Answer
299.39 grams
1 C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂O
100 g C₃H₈ 1 mol C₃H₈ 3 mol CO₂ 44.01 g CO₂
44.1 g C₃H₈ 1 mol C₃H₈ 1 mol CO₂
299.39 g CO₂
Explanation
Given:
Mass of propane (C₃H₈) = 100 grams
What to find:
The mass of carbon dioxide (CO₂) produced.
Solution:
The balanced chemical equation for the combustion of propane, C₃H₈ is
1 C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂O
The next step is to convert 100 grams of propane (C₃H₈) to moles using the mole formula and molar mass of propane (C₃H₈).
[tex]\begin{gathered} Moles=\frac{Mass}{Molar\text{ }mass} \\ \\ Molar\text{ }mass\text{ }of\text{ }propane\text{ }(C₃H₈)=44.1\text{ }g\text{/}mol \\ \\ Moles=\frac{100\text{ }g}{44.1\text{ }g\text{/}mol}=2.2676\text{ }mol\text{ }C₃H₈ \end{gathered}[/tex]The step that follows is to determine the mole of carbon dioxide produced using the mole ratio from the equation and the mole of propane (C₃H₈) above.
[tex]\begin{gathered} 1\text{ }mol\text{ }C₃H₈=3\text{ }mol\text{ }CO₂ \\ \\ 2.2676\text{ }mol\text{ }C₃H₈=x\text{ }mol\text{ }CO₂ \\ \\ x=\frac{2.2676\text{ }mol\text{ }C₃H₈}{1\text{ }mol\text{ }C₃H₈}\times3\text{ }mol\text{ }CO₂ \\ \\ x=6.8028\text{ }mol\text{ }CO₂ \end{gathered}[/tex]The final step is to convert 6.8028 moles of CO₂ to mass in grams of CO₂.
[tex]\begin{gathered} Moles=\frac{Mass}{Molar\text{ }mass} \\ \\ Mass=Moles\times Molar\text{ }mass \\ \\ Molar\text{ }mass\text{ }of\text{ }carbon\text{ }dioxide\text{ }(CO₂)=44.01\text{ }g\text{/}mol \\ \\ Mass=6.8028\text{ }mol\times44.01\text{ }g\text{/}mol \\ \\ Mass=299.39\text{ }grams \end{gathered}[/tex]Hence, the mass of carbon dioxide (CO₂) produced is 299.39 grams.
In summary,
1 C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂O
100 g C₃H₈ 1 mol C₃H₈ 3 mol CO₂ 44.01 g CO₂
44.1 g C₃H₈ 1 mol C₃H₈ 1 mol CO₂
299.39 g CO₂
