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:
\(\dfrac{V_{\mathrm{\ce{C3H8}}}}{ν_{\mathrm{\ce{C3H8}}}} = \dfrac{V_{\mathrm{\ce{O2}}}}{ν_{\mathrm{\ce{O2(g)}}}}\)
\(ν_{\mathrm{\ce{C3H8(g)}}}\) \(= 1\)
\(ν_{\mathrm{\ce{O2(g)}}}\) \(= 5\)
\(V_{\mathrm{\ce{C3H8}}}\) \(= 2.7\ \mathrm{L}\)
\(V_{\mathrm{\ce{O2}}}\) = ?
\(V_{\mathrm{\ce{O2}}}\) \(= V_{\mathrm{\ce{C3H8}}} \cdot \dfrac{ν_{\mathrm{\ce{O2(g)}}}}{ν_{\mathrm{\ce{C3H8(g)}}}}\)
\(\ \ \ =2.7\ \mathrm{L} \cdot \dfrac{5}{1}\)
\(\ \ \ =2.7\ \mathrm{L} \cdot 5\)
\(\ \ \ =13.5\ \mathrm{L}\)