A blast furnace is used to reduce iron oxides to elemental...

A blast furnace is used to reduce iron oxides to elemental iron. The reducing agent for this reduction process is carbon monoxide. a. Given the following data: $\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{CO}(g) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{CO}_{2}(g) \quad \Delta H^{\circ}=-23 \mathrm{~kJ}$ $3 \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{CO}(g) \longrightarrow 2 \mathrm{Fe}_{3} \mathrm{O}_{4}(s)+\mathrm{CO}_{2}(g) \quad \Delta H^{\circ}=-39 \mathrm{~kJ}$ $\mathrm{Fe}_{3} \mathrm{O}_{4}(s)+\mathrm{CO}(g) \longrightarrow 3 \mathrm{FeO}(s)+\mathrm{CO}_{2}(g) \quad \Delta H^{\circ}=18 \mathrm{~kJ}$ determine $\Delta H^{\circ}$ for the reaction $$\mathrm{FeO}(s)+\mathrm{CO}(g) \longrightarrow \mathrm{Fe}(s)+\mathrm{CO}_{2}(g)$$ b. The $\mathrm{CO}_{2}$ produced in a blast furnace during the reduction process actually can oxidize iron into $\mathrm{FeO}$. To eliminate this reaction, excess coke is added to convert $\mathrm{CO}_{2}$ into $\mathrm{CO}$ by the reaction $$\mathrm{CO}_{2}(g)+\mathrm{C}(s) \longrightarrow 2 \mathrm{CO}(g)$$ Using data from Appendix 4, determine $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for this reaction. Assuming $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not depend on temperature, at what temperature is the conversion reaction of $\mathrm{CO}_{2}$ into CO spontaneous at standard conditions?

A blast furnace is used to reduce iron oxides to elemental iron. The reducing agent for this reduction process is carbon monoxide.
a. Given the following data:
$\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{CO}(g) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{CO}_{2}(g) \quad \Delta H^{\circ}=-23 \mathrm{~kJ}$
$3 \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{CO}(g) \longrightarrow 2 \mathrm{Fe}_{3} \mathrm{O}_{4}(s)+\mathrm{CO}_{2}(g) \quad \Delta H^{\circ}=-39 \mathrm{~kJ}$
$\mathrm{Fe}_{3} \mathrm{O}_{4}(s)+\mathrm{CO}(g) \longrightarrow 3 \mathrm{FeO}(s)+\mathrm{CO}_{2}(g) \quad \Delta H^{\circ}=18 \mathrm{~kJ}$
determine $\Delta H^{\circ}$ for the reaction
$$\mathrm{FeO}(s)+\mathrm{CO}(g) \longrightarrow \mathrm{Fe}(s)+\mathrm{CO}_{2}(g)$$
b. The $\mathrm{CO}_{2}$ produced in a blast furnace during the reduction process actually can oxidize iron into $\mathrm{FeO}$. To eliminate this reaction, excess coke is added to convert $\mathrm{CO}_{2}$ into $\mathrm{CO}$ by the reaction
$$\mathrm{CO}_{2}(g)+\mathrm{C}(s) \longrightarrow 2 \mathrm{CO}(g)$$
Using data from Appendix 4, determine $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for this reaction. Assuming $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not depend on temperature, at what temperature is the conversion reaction of $\mathrm{CO}_{2}$ into CO spontaneous at standard conditions?

Key Concepts

Hess's Law

Hess's Law is the principle that the total enthalpy change for a chemical reaction is the same, no matter how many intermediate steps or pathways are taken. This allows one to determine unknown reaction enthalpies by algebraically adding or subtracting known enthalpy changes of related reactions.

Standard Enthalpy Change

The standard enthalpy change of a reaction (?H°) is the heat absorbed or evolved when reactants in their standard states convert to products in their standard states. It is a fundamental thermodynamic quantity that can be calculated by combining known enthalpy changes from multiple reactions or using standard formation enthalpies.

Standard Entropy Change

The standard entropy change (?S°) of a reaction is a measure of the change in disorder or randomness when reactants are converted into products under standard conditions. It is essential for predicting the spontaneity of a reaction when combined with enthalpy changes in the Gibbs free energy equation.

Gibbs Free Energy and Reaction Spontaneity

Gibbs free energy (?G) is a thermodynamic potential that helps predict whether a reaction will occur spontaneously. The relationship ?G = ?H - T?S provides a criterion for spontaneity: a reaction is spontaneous at a given temperature if ?G is negative, linking the roles of both enthalpy and entropy.

Temperature Dependence of Reaction Spontaneity

The temperature dependence of reaction spontaneity is determined by the balance between the enthalpy change and the entropy change. When ?H and ?S for a reaction are temperature independent, the critical temperature at which the reaction becomes spontaneous can be estimated by setting ?G = 0, leading to the threshold condition T = ?H/?S.

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