To solve the problem, let's break it down step by step using the balanced chemical equation provided:
[tex]\[2 H_2 + O_2 \rightarrow 2 H_2O\][/tex]
This equation tells us that:
- 2 moles of hydrogen gas ([tex]\(H_2\)[/tex]) react with 1 mole of oxygen gas ([tex]\(O_2\)[/tex]) to produce 2 moles of water ([tex]\(H_2O\)[/tex]).
Now, we need to determine how many moles of [tex]\(O_2\)[/tex] and [tex]\(H_2O\)[/tex] are involved when we have 4 moles of [tex]\(H_2\)[/tex]. Here is the step-by-step process:
1. Determine the ratio of [tex]\(H_2\)[/tex] to [tex]\(O_2\)[/tex] from the chemical equation:
The balanced chemical equation shows that 2 moles of [tex]\(H_2\)[/tex] react with 1 mole of [tex]\(O_2\)[/tex]. Therefore, the ratio is:
[tex]\[
\frac{2 \text{ moles of } H_2}{1 \text{ mole of } O_2}
\][/tex]
2. Calculate the moles of [tex]\(O_2\)[/tex] required for 4 moles of [tex]\(H_2\)[/tex]:
Since the ratio of [tex]\(H_2\)[/tex] to [tex]\(O_2\)[/tex] is 2:1, we can find the moles of [tex]\(O_2\)[/tex] needed by dividing the moles of [tex]\(H_2\)[/tex] by 2:
[tex]\[
\text{Moles of } O_2 = \frac{4 \text{ moles of } H_2}{2} = 2 \text{ moles of } O_2
\][/tex]
3. Determine the moles of [tex]\(H_2O\)[/tex] produced:
From the balanced equation, we know that 2 moles of [tex]\(H_2\)[/tex] produce 2 moles of [tex]\(H_2O\)[/tex]. Therefore, the amount of [tex]\(H_2O\)[/tex] produced is directly proportional to the amount of [tex]\(H_2\)[/tex] used. Since we are using 4 moles of [tex]\(H_2\)[/tex], we will produce:
[tex]\[
\text{Moles of } H_2O = 4 \text{ moles of } H_2 = 4 \text{ moles of } H_2O
\][/tex]
Thus, given 4 moles of [tex]\(H_2\)[/tex], they will react with 2 moles of [tex]\(O_2\)[/tex] to produce 4 moles of [tex]\(H_2O\)[/tex].
