Example 9.17: Reaction of Gases

Propane, \(\ce{C3H8(g)}\), is used in gas grills to provide the heat for cooking. What volume of \(\ce{O2(g)}\) measured at 25 °C and 760 torr is required to react with 2.7 L of propane measured under the same conditions of temperature and pressure? Assume that the propane undergoes complete combustion.

Solution

The ratio of the volumes of \(\ce{C3H8}\) and \(\ce{O2}\) will be equal to the ratio of their coefficients in the balanced equation for the reaction:

\(\ce{C3H8(g)}\)\(\ce{ + }\)\(\ce{5O2(g)}\)\(\ce{->}\)\(\ce{3CO2(g)}\)\(\ce{ + }\)\(\ce{4H2O(l)}\)\(\ce{ }\)

From the equation, we see that one volume of \(\ce{C3H8}\) will react with five volumes of O2:

\(\dfrac{V_{\mathrm{\ce{C3H8}}}}{ν_{\mathrm{\ce{C3H8}}}} = \dfrac{V_{\mathrm{\ce{O2}}}}{ν_{\mathrm{\ce{O2(g)}}}}\)     

\(ν_{\mathrm{\ce{C3H8(g)}}}\) \(= 1\)


\(ν_{\mathrm{\ce{O2(g)}}}\) \(= 5\)


\(V_{\mathrm{\ce{C3H8}}}\) \(= 2.7\ \mathrm{L}\)


\(V_{\mathrm{\ce{O2}}}\) = ?


\(V_{\mathrm{\ce{O2}}}\) \(= V_{\mathrm{\ce{C3H8}}} \cdot \dfrac{ν_{\mathrm{\ce{O2(g)}}}}{ν_{\mathrm{\ce{C3H8(g)}}}}\)

\(\ \ \ =2.7\ \mathrm{L} \cdot \dfrac{5}{1}\)

\(\ \ \ =2.7\ \mathrm{L} \cdot 5\)

\(\ \ \ =13.5\ \mathrm{L}\)