Let's carefully analyze the chemical equation:
[tex]\[2 C_2 H_2 + 5 O_2 \rightarrow 4 CO_2 + 2 H_2 O \][/tex]
We need to determine what happens if one mole of [tex]\(C_2 H_2\)[/tex] is used in this reaction. To do this, we'll use the stoichiometric ratios from the balanced chemical equation.
1. Amount of [tex]\(O_2\)[/tex] Used:
The balanced equation tells us that 2 moles of [tex]\(C_2 H_2\)[/tex] react with 5 moles of [tex]\(O_2\)[/tex].
- The ratio of moles of [tex]\(C_2 H_2\)[/tex] to moles of [tex]\(O_2\)[/tex] is [tex]\( \frac{2}{5} \)[/tex].
Thus, for [tex]\(1\)[/tex] mole of [tex]\(C_2 H_2\)[/tex]:
[tex]\[
\left(\frac{5 \text{ moles of } O_2 }{2 \text{ moles of } C_2 H_2}\right) \times 1 \text{ mole of } C_2 H_2 = 2.5 \text{ moles of } O_2
\][/tex]
So, 2.5 moles of oxygen are used in this reaction when one mole of [tex]\(C_2 H_2\)[/tex] is used.
2. Amount of [tex]\(CO_2\)[/tex] Produced:
The balanced equation also tells us that 2 moles of [tex]\(C_2 H_2\)[/tex] produce 4 moles of [tex]\(CO_2\)[/tex].
- The ratio of moles of [tex]\(C_2 H_2\)[/tex] to moles of [tex]\(CO_2\)[/tex] is [tex]\( \frac{2}{4} \)[/tex].
Thus, for 1 mole of [tex]\(C_2 H_2\)[/tex]:
[tex]\[
\left(\frac{4 \text{ moles of } CO_2}{2 \text{ moles of } C_2 H_2}\right) \times 1 \text{ mole of } C_2 H_2 = 2 \text{ moles of } CO_2
\][/tex]
Therefore, 2 moles of carbon dioxide are produced in this reaction when one mole of [tex]\(C_2 H_2\)[/tex] is used.
Now, we can evaluate the given statements:
- One mole of oxygen was used in this reaction. (Incorrect: 2.5 moles of oxygen are used).
- Five moles of oxygen were used in this reaction. (Incorrect: 2.5 moles of oxygen are used).
- Four moles of carbon dioxide were produced from this reaction. (Incorrect: 2 moles of [tex]\(CO_2\)[/tex] are produced).
- Two moles of carbon dioxide were produced from this reaction. (Correct: 2 moles of [tex]\(CO_2\)[/tex] are produced).
Therefore, the correct statement is:
- Two moles of carbon dioxide were produced from this reaction.
