Question

what is the total volume of gaseous products formed when 36.9 liters of propane (c₃h₈) react completely according to the following reaction? (all gases are at the same temperature and pressure.) propane (c₃h₈)(g) + oxygen (g) → carbon dioxide (g) + water (g)

Explanation:

Step1: Balance the chemical equation

The balanced equation for the combustion of propane is \(C_{3}H_{8}(g)+5O_{2}(g)
ightarrow3CO_{2}(g)+4H_{2}O(g)\)

Step2: Use Avogadro's law (at same \(T\) and \(P\), \(V\propto n\))

From the balanced equation, 1 volume of \(C_{3}H_{8}\) reacts to produce \(3 + 4=7\) volumes of gaseous products (\(3\) volumes of \(CO_{2}\) and \(4\) volumes of \(H_{2}O\)).
If \(V_{C_{3}H_{8}} = 36.9\space L\), then the volume of products \(V_{products}\) is calculated as follows:
Since the ratio of \(V_{C_{3}H_{8}}\) to \(V_{products}\) is \(1:7\) (from the mole - ratio in the balanced equation, and using Avogadro's law \(V = n\times V_m\) where \(V_m\) is constant at same \(T\) and \(P\)), we have \(V_{products}=7\times V_{C_{3}H_{8}}\)
Substitute \(V_{C_{3}H_{8}} = 36.9\space L\) into the equation: \(V_{products}=7\times36.9\space L\)

Answer:

\(258.3\space L\)