Calculate the mass of iron which will be converted into its oxide (`Fe_3O_4`) by the action of 13g of steam on it. [At mass of Fe=56] `Fe+H_2​O→Fe_3O_4+4H_2` ​

Options

A. 10g
B. 20g
C. 30g
D. 40g

Answer

To solve the problem of calculating the mass of iron that will be converted into its oxide (Fe₃O₄) by the action of 13g of steam, we can follow these steps:

### Step 1: Write the balanced chemical equation
The reaction between iron and steam can be represented as:
\[ \text{3Fe} + \text{4H}_2\text{O} \rightarrow \text{Fe}_3\text{O}_4 + \text{4H}_2 \]

### Step 2: Determine the molar masses
- The molar mass of iron (Fe) is given as 56 g/mol.
- The molar mass of water (H₂O) is approximately 18 g/mol. Therefore, the molar mass of 4H₂O is:
\[ 4 \times 18 = 72 \text{ g/mol} \]

### Step 3: Calculate the mass of iron needed for the reaction
From the balanced equation, we see that 3 moles of iron react with 4 moles of water. The mass of iron required for this reaction can be calculated as:
\[ \text{Mass of Fe} = 3 \text{ moles} \times 56 \text{ g/mol} = 168 \text{ g} \]

### Step 4: Set up a proportion to find the mass of iron for 13g of steam
We know that 72g of steam reacts with 168g of iron. We need to find out how much iron reacts with 13g of steam. We can set up the following proportion:
\[ \frac{168 \text{ g Fe}}{72 \text{ g H}_2\text{O}} = \frac{x \text{ g Fe}}{13 \text{ g H}_2\text{O}} \]

### Step 5: Solve for x (mass of iron)
Cross-multiplying gives us:
\[ 168 \text{ g Fe} \times 13 \text{ g H}_2\text{O} = 72 \text{ g H}_2\text{O} \times x \text{ g Fe} \]
\[ 2184 = 72x \]
Now, divide both sides by 72:
\[ x = \frac{2184}{72} \approx 30.33 \text{ g} \]

### Step 6: Round the answer
The mass of iron that will be converted into its oxide by the action of 13g of steam is approximately 30g.

### Final Answer
The mass of iron converted into its oxide (Fe₃O₄) is approximately **30 g**.

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