# Converting between Moles of Different Substances

Moles of a substance are converted to moles of another substance by comparing the mole ratios of a balanced chemical equation.

The steps that can be used to convert moles of substance A to moles of substance B are:

1. Write the balanced chemical equation for the reaction.
2. Determine the mole ratio between substance A and substance B.
3. Use dimensional analysis to calculate the moles of substance B to the corresponding moles of substance A.

Step-By-Step Example
Converting from Moles of Substance A to Moles of Substance B in the Reaction of Sulfur and Oxygen Gas
Determine the number of moles of oxygen required to react with 6.2 moles (mol) of sulfur to produce sulfur trioxide.
Step 1
Write the balanced equation.
$2\rm S+3{\rm O}_2\rightarrow2{\rm{SO}}_3$
Step 2
The coefficients of the balanced equation show that the mole ratio of sulfur to oxygen is 2:3. This means 2 mol of sulfur react with 3 mol of oxygen to produce 2 mol of sulfur trioxide.
Solution
Use dimensional analysis to convert moles of sulfur to moles of oxygen using the mole ratio.
\begin{aligned}{\text{Moles of oxygen}}&=(6.2\rm{\; mol\; S})\!\left(\frac{3\rm{\; mol\; O}_2}{2\rm{\; mol\; S}}\right)\\&=9.3\rm{\; mol\; O}_2\end{aligned}
Step-By-Step Example
Converting from Moles of Substance A to Moles of Substance B in the Reaction of Nitrogen and Hydrogen Gas
Determine the number of moles of nitrogen gas (N2) required to react with 11 moles of hydrogen gas (H2) to produce ammonia (NH3).
Step 1
Write the balanced equation.
${\rm N}_2+3{\rm H}_2\rightarrow 2{\rm{NH}}_3$
Step 2
The coefficients of the balanced equation show that the mole ratio of nitrogen gas to hydrogen gas is 1:3. This means that 1 mol of nitrogen reacts with 3 mol of hydrogen gas to produce 2 mol of ammonia.
Solution
Use dimensional analysis to convert moles of hydrogen gas to moles of nitrogen gas using the mole ratio.
\begin{aligned}{\text{Moles of nitrogen gas}}&=(11\rm{\; mol\; H}_2)\!\left(\frac{1\rm{\; mol\; N}_2}{3\rm{\; mol\; H}_2}\right)\\&=3.7\rm{\; mol\; N}_2\end{aligned}
Step-By-Step Example
Converting from Moles of Substance A to Moles of Substance B in the Reaction of Methane and Oxygen Gas
Determine the number of moles of methane (CH4) required to react with 6.4 mol of oxygen gas (O2) in a combustion reaction.
Step 1
Write the balanced equation.
${\rm{CH}}_4+2{\rm O}_2\rightarrow{\rm{CO}}_2+2{\rm H}_2\rm O$
Step 2
The coefficients of the balanced equation show that the mole ratio of methane to oxygen gas is 1:2. This means 1 mol of methane reacts with 2 mol of oxygen gas to produce 1 mol of carbon dioxide and 2 mol of water.
Solution
Use dimensional analysis to convert moles of oxygen gas to moles of methane using the mole ratio.
\begin{aligned}{\text{Moles of methane}}&=(6.4\rm{\; mol\; O}_2)\!\left(\frac{1\rm{\; mol\; CH}_4}{2\rm{\; mol\; O}_2}\right)\\&=3.2\rm{\; mol\; CH}_4\end{aligned}