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Example 4.9: Number of Product Molecules Generated by a Reaction

Number of Product Molecules Generated by a Reaction

How many carbon dioxide molecules are produced when 0.75 mol of propane is combusted according to this equation?

Solution

\(n_{\mathrm{\ce{C3H8}}}\) \(= 0.75\ \mathrm{mol}\)


The approach here is the same as for Example 7, though the absolute number of molecules is requested, not the number of moles of molecules. This will simply require use of Avogadro’s constant relating chemical amount and number of molecules.
The balanced equation shows that carbon dioxide is produced from propane in a 3:1 ratio:


Using this stoichiometric factor, the provided molar amount of propane, and Avogadro’s number,

\(n_{\mathrm{\ce{CO2}}}\) \(= \frac{1 }{ 3} \cdot n_{\mathrm{\ce{C3H8}}}\)

\(\ \ \ =\frac{1 }{ 3} \cdot 0.75\ \mathrm{mol}\)

\(\ \ \ =0.250\ \mathrm{mol}\)


\(N_{\mathrm{A}}\) \(= 6.022\times 10^{23}\frac{1}{\mathrm{mol}}\)


\(N_{\mathrm{\ce{CO2 molecules}}}\) \(= N_{\mathrm{A}} \cdot n_{\mathrm{\ce{CO2}}}\)

\(\ \ \ =6.022\times 10^{23}\frac{1}{\mathrm{mol}} \cdot 0.250\ \mathrm{mol}\)

\(\ \ \ =1.51\times 10^{23}\)