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To solve this problem, we need to use stoichiometry. Stoichiometry is a mathematical method that allows us to calculate the quantities of reactants and products in a chemical reaction.
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First, we need to balance the chemical equation:
C3H8 + 5O2 → 3CO2 + 4H2O
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Now, we need to determine the mole ratio between propane and water. From the balanced equation, we can see that 1 mole of propane reacts with 4 moles of water:
C3H8 + 5O2 → 3CO2 + 4H2O
1 4
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Next, we need to determine the number of moles of water produced by 36.0 g of water vapor. We can use the molar mass of water to convert grams to moles:
molar mass of water = 18.015 g/mol
moles of water = mass / molar mass
moles of water = 36.0 g / 18.015 g/mol
moles of water = 1.998 mol
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Finally, we can use the mole ratio to calculate the number of moles of propane required to produce 1.998 moles of water:
moles of propane = moles of water / mole ratio
moles of propane = 1.998 mol / 4
moles of propane = 0.4995 mol
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Now, we can use the molar mass of propane to convert moles to grams:
molar mass of propane = 44.097 g/mol
grams of propane = moles of propane x molar mass of propane
grams of propane = 0.4995 mol x 44.097 g/mol
grams of propane = 22.03 g
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Therefore, 22.03 grams of propane are required to produce 36.0 g of water vapor.
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