To determine which equation would have the same coefficients in the same order as [tex]\(2 \: CO_2 + 3 \: H_2O \rightarrow C_2H_6O + 3 \: O_2\)[/tex], we need to compare it with each of the provided equations.
Let's write down the given balanced chemical equation first:
[tex]\[2 \: CO_2 + 3 \: H_2O \rightarrow C_2H_6O + 3 \: O_2\][/tex]
This equation has the coefficients [tex]\(2\)[/tex], [tex]\(3\)[/tex], [tex]\((implied 1)\)[/tex], and [tex]\(3\)[/tex].
Now let's look at each of the provided equations and see which one matches:
1. Equation 1: [tex]\(FeCl_3 + NH_4OH \rightarrow Fe(OH)_3 + NH_4Cl\)[/tex]
- Coefficients: [tex]\(1\)[/tex], [tex]\(1\)[/tex], [tex]\(1\)[/tex], [tex]\(1\)[/tex]
- This does not match.
2. Equation 2: [tex]\(CH_4 + O_2 \rightarrow CO_2 + H_2O\)[/tex]
- Coefficients: [tex]\(1\)[/tex], [tex]\(1\)[/tex], [tex]\(1\)[/tex], [tex]\(1\)[/tex]
- This does not match.
3. Equation 3: [tex]\(Fe + H_2SO_4 \rightarrow Fe_2(SO_4)_3 + H_2\)[/tex]
- Coefficients: [tex]\(1\)[/tex], [tex]\(1\)[/tex], [tex]\(2\)[/tex], [tex]\(1\)[/tex]
- This does not match.
4. Equation 4: [tex]\(PCl_5 + H_2O \rightarrow HCl + H_3PO_4\)[/tex]
- Coefficients: [tex]\(1\)[/tex], [tex]\(1\)[/tex], [tex]\(1\)[/tex], [tex]\(1\)[/tex]
- This does not match.
None of the provided equations have the same coefficients [tex]\(2\)[/tex], [tex]\(3\)[/tex], [tex]\(1\)[/tex], and [tex]\(3\)[/tex] in that order. Thus, based on the given answer, none of these equations have the same coefficients in the same order as [tex]\(2 \: CO_2 + 3 \: H_2O \rightarrow C_2H_6O + 3 \: O_2\)[/tex].
