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To determine how many moles of acetylene (C2H2) were used, we need to use the balanced chemical equation for the reaction:
2C2H2(g) + 5O2(g) โ 4CO2(g) + 2H2O(g)
From the balanced equation, we can see that the coefficient in front of acetylene (C2H2) is 2. This means that for every 2 moles of C2H2 used, we will produce 4 moles of CO2.
We are given that 50.0 moles of carbon dioxide (CO2) were produced. Since the stoichiometric ratio of CO2 to C2H2 is 4:2, we can set up a proportion to find the number of moles of C2H2 used.
(50.0 mol CO2 / 4 mol CO2) = (x mol C2H2 / 2 mol C2H2)
Cross-multiplying and solving for x, we get:
x = (50.0 mol CO2 * 2 mol C2H2) / 4 mol CO2
x = 100.0 mol C2H2
Therefore, 100.0 moles of acetylene (C2H2) were used in the reaction.