To determine how many moles of hydrogen are produced when 6.28 moles of oxygen form, we need to consider the balanced chemical equation provided:
[tex]\[ 2 H_2O \rightarrow 2 H_2 + O_2 \][/tex]
This equation shows that 2 moles of [tex]\( H_2O \)[/tex] decompose to produce 2 moles of [tex]\( H_2 \)[/tex] and 1 mole of [tex]\( O_2 \)[/tex]. From this, we can deduce the molar ratio between oxygen and hydrogen:
For every 1 mole of [tex]\( O_2 \)[/tex] produced, 2 moles of [tex]\( H_2 \)[/tex] are produced.
Given that we have 6.28 moles of [tex]\( O_2 \)[/tex], we can use the molar ratio to find the moles of [tex]\( H_2 \)[/tex] produced. Since the ratio is 1:2 (oxygen to hydrogen), we multiply the moles of oxygen by 2 to find the moles of hydrogen:
[tex]\[ \text{Moles of } H_2 = 6.28 \, \text{moles of } O_2 \times 2 \][/tex]
[tex]\[ \text{Moles of } H_2 = 12.56 \, \text{moles} \][/tex]
Thus, 12.56 moles of hydrogen are produced when 6.28 moles of oxygen form. Therefore, the correct answer is:
12.6 mol
