Let's start by examining the balanced chemical equation:
[tex]\[ 2 H_2 + O_2 \rightarrow 2 H_2O \][/tex]
This equation tells us that 2 moles of [tex]\( H_2 \)[/tex] react with 1 mole of [tex]\( O_2 \)[/tex] to produce 2 moles of [tex]\( H_2O \)[/tex].
Now, let's analyze what happens if only 1 mole of [tex]\( H_2 \)[/tex] is used in the reaction:
1. Determine the moles of [tex]\( O_2 \)[/tex] used:
According to the balanced equation, 2 moles of [tex]\( H_2 \)[/tex] react with 1 mole of [tex]\( O_2 \)[/tex]. We can set up a proportion to find out how many moles of [tex]\( O_2 \)[/tex] react with 1 mole of [tex]\( H_2 \)[/tex]:
[tex]\[
\frac{1\ \text{mole}\ O_2}{2\ \text{moles}\ H_2} = \frac{x\ \text{moles}\ O_2}{1\ \text{mole}\ H_2}
\][/tex]
Solving the proportion:
[tex]\[
x = \frac{1\ \text{mole}\ O_2 \times 1\ \text{mole}\ H_2}{2\ \text{moles}\ H_2} = 0.5\ \text{moles}\ O_2
\][/tex]
So, 0.5 moles of [tex]\( O_2 \)[/tex] are used when 1 mole of [tex]\( H_2 \)[/tex] reacts.
2. Determine the moles of [tex]\( H_2O \)[/tex] produced:
Similarly, from the balanced equation, 2 moles of [tex]\( H_2 \)[/tex] produce 2 moles of [tex]\( H_2O \)[/tex]. We set up a proportion to find out how many moles of [tex]\( H_2O \)[/tex] are produced from 1 mole of [tex]\( H_2 \)[/tex]:
[tex]\[
\frac{2\ \text{moles}\ H_2O}{2\ \text{moles}\ H_2} = \frac{y\ \text{moles}\ H_2O}{1\ \text{mole}\ H_2}
\][/tex]
Solving the proportion:
[tex]\[
y = \frac{2\ \text{moles}\ H_2O \times 1\ \text{mole}\ H_2}{2\ \text{moles}\ H_2} = 1\ \text{mole}\ H_2O
\][/tex]
So, 1 mole of [tex]\( H_2O \)[/tex] is produced when 1 mole of [tex]\( H_2 \)[/tex] reacts.
Given these results, the correct statements are:
- One mole of oxygen was used in this reaction: This statement is incorrect because only 0.5 moles of [tex]\( O_2 \)[/tex] were used.
- Two moles of oxygen were used in this reaction: This statement is also incorrect because, as established, only 0.5 moles of [tex]\( O_2 \)[/tex] were used.
- One mole of water was produced from this reaction: This statement is correct because 1 mole of [tex]\( H_2O \)[/tex] was produced.
- Two moles of water were produced from this reaction: This statement is incorrect because only 1 mole of [tex]\( H_2O \)[/tex] was produced.
Thus, the correct statement is:
- One mole of water was produced from this reaction.
