Sure, let's solve the problem by analyzing the balanced chemical equation:
[tex]\[
N_2H_4 + 2 H_2O_2 \rightarrow N_2 + 4 H_2O
\][/tex]
We need to determine the mole ratios of hydrazine ([tex]\(N_2H_4\)[/tex]) to hydrogen peroxide ([tex]\(H_2O_2\)[/tex]), and hydrazine to water ([tex]\(H_2O\)[/tex]) from this equation.
1. Mole Ratio of N_2H_4 to H_2O_2:
- According to the balanced equation, 1 mole of [tex]\(N_2H_4\)[/tex] reacts with 2 moles of [tex]\(H_2O_2\)[/tex].
- Therefore, the mole ratio of [tex]\(N_2H_4\)[/tex] to [tex]\(H_2O_2\)[/tex] is:
[tex]\[
\frac{1 \text{ mole } N_2H_4}{2 \text{ moles } H_2O_2} = 1:2
\][/tex]
2. Mole Ratio of N_2H_4 to H_2O:
- According to the balanced equation, 1 mole of [tex]\(N_2H_4\)[/tex] produces 4 moles of [tex]\(H_2O\)[/tex].
- Therefore, the mole ratio of [tex]\(N_2H_4\)[/tex] to [tex]\(H_2O\)[/tex] is:
[tex]\[
\frac{1 \text{ mole } N_2H_4}{4 \text{ moles } H_2O} = 1:4
\][/tex]
So, the correct mole ratios are:
- [tex]\(N_2H_4\)[/tex] to [tex]\(H_2O_2\)[/tex]: [tex]\(1:2\)[/tex]
- [tex]\(N_2H_4\)[/tex] to [tex]\(H_2O\)[/tex]: [tex]\(1:4\)[/tex]
Matching these ratios with the given choices:
- [tex]\(1:2\)[/tex] and [tex]\(1:4\)[/tex]
- [tex]\(4i3\)[/tex] and [tex]\(1.8\)[/tex]
- [tex]\(1:2\)[/tex] and [tex]\(3:5\)[/tex]
The correct choice is:
[tex]\[ \boxed{1:2 \text{ and } 1:4} \][/tex]
