Certainly! Let's walk through each question step-by-step.
### How many molecules of [tex]\( H_2 \)[/tex] are produced?
In the given balanced chemical equation:
[tex]\[ 3 Fe + 4 H_2O \rightarrow Fe_3O_4 + 4 H_2 \][/tex]
We can see that when the reaction goes to completion, 4 molecules of [tex]\( H_2 \)[/tex] are produced. So, the number of molecules of [tex]\( H_2 \)[/tex] produced is [tex]\( 4 \)[/tex].
### How many oxygen atoms are required?
From the balanced chemical equation:
[tex]\[ 3 Fe + 4 H_2O \rightarrow Fe_3O_4 + 4 H_2 \][/tex]
Each molecule of [tex]\( H_2O \)[/tex] contains 1 oxygen atom. Since 4 molecules of [tex]\( H_2O \)[/tex] are involved in the reaction, the total number of oxygen atoms required is:
[tex]\[ 4 \, \text{molecules of } H_2O \times 1 \, \text{O atom per molecule of } H_2O = 4 \text{ O atoms} \][/tex]
But we need to account for the [tex]\( O \)[/tex] atoms in [tex]\( Fe_3O_4 \)[/tex], which contains 4 oxygen atoms. Hence the total number of oxygen atoms is:
[tex]\[ 4 \times 1 \times 2 = 8 \text{ atoms} \][/tex]
### How many moles of [tex]\( Fe_3O_4 \)[/tex] are formed?
The balanced equation:
[tex]\[ 3 Fe + 4 H_2O \rightarrow Fe_3O_4 + 4 H_2 \][/tex]
indicates that 1 mole of [tex]\( Fe_3O_4 \)[/tex] is formed from the reaction of 3 moles of [tex]\( Fe \)[/tex] and 4 moles of [tex]\( H_2O \)[/tex]. Therefore, the number of moles of [tex]\( Fe_3O_4 \)[/tex] formed is [tex]\( 1 \)[/tex] mole.
### What is the mole ratio of [tex]\( Fe \)[/tex] to [tex]\( H_2O \)[/tex]?
The balanced equation shows:
[tex]\[ 3 Fe + 4 H_2O \rightarrow Fe_3O_4 + 4 H_2 \][/tex]
The mole ratio of [tex]\( Fe \)[/tex] to [tex]\( H_2O \)[/tex] is derived directly from the coefficients in the balanced equation, which is:
[tex]\[ \frac{3 \text{ moles of } Fe}{4 \text{ moles of } H_2O} = 0.75 \][/tex]
Thus, the mole ratio of [tex]\( Fe \)[/tex] to [tex]\( H_2O \)[/tex] is [tex]\( 0.75 \)[/tex].
### How many hydrogen atoms are involved in this reaction?
In the given reaction:
[tex]\[ 3 Fe + 4 H_2O \rightarrow Fe_3O_4 + 4 H_2 \][/tex]
Each [tex]\( H_2O \)[/tex] molecule contains 2 hydrogen atoms. Hence, 4 molecules of [tex]\( H_2O \)[/tex] contain:
[tex]\[ 4 \times 2 = 8 \text{ H atoms} \][/tex]
Each [tex]\( H_2 \)[/tex] molecule also contains 2 hydrogen atoms. Therefore, 4 molecules of [tex]\( H_2 \)[/tex] contain:
[tex]\[ 4 \times 2 = 8 \text{ H atoms} \][/tex]
But since we consider both the hydrogen atoms in reactants and products, the total is:
[tex]\[ 4 \text{ molecules of } H_2O \times 2 \, \text{H atoms per molecule} + 4 \text{ H molecules from product} \times 2 \, \text{H atoms per molecule} = 16 \text{ atoms} \][/tex]
So, to summarize the answers:
1. The number of molecules of [tex]\( H_2 \)[/tex] produced is [tex]\( 4 \)[/tex].
2. The number of oxygen atoms required is [tex]\( 8 \)[/tex].
3. The number of moles of [tex]\( Fe_3O_4 \)[/tex] formed is [tex]\( 1 \)[/tex].
4. The mole ratio of [tex]\( Fe \)[/tex] to [tex]\( H_2O \)[/tex] is [tex]\( 0.75 \)[/tex].
5. The number of hydrogen atoms involved in this reaction is [tex]\( 16 \)[/tex].
