Given The Following Reaction: Use Stoichiometry To Answer

Given The Following Reactionuse Stoichiometry To Answer the Following

Given the following reaction use Stoichiometry To Answer the Following

Given the following reaction use Stoichiometry To Answer the Following

Given the following reaction use Stoichiometry To Answer the Following

Given the following reaction use Stoichiometry To Answer the Following

Paper For Above instruction

The problem presents a chemical reaction involving the oxidation of iron to form rust, specifically iron(III) oxide (Fe2O3), and asks for various stoichiometric calculations based on this reaction. Additionally, it includes a second problem involving the decomposition of calcium carbonate into calcium oxide and carbon dioxide. The core goals are to determine the amount of oxygen needed to produce a certain amount of Fe2O3, the heat exchanged during rusting of a specified mass of iron, the rust mass formed when a certain amount of heat is released, and the enthalpy change for calcium carbonate decomposition.

Introduction

Stoichiometry is a fundamental concept in chemistry that allows us to relate quantities of reactants and products in chemical reactions. By understanding mole ratios, molar masses, and enthalpy changes, we can predict how much product will be formed, the amount of reactant consumed, or the heat exchanged during a reaction. The given reactions and data provide a basis for solving these problems through stoichiometric calculations, which are essential in both laboratory and industrial settings.

Reaction and Data Overview

The primary reaction involves the oxidation of iron:

  • 4 Fe (s) + 3 O2 (g) → 2 Fe2O3 (s)

where ∆H° = -1650 kJ (the reaction releases heat). The known data include molar enthalpies of formation for calcium carbonate, calcium oxide, and carbon dioxide, which are used in calculating the enthalpy change of calcium carbonate decomposition.

Calculations

1. Moles of O2 required to form 3.20 mol Fe2O3

The molar ratio from the balanced equation shows that 2 mol of Fe2O3 are produced from 3 mol of O2. Therefore, we can set up the relation:

O2 needed = (3 mol O2 / 2 mol Fe2O3) × 3.20 mol Fe2O3 = 4.80 mol O2

2. Heat exchanged when 14.3 kg of iron rusts

First, convert the mass of iron to moles:

Mass of Fe = 14.3 kg = 14,300 g

Molar mass of Fe ≈ 55.85 g/mol

Moles of Fe = 14,300 g / 55.85 g/mol ≈ 256 mol

From the reaction, 4 mol of Fe produce -1650 kJ of heat. So, the heat per mol of Fe:

Heat per mol Fe = -1650 kJ / 4 mol ≈ -412.5 kJ/mol

Hence, the total heat exchanged for 256 mol Fe is:

Q = 256 mol × -412.5 kJ/mol ≈ -105,600 kJ

3. Mass of Fe2O3 formed when 200 kJ of heat is released

Using the heat per mol of Fe (−412.5 kJ/mol), the moles of Fe corresponding to 200 kJ is:

Moles of Fe = 200 kJ / 412.5 kJ/mol ≈ 0.485 mol

From the reaction stoichiometry, 4 mol of Fe produce 2 mol of Fe2O3, so 0.485 mol Fe produces:

Moles of Fe2O3 = (2 mol Fe2O3 / 4 mol Fe) × 0.485 mol ≈ 0.2425 mol

Finally, convert moles of Fe2O3 to grams using molar mass (159.69 g/mol):

Mass of Fe2O3 = 0.2425 mol × 159.69 g/mol ≈ 38.74 g

4. Enthalpy change (ΔH°rxn) for decomposition of calcium carbonate

The reaction is:

  • CaCO3 (s) → CaO (s) + CO2 (g)

The standard enthalpy change is calculated via Hess’s Law:

ΔH°rxn = [ΔH°f (CaO) + ΔH°f (CO2)] - ΔH°f (CaCO3)

= [(-635.1 kJ/mol) + (-393.5 kJ/mol)] - (-1206.9 kJ/mol)

= (-1028.6 kJ/mol) - (-1206.9 kJ/mol) = 178.3 kJ/mol

Thus, the decomposition of calcium carbonate has a standard enthalpy change of approximately +178.3 kJ/mol, indicating it is an endothermic process.

Conclusion

Using stoichiometry, we can accurately determine reactant requirements and heat exchanges in chemical reactions. The calculations demonstrate that 4.80 mol of O2 are needed to produce 3.20 mol of Fe2O3, and rusting 14.3 kg of iron results in a significant heat release of approximately 105,600 kJ. When 200 kJ of heat is released, about 38.74 grams of Fe2O3 form. Furthermore, the decomposition of calcium carbonate is endothermic with a ΔH°rxn of +178.3 kJ/mol, emphasizing the energy changes involved in mineral transformations. These principles are fundamental for process design and energy management in industrial chemistry and environmental applications.

References

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