Let's carefully analyze the balanced chemical equation:
[tex]\[ 2 \, C_2H_2 + 5 \, O_2 \rightarrow 4 \, CO_2 + 2 \, H_2O \][/tex]
To determine how many moles of each reactant and product would be involved if one mole of \(C_2H_2\) was used, we'll scale down the coefficients in the equation accordingly.
### Understanding the Coefficients
1. The equation states that 2 moles of \( C_2H_2 \) react with 5 moles of \( O_2 \) to produce 4 moles of \( CO_2 \) and 2 moles of \( H_2O \).
2. If we are using 1 mole of \( C_2H_2 \), we need to scale down everything by a factor of 2 (since the coefficient of \( C_2H_2 \) is 2).
### Adjusting for One Mole of \(C_2H_2\):
- Moles of \( O_2 \) needed:
[tex]\[ \frac{5}{2} \times 1 = 2.5 \][/tex]
So, 2.5 moles of \( O_2 \) are needed.
- Moles of \( CO_2 \) produced:
[tex]\[ \frac{4}{2} \times 1 = 2 \][/tex]
So, 2 moles of \( CO_2 \) are produced.
- Moles of \( H_2O \) produced:
[tex]\[ \frac{2}{2} \times 1 = 1 \][/tex]
So, 1 mole of \( H_2O \) is produced.
### Verifying Each Statement:
1. One mole of oxygen was used in this reaction.
- This is incorrect. From our calculation, 2.5 moles of \( O_2 \) are needed.
2. Five moles of oxygen were used in this reaction.
- This is incorrect. Only 2.5 moles of \( O_2 \) are needed.
3. Four moles of carbon dioxide were produced from this reaction.
- This is incorrect. Only 2 moles of \( CO_2 \) are produced.
4. Two moles of carbon dioxide were produced from this reaction.
- This is correct. We've determined that 2 moles of \( CO_2 \) are produced.
Thus, the correct statement is:
Two moles of carbon dioxide were produced from this reaction.
