To solve the questions about the reaction between iron(III) oxide (Fe₂O₃) and carbon, let's tackle them one by one.
a. Use the law of conservation of mass to work out the mass of carbon that reacted. (1 mark)
According to the law of conservation of mass, the total mass of reactants must equal the total mass of products.
Given:
- Mass of Fe₂O₃ = 480 g
- Mass of Fe produced = 336 g
- Mass of CO₂ produced = 198 g
First, calculate the total mass of products: \[ \text{Total mass of products} = \text{mass of Fe} + \text{mass of CO}_2 = 336 , g + 198 , g = 534 , g \]
Now, using conservation of mass: \[ \text{Mass of carbon (C)} = \text{mass of Fe₂O₃} - \text{Total mass of products} \] \[ \text{Mass of carbon} = 480 , g - 534 , g = -54 , g \]
Since we cannot have a negative mass, probably we need to consider that the reaction also consumes carbon.
The calculation should actually consider the mass of carbon added, resulting in: \[ \text{Mass of carbon} = \text{Total mass of products} - \text{mass of Fe₂O₃} \] \[ \text{Mass of carbon} = 534 , g - 480 , g = 54 , g \]
However, upon recalculating, we realize that the total products (Fe + CO2) seem to be within balance considering the carbon's reactive capacity, which was indeed an oversight at the start.
After looking at the products only, carbon was consumed in the reaction therefore: \[ \text{Mass of carbon that reacted} = 534 g - 480 g = 54 g \]
So, the mass of carbon that reacted is 54 g.
b. Calculate the simplest whole number ratio of moles of Fe₂O₃, C, Fe, and CO₂. (4 marks)
First, we need to calculate the number of moles of each substance.
Molar masses:
- Molar mass of Fe₂O₃ = (2 × 55.85) + (3 × 16.00) = 159.70 g/mol
- Molar mass of C = 12.01 g/mol
- Molar mass of Fe = 55.85 g/mol
- Molar mass of CO₂ = 12.01 g + (2 × 16.00) = 44.01 g/mol
Now, calculate the moles for each:
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For Fe₂O₃: \[ \text{Moles of Fe}_2\text{O}_3 = \frac{480 , g}{159.70 , g/mol} \approx 3.00 \text{ moles} \]
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For C: \[ \text{Moles of C} = \frac{54 , g}{12.01 , g/mol} \approx 4.49 \text{ moles} \]
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For Fe: \[ \text{Moles of Fe} = \frac{336 , g}{55.85 , g/mol} \approx 6.00 \text{ moles} \]
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For CO₂: \[ \text{Moles of CO}_2 = \frac{198 , g}{44.01 , g/mol} \approx 4.50 \text{ moles} \]
Now we can find the simplest ratio:
- Fe₂O₃ : C : Fe : CO₂ is approximately 3 : 4.49 : 6 : 4.50
Dividing each by the smallest value (3):
- Fe₂O₃ : C : Fe : CO₂ = 1 : 1.5 : 2 : 1.5
To convert to whole numbers, multiply by 2:
- 2 : 3 : 4 : 3
Thus, the simplest whole number ratio is 2 : 3 : 4 : 3.
c. Write a balanced equation for the reaction. (1 mark)
The balanced equation for the reaction of iron(III) oxide with carbon is: \[ \text{Fe}_2\text{O}_3 + 3 \text{C} \rightarrow 2 \text{Fe} + 3 \text{CO}_2 \]
d. Explain why this is an important industrial process. (1 mark)
This process is important because it is a primary method for producing iron metal from iron ore (Fe₂O₃), which is essential for manufacturing steel. Steel is a critical material used in construction, transportation, and various manufacturing industries. This reduction process helps to convert low-cost raw materials into valuable products, contributing to the economic viability of the metallurgical industry.
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