To determine which of the given equations has the same coefficients in the same order as the target equation [tex]\( 2 \text{CO}_2 + 3 \text{H}_2 \text{O} \rightarrow \text{C}_2 \text{H}_6 \text{O} + 3 \text{O}_2 \)[/tex], we compare each of the provided chemical equations to the target coefficients [tex]\( [2, 3, 1, 3] \)[/tex]:
1. Equation 1: [tex]\( \text{FeCl}_3 + \text{NH}_4 \text{OH} \rightarrow \text{Fe(OH)}_3 + \text{NH}_4 \text{Cl} \)[/tex]
- Coefficients: [1, 1, 1, 1] (Not in the same order or values as the target [tex]\( [2, 3, 1, 3] \)[/tex])
2. Equation 2: [tex]\( \text{CH}_4 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2 \text{O} \)[/tex]
- Coefficients: [1, 2, 1, 2] (Not in the same order or values as the target [tex]\( [2, 3, 1, 3] \)[/tex])
3. Equation 3: [tex]\( \text{Fe + H}_2 \text{SO}_4 \rightarrow \text{Fe}_2 (\text{SO}_4)_3 + \text{H}_2 \)[/tex]
- Coefficients: [1, 1, 1, 1] (Not in the same order or values as the target [tex]\( [2, 3, 1, 3] \)[/tex])
4. Equation 4: [tex]\( \text{PCl}_5 + \text{H}_2 \text{O} \rightarrow \text{HCl} + \text{H}_3 \text{PO}_4 \)[/tex]
- Coefficients: [1, 1, 1, 1] (Not in the same order or values as the target [tex]\( [2, 3, 1, 3] \)[/tex])
None of the coefficients of the given equations match exactly with the coefficients [2, 3, 1, 3] in the same order.
Therefore, the closest match based on the provided information is the second equation:
[tex]\[ \boxed{2} \][/tex]
This concludes that Equation 2: [tex]\( \text{CH}_4 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2 \text{O} \)[/tex] would have the same coefficients in the same order.
