**Title: Thermodynamics and Chemical Reactions****Problem:**1. **Determining Heat Requirement** How much heat (in kJ) is needed to convert 387 g of Fe₂O₃ into pure iron in the presence of excess carbon? **Answer:** \[ \_\_\_\_ \text{ kJ} \]2. **Calculating Iron Production** When $1.58 \times 10^7$ kJ of heat is added to Fe₂O₃ in the presence of excess carbon, how many kilograms of Fe can be produced? **Answer:** \[ \_\_\_\_ \text{ kg} \]**Explanation:**These questions explore the relationship between heat energy and chemical processes, specifically the conversion of iron(III) oxide ($ \text{Fe}_2\text{O}_3 $) to iron (Fe) using carbon, a common method in metallurgy. Understanding how to calculate the energy requirements for such reactions is crucial for efficiently operating thermal processes. Iron can be extracted from the iron(III) oxide found in iron ores (such as haematite) via an oxidation-reduction reaction with carbon. The thermochemical equation for this process is:\[ 2 \text{Fe}_2\text{O}_3(s) + 3 \text{C}(s) \rightarrow 4 \text{Fe}(l) + 3 \text{CO}_2(g) \quad \Delta H^\circ = +467.9 \, \text{kJ} \]### Explanation:- **Chemical Reaction**: This equation represents the conversion of iron(III) oxide and carbon into liquid iron and carbon dioxide gas.- **Phase Indications**: - $ (s) $ denotes a solid. - $ (l) $ denotes a liquid. - $ (g) $ denotes a gas.- **Enthalpy Change ($ \Delta H^\circ $)**: The positive value (+467.9 kJ) indicates that the reaction is endothermic, meaning it absorbs energy from the surroundings.

Given: The weight of Fe2O3 is 387 g. The given reaction is, 2Fe2O3g+3Cs→4Fel+3CO2g ∆H°=+467.9 kJThe molar mass of Fe2O3 is 159.69 g/mol. The number of moles is, Moles=MassMolar mass=387 g159.69 g/mol=2.42 mol From the given reaction, it is clear that 2 moles of Fe2O3 produce 467.9 kJ heat. Therefore, 2.42 mol of will Fe2O3 produce, 2 mol of Fe2O3=467.9 kJ1 mol of Fe2O3=467.92 kJ2.42 mol of Fe2O3=2.42×467.92 kJ=566.159 kJ The given amount of heat added is 1.58×107 kJ. From the calculated value, it is clear that 566.159 kJ heat is required for 387 g or 0.387 kg of Fe2O3. Therefore, 1.58×107 kJ will produce, 566.159 kJ=0.387 kg of Fe2O31 kJ=0.387566.159 kg of Fe2O31.58×107 kJ=0.387566.159×1.58×107 kg of Fe2O3=10800.1462 kgAnswer: The heat required to convert 387 g of Fe2O3 is 566.159 kJ. The weight of Fe produced is 10800.1462 kg.

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Chemistry

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ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

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Question

**Title: Thermodynamics and Chemical Reactions**

**Problem:**

1. **Determining Heat Requirement**

How much heat (in kJ) is needed to convert 387 g of Fe₂O₃ into pure iron in the presence of excess carbon?

**Answer:**
\[ \_\_\_\_ \text{ kJ} \]

2. **Calculating Iron Production**

When $1.58 \times 10^7$ kJ of heat is added to Fe₂O₃ in the presence of excess carbon, how many kilograms of Fe can be produced?

**Answer:**
\[ \_\_\_\_ \text{ kg} \]

**Explanation:**

These questions explore the relationship between heat energy and chemical processes, specifically the conversion of iron(III) oxide ($ \text{Fe}_2\text{O}_3 $) to iron (Fe) using carbon, a common method in metallurgy. Understanding how to calculate the energy requirements for such reactions is crucial for efficiently operating thermal processes.

Iron can be extracted from the iron(III) oxide found in iron ores (such as haematite) via an oxidation-reduction reaction with carbon. The thermochemical equation for this process is:

\[ 2 \text{Fe}_2\text{O}_3(s) + 3 \text{C}(s) \rightarrow 4 \text{Fe}(l) + 3 \text{CO}_2(g) \quad \Delta H^\circ = +467.9 \, \text{kJ} \]

### Explanation:

- **Chemical Reaction**: This equation represents the conversion of iron(III) oxide and carbon into liquid iron and carbon dioxide gas.
- **Phase Indications**:
- $ (s) $ denotes a solid.
- $ (l) $ denotes a liquid.
- $ (g) $ denotes a gas.
- **Enthalpy Change ($ \Delta H^\circ $)**: The positive value (+467.9 kJ) indicates that the reaction is endothermic, meaning it absorbs energy from the surroundings.

Expert Solution

Step 1

Given:

The weight of Fe₂O₃ is 387 g.

The given reaction is,

$2 F e_{2} O_{3} (g) + 3 C (s) \to 4 F e (l) + 3 C O_{2} (g) ∆ H ° = + 467.9 k J$

Step 2

The molar mass of Fe₂O₃is 159.69 g/mol.

The number of moles is,

$\begin{array}{rcl} M o l e s & = & \frac{M a s s}{M o l a r m a s s} \\ = & \frac{387 g}{159.69 g / m o l} \\ = & 2.42 m o l \end{array}$

From the given reaction, it is clear that 2 moles of Fe₂O₃ produce 467.9 kJ heat. Therefore, 2.42 mol of will Fe₂O₃ produce,

$\begin{array}{rcl} 2 m o l o f F e_{2} O_{3} & = & 467.9 k J \\ 1 m o l o f F e_{2} O_{3} & = & \frac{467.9}{2} k J \\ 2.42 m o l o f F e_{2} O_{3} & = & 2.42 \times \frac{467.9}{2} k J \\ = & 566.159 k J \end{array}$

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