a reactant and mass of a product, our first step is to double-check that our chemical equation is balanced. This will give us our mole ratio.

Our next step is to convert the volume of our reactant in question to moles. But how do we do this? Through density and molecular weight! Or if your reactant is a gas, you would use the conversion factor (1 mol equals 22.4 L of gas).

Next, using our mole ratio from our balanced chemical equation, we convert moles of reactant to moles of product. What comes next?

Note: Anytime you’re moving from one side of a chemical equation to the other you use moles.

Because we are now converting from moles back to volume, we are able to use the same steps from the first part of our calculations. How do we go from moles to volume? We can use the molar mass to convert moles to mass. Then from mass, we use density to obtain a volume. If we were converting from a mole of product to gas volume, our calculations are even simpler. We get to use the conversion factor, 1 mol gas = 22.4 L gas!

Remember, that in many chemical reactions there is a limiting reactant. It stops any excess reactants from continuing the reaction. So, only the number of moles from the limiting reactant would actually react.

Let’s try two examples!

Example 1: For the double-replacement reaction below, what volume of water in milliliters will be produced when 10 mL of solid sodium hydroxide ($NaOH_{(s)}$) reacts with excess hydrogen chloride gas ($HCl_{(g)}$)? The products are sodium chloride and water.

$NaOH_{(s)} + HCl_{(g)} \rightarrow NaCl_{(s)} + H_{2}O_{(l)}$

Example 2: What volume, in liters, of water vapor is produced from the combustion of 2L of methane $CH_{4(g)}$ at standard temperature and pressure?

$$CH_{4(g)} + O_{2(g)} \rightarrow CO_{2(g)} + H_{2}O_{(g)}$$

(Video) Molar Gas Volume: Stoichiometry With Gases

by Professor Dave Explains

In this video, Professor Dave explains the molar volume of gases. At STP, one mole of any gas takes up 22.4 liters. You can use this conversion in stoichiometry problems. Professor Dave will show you how!