Fe2O3 + FeS2 = SO2 + Fe3O4

Fe_2O_3 iron(III) oxide + FeS_2 pyrite ⟶ SO_2 sulfur dioxide + FeO·Fe_2O_3 iron(II, III) oxide

Balance the chemical equation algebraically: Fe_2O_3 + FeS_2 ⟶ SO_2 + FeO·Fe_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Fe_2O_3 + c_2 FeS_2 ⟶ c_3 SO_2 + c_4 FeO·Fe_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Fe, O and S: Fe: | 2 c_1 + c_2 = 3 c_4 O: | 3 c_1 = 2 c_3 + 4 c_4 S: | 2 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 16 c_2 = 1 c_3 = 2 c_4 = 11 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 Fe_2O_3 + FeS_2 ⟶ 2 SO_2 + 11 FeO·Fe_2O_3

+ ⟶ +

iron(III) oxide + pyrite ⟶ sulfur dioxide + iron(II, III) oxide

Construct the equilibrium constant, K, expression for: Fe_2O_3 + FeS_2 ⟶ SO_2 + FeO·Fe_2O_3 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: 16 Fe_2O_3 + FeS_2 ⟶ 2 SO_2 + 11 FeO·Fe_2O_3 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 | 16 | -16 FeS_2 | 1 | -1 SO_2 | 2 | 2 FeO·Fe_2O_3 | 11 | 11 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Fe_2O_3 | 16 | -16 | ([Fe2O3])^(-16) FeS_2 | 1 | -1 | ([FeS2])^(-1) SO_2 | 2 | 2 | ([SO2])^2 FeO·Fe_2O_3 | 11 | 11 | ([FeO·Fe2O3])^11 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])^(-16) ([FeS2])^(-1) ([SO2])^2 ([FeO·Fe2O3])^11 = (([SO2])^2 ([FeO·Fe2O3])^11)/(([Fe2O3])^16 [FeS2])

Construct the rate of reaction expression for: Fe_2O_3 + FeS_2 ⟶ SO_2 + FeO·Fe_2O_3 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: 16 Fe_2O_3 + FeS_2 ⟶ 2 SO_2 + 11 FeO·Fe_2O_3 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 | 16 | -16 FeS_2 | 1 | -1 SO_2 | 2 | 2 FeO·Fe_2O_3 | 11 | 11 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 | 16 | -16 | -1/16 (Δ[Fe2O3])/(Δt) FeS_2 | 1 | -1 | -(Δ[FeS2])/(Δt) SO_2 | 2 | 2 | 1/2 (Δ[SO2])/(Δt) FeO·Fe_2O_3 | 11 | 11 | 1/11 (Δ[FeO·Fe2O3])/(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 = -1/16 (Δ[Fe2O3])/(Δt) = -(Δ[FeS2])/(Δt) = 1/2 (Δ[SO2])/(Δt) = 1/11 (Δ[FeO·Fe2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| iron(III) oxide | pyrite | sulfur dioxide | iron(II, III) oxide formula | Fe_2O_3 | FeS_2 | SO_2 | FeO·Fe_2O_3 Hill formula | Fe_2O_3 | FeS_2 | O_2S | Fe_3O_4 name | iron(III) oxide | pyrite | sulfur dioxide | iron(II, III) oxide IUPAC name | | bis(sulfanylidene)iron | sulfur dioxide |

| iron(III) oxide | pyrite | sulfur dioxide | iron(II, III) oxide molar mass | 159.69 g/mol | 120 g/mol | 64.06 g/mol | 231.53 g/mol phase | solid (at STP) | | gas (at STP) | solid (at STP) melting point | 1565 °C | | -73 °C | 1538 °C boiling point | | | -10 °C | density | 5.26 g/cm^3 | 4.89 g/cm^3 | 0.002619 g/cm^3 (at 25 °C) | 5 g/cm^3 solubility in water | insoluble | | | surface tension | | | 0.02859 N/m | dynamic viscosity | | | 1.282×10^-5 Pa s (at 25 °C) | odor | odorless | odorless | |