Questions: The combustion of propane produces carbon dioxide gas and water vapor according to the reaction
C3H8(l) + 5 O2(g) → 3 CO2(g) + 4 H2O(g)
A sample of propane is added to a 260-L container containing excess oxygen to a final pressure of 10.8 atm and combusted at 650 K. Calculate the moles of carbon dioxide gas produced.
158 mol
52.6 mol
210 mol
263 mol
Transcript text: The combustion of propane produces carbon dioxide gas and water vapor according to the reaction
\[
\mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{l})+5 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 3 \mathrm{CO}_{2}(\mathrm{~g})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{~g})
\]
A sample of propane is added to a 260-L container containing excess oxygen to a final pressure of 10.8 atm and combusted at 650 K . Calculate the moles of carbon dioxide gas produced.
158 mol
52.6 mol
210 mol
263 mol
Solution
Solution Steps
Step 1: Identify the Given Data
We are given:
Volume of the container, V=260L
Final pressure, P=10.8atm
Temperature, T=650K
The reaction:
C3H8(l)+5O2(g)→3CO2(g)+4H2O(g)
Step 2: Use the Ideal Gas Law to Find Moles of Propane
The ideal gas law is given by:
PV=nRT
where:
P is the pressure,
V is the volume,
n is the number of moles,
R is the ideal gas constant (0.0821L⋅atm/mol⋅K),
T is the temperature.
Rearranging for n:
n=RTPV
Substituting the given values:
n=0.0821L⋅atm/mol⋅K×650K10.8atm×260L
Step 3: Calculate the Moles of Propane
n=53.3652808≈52.6255mol
Step 4: Determine the Moles of Carbon Dioxide Produced
From the balanced chemical equation, 1 mole of propane (C3H8) produces 3 moles of carbon dioxide (CO2).
Thus, the moles of CO2 produced:
nCO2=3×52.6255≈157.8765mol