Fe2O3 + Ca = Fe + CaO

Fe_2O_3 iron(III) oxide + Ca calcium ⟶ Fe iron + CaO lime

Balance the chemical equation algebraically: Fe_2O_3 + Ca ⟶ Fe + CaO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Fe_2O_3 + c_2 Ca ⟶ c_3 Fe + c_4 CaO Set the number of atoms in the reactants equal to the number of atoms in the products for Fe, O and Ca: Fe: | 2 c_1 = c_3 O: | 3 c_1 = c_4 Ca: | c_2 = c_4 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 3 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Fe_2O_3 + 3 Ca ⟶ 2 Fe + 3 CaO

+ ⟶ +

iron(III) oxide + calcium ⟶ iron + lime

| iron(III) oxide | calcium | iron | lime molecular enthalpy | -826 kJ/mol | 0 kJ/mol | 0 kJ/mol | -634.9 kJ/mol total enthalpy | -826 kJ/mol | 0 kJ/mol | 0 kJ/mol | -1905 kJ/mol | H_initial = -826 kJ/mol | | H_final = -1905 kJ/mol | ΔH_rxn^0 | -1905 kJ/mol - -826 kJ/mol = -1079 kJ/mol (exothermic) | | |

| iron(III) oxide | calcium | iron | lime molecular entropy | 90 J/(mol K) | 41 J/(mol K) | 27 J/(mol K) | 40 J/(mol K) total entropy | 90 J/(mol K) | 123 J/(mol K) | 54 J/(mol K) | 120 J/(mol K) | S_initial = 213 J/(mol K) | | S_final = 174 J/(mol K) | ΔS_rxn^0 | 174 J/(mol K) - 213 J/(mol K) = -39 J/(mol K) (exoentropic) | | |

Construct the equilibrium constant, K, expression for: Fe_2O_3 + Ca ⟶ Fe + CaO Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: Fe_2O_3 + 3 Ca ⟶ 2 Fe + 3 CaO Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i Fe_2O_3 | 1 | -1 Ca | 3 | -3 Fe | 2 | 2 CaO | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Fe_2O_3 | 1 | -1 | ([Fe2O3])^(-1) Ca | 3 | -3 | ([Ca])^(-3) Fe | 2 | 2 | ([Fe])^2 CaO | 3 | 3 | ([CaO])^3 The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([Fe2O3])^(-1) ([Ca])^(-3) ([Fe])^2 ([CaO])^3 = (([Fe])^2 ([CaO])^3)/([Fe2O3] ([Ca])^3)

Construct the rate of reaction expression for: Fe_2O_3 + Ca ⟶ Fe + CaO Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: Fe_2O_3 + 3 Ca ⟶ 2 Fe + 3 CaO Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i Fe_2O_3 | 1 | -1 Ca | 3 | -3 Fe | 2 | 2 CaO | 3 | 3 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term Fe_2O_3 | 1 | -1 | -(Δ[Fe2O3])/(Δt) Ca | 3 | -3 | -1/3 (Δ[Ca])/(Δt) Fe | 2 | 2 | 1/2 (Δ[Fe])/(Δt) CaO | 3 | 3 | 1/3 (Δ[CaO])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -(Δ[Fe2O3])/(Δt) = -1/3 (Δ[Ca])/(Δt) = 1/2 (Δ[Fe])/(Δt) = 1/3 (Δ[CaO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| iron(III) oxide | calcium | iron | lime formula | Fe_2O_3 | Ca | Fe | CaO name | iron(III) oxide | calcium | iron | lime

| iron(III) oxide | calcium | iron | lime molar mass | 159.69 g/mol | 40.078 g/mol | 55.845 g/mol | 56.077 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 1565 °C | 850 °C | 1535 °C | 2580 °C boiling point | | 1484 °C | 2750 °C | 2850 °C density | 5.26 g/cm^3 | 1.54 g/cm^3 | 7.874 g/cm^3 | 3.3 g/cm^3 solubility in water | insoluble | decomposes | insoluble | reacts odor | odorless | | |