To determine how many moles of oxygen ([tex]\(O_2\)[/tex]) are required to react completely with [tex]\(1.67\)[/tex] moles of hydrogen ([tex]\(H_2\)[/tex]), let's first examine the given balanced chemical equation:
[tex]\[
H_2 + O_2 \rightarrow 2 H_2O
\][/tex]
The balanced equation indicates the stoichiometric relationship between the reactants and products. According to this equation:
- 1 mole of [tex]\(O_2\)[/tex] reacts with 2 moles of [tex]\(H_2\)[/tex].
Given this stoichiometric relationship:
[tex]\[
1 \text{ mole of } O_2 \text{ reacts with } 2 \text{ moles of } H_2
\][/tex]
we can set up the following proportion to find out how many moles of [tex]\(O_2\)[/tex] are needed for [tex]\(1.67\)[/tex] moles of [tex]\(H_2\)[/tex]:
[tex]\[
\frac{\text{moles of } O_2}{1} = \frac{\text{moles of } H_2}{2}
\][/tex]
We know the moles of [tex]\(H_2\)[/tex] is [tex]\(1.67\)[/tex]:
[tex]\[
\frac{\text{moles of } O_2}{1} = \frac{1.67}{2}
\][/tex]
Solving for the moles of [tex]\(O_2\)[/tex]:
[tex]\[
\text{moles of } O_2 = \frac{1.67}{2} = 0.835
\][/tex]
Therefore, the number of moles of [tex]\(O_2\)[/tex] required to react completely with [tex]\(1.67\)[/tex] moles of [tex]\(H_2\)[/tex] is:
[tex]\[
0.835 \text{ moles of } O_2
\][/tex]
So, the correct choice is:
[tex]\[
\boxed{0.835 \text{ mol } O_2}
\][/tex]
