What volume at STP of` CO` is required to reduce one mole of `Fe_2O_3` in the following reaction `Fe_2O_3 + CO to Fe + CO_2`

Options

A. `11200 cm^3`
B. `22400 cm^3`
C. `67200 cm^3`
D. `33600 cm^3`

Answer

To solve the problem of determining the volume of carbon monoxide (CO) required to reduce one mole of iron(III) oxide (Fe₂O₃) at standard temperature and pressure (STP), we will follow these steps:

### Step 1: Write the balanced chemical equation.
The unbalanced reaction is:
\[ \text{Fe}_2\text{O}_3 + \text{CO} \rightarrow \text{Fe} + \text{CO}_2 \]

Balancing the equation, we get:
\[ \text{Fe}_2\text{O}_3 + 3\text{CO} \rightarrow 2\text{Fe} + 3\text{CO}_2 \]

### Step 2: Determine the mole ratio.
From the balanced equation, we see that 1 mole of Fe₂O₃ reacts with 3 moles of CO. Therefore, to reduce 1 mole of Fe₂O₃, we need 3 moles of CO.

### Step 3: Calculate the volume of CO at STP.
At STP (Standard Temperature and Pressure), 1 mole of any gas occupies 22.4 liters. Therefore, the volume of 3 moles of CO can be calculated as follows:
\[ \text{Volume of CO} = \text{Number of moles} \times \text{Volume per mole} \]
\[ \text{Volume of CO} = 3 \, \text{moles} \times 22.4 \, \text{liters/mole} \]
\[ \text{Volume of CO} = 67.2 \, \text{liters} \]

### Step 4: Convert liters to cubic centimeters.
Since 1 liter is equal to 1000 cubic centimeters, we convert the volume:
\[ \text{Volume in cm}^3 = 67.2 \, \text{liters} \times 1000 \, \text{cm}^3/\text{liter} \]
\[ \text{Volume in cm}^3 = 67200 \, \text{cm}^3 \]

### Final Answer:
The volume of CO required to reduce 1 mole of Fe₂O₃ at STP is **67,200 cm³**.

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