Question

The mass of oxygen that would be required to produce enough CO which completely reduces 1.6 kg \( Fe_2O_3 \) (at. mass \( Fe = 56 \)), is

• A. 240 g
• B. 480 g
• C. 720 g
• D. 960 g

Hint:

Always balance the chemical equations to find the correct stoichiometric relationship between reactants and products in multi-step processes.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
First, CO is produced from oxygen: \(2C + O_2 \rightarrow 2CO\). Then, CO reduces \(Fe_2O_3\): \(Fe_2O_3 + 3CO \rightarrow 2Fe + 3CO_2\). We need to find the mass of \(O_2\) required for the CO that reacts with a given amount of \(Fe_2O_3\).
Step 2: Detailed Explanation:
Molar mass of \(Fe_2O_3 = (2 \times 56) + (3 \times 16) = 112 + 48 = 160\) g/mol. Moles of \(Fe_2O_3\) in 1.6 kg (1600 g) = \( \frac{1600}{160} = 10\) mol. From the reduction equation: \(Fe_2O_3 + 3CO \rightarrow 2Fe + 3CO_2\) 1 mole of \(Fe_2O_3\) requires 3 moles of CO. So, 10 moles of \(Fe_2O_3\) require \(10 \times 3 = 30\) moles of CO. From the formation of CO: \(2C + O_2 \rightarrow 2CO\) 2 moles of CO are produced from 1 mole of \(O_2\). Thus, 30 moles of CO require \( \frac{30}{2} = 15 \) moles of \(O_2\). Mass of \(O_2\) required = \(15 \times 32 = 480\) g.
Step 3: Final Answer:
Hence, the required mass of oxygen is 480 g, which corresponds to option (B).