Question

If 3.6 L of CO2 is formed at STP, exactly how many molecules of C3H8 would have been needed? Assume that the other reactant was in excess.

Answer 1

To determine the number of molecules of C₃H₈ needed to form 3.6 L of CO₂ at STP, we use the stoichiometry of the balanced chemical equation for the reaction. If 3.6 L of CO₂ is produced, it corresponds to the complete combustion of 1 mole of C₃H₈. Therefore, the number of molecules of C₃H₈ needed is Avogadro's number, approximately 6.022 × 10²³ molecules.

Step-by-step explanation:

In the balanced chemical equation for the combustion of C₃H₈:

C₃H₈ + 5O₂ → 3CO₂ + 4H₂O

We see that 1 mole of C₃H₈ produces 3 moles of CO₂. Given that 3.6 L of CO₂ is formed at STP, we can use the ideal gas law to find the moles of CO₂ produced. At STP, 1 mole of any gas occupies 22.4 L. Therefore, the moles of CO₂ produced are:

`\[ \text{Moles of CO₂} = \frac{\text{Volume of CO₂ (in liters)}}{\text{Molar volume at STP}} \]`

`\[ \text{Moles of CO₂} = \frac{3.6 \, \text{L}}{22.4 \, \text{L/mol}} \]`

`\[ \text{Moles of CO₂} \approx 0.161 \, \text{mol} \]`

Since the balanced equation indicates a 1:1 ratio between C₃H₈ and CO₂, the moles of C₃H₈ needed is also 0.161 mol. Finally, using Avogadro's number, we convert moles to molecules:

`\[ \text{Number of molecules of C₃H₈} = \text{Moles of C₃H₈} * \text{Avogadro's number} \]`

`\[ \text{Number of molecules of C₃H₈} = 0.161 \, \text{mol} * 6.022 * 10^(23) \, \text{molecules/mol} \]`

`\[ \text{Number of molecules of C₃H₈} \approx 9.66 * 10^(22) \, \text{molecules} \]`

Therefore, approximately 9.66 × 10²² molecules of C₃H₈ would be needed to form 3.6 L of CO₂ at STP.