Fe2O3 + CaO = Ca(FeO2)2

Fe_2O_3 iron(III) oxide + CaO lime ⟶ Ca(FeO2)2

Balance the chemical equation algebraically: Fe_2O_3 + CaO ⟶ Ca(FeO2)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Fe_2O_3 + c_2 CaO ⟶ c_3 Ca(FeO2)2 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 = 2 c_3 O: | 3 c_1 + c_2 = 4 c_3 Ca: | c_2 = c_3 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 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Fe_2O_3 + CaO ⟶ Ca(FeO2)2

+ ⟶ Ca(FeO2)2

iron(III) oxide + lime ⟶ Ca(FeO2)2

Construct the equilibrium constant, K, expression for: Fe_2O_3 + CaO ⟶ Ca(FeO2)2 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 + CaO ⟶ Ca(FeO2)2 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 CaO | 1 | -1 Ca(FeO2)2 | 1 | 1 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) CaO | 1 | -1 | ([CaO])^(-1) Ca(FeO2)2 | 1 | 1 | [Ca(FeO2)2] 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) ([CaO])^(-1) [Ca(FeO2)2] = ([Ca(FeO2)2])/([Fe2O3] [CaO])

Construct the rate of reaction expression for: Fe_2O_3 + CaO ⟶ Ca(FeO2)2 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 + CaO ⟶ Ca(FeO2)2 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 CaO | 1 | -1 Ca(FeO2)2 | 1 | 1 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) CaO | 1 | -1 | -(Δ[CaO])/(Δt) Ca(FeO2)2 | 1 | 1 | (Δ[Ca(FeO2)2])/(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) = -(Δ[CaO])/(Δt) = (Δ[Ca(FeO2)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| iron(III) oxide | lime | Ca(FeO2)2 formula | Fe_2O_3 | CaO | Ca(FeO2)2 Hill formula | Fe_2O_3 | CaO | CaFe2O4 name | iron(III) oxide | lime |

| iron(III) oxide | lime | Ca(FeO2)2 molar mass | 159.69 g/mol | 56.077 g/mol | 215.76 g/mol phase | solid (at STP) | solid (at STP) | melting point | 1565 °C | 2580 °C | boiling point | | 2850 °C | density | 5.26 g/cm^3 | 3.3 g/cm^3 | solubility in water | insoluble | reacts | odor | odorless | |