O2 + FeS = SO2 + Fe3O4

O_2 oxygen + FeS ferrous sulfide ⟶ SO_2 sulfur dioxide + FeO·Fe_2O_3 iron(II, III) oxide

Balance the chemical equation algebraically: O_2 + FeS ⟶ SO_2 + FeO·Fe_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 FeS ⟶ 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 O, Fe and S: O: | 2 c_1 = 2 c_3 + 4 c_4 Fe: | c_2 = 3 c_4 S: | 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 5 c_2 = 3 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 O_2 + 3 FeS ⟶ 3 SO_2 + FeO·Fe_2O_3

+ ⟶ +

oxygen + ferrous sulfide ⟶ sulfur dioxide + iron(II, III) oxide

| oxygen | ferrous sulfide | sulfur dioxide | iron(II, III) oxide molecular enthalpy | 0 kJ/mol | -100 kJ/mol | -296.8 kJ/mol | -1118 kJ/mol total enthalpy | 0 kJ/mol | -300 kJ/mol | -890.4 kJ/mol | -1118 kJ/mol | H_initial = -300 kJ/mol | | H_final = -2009 kJ/mol | ΔH_rxn^0 | -2009 kJ/mol - -300 kJ/mol = -1709 kJ/mol (exothermic) | | |

| oxygen | ferrous sulfide | sulfur dioxide | iron(II, III) oxide molecular free energy | 231.7 kJ/mol | -100.4 kJ/mol | -300.1 kJ/mol | -1015 kJ/mol total free energy | 1159 kJ/mol | -301.2 kJ/mol | -900.3 kJ/mol | -1015 kJ/mol | G_initial = 857.3 kJ/mol | | G_final = -1916 kJ/mol | ΔG_rxn^0 | -1916 kJ/mol - 857.3 kJ/mol = -2773 kJ/mol (exergonic) | | |

Construct the equilibrium constant, K, expression for: O_2 + FeS ⟶ 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: 5 O_2 + 3 FeS ⟶ 3 SO_2 + 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 O_2 | 5 | -5 FeS | 3 | -3 SO_2 | 3 | 3 FeO·Fe_2O_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 5 | -5 | ([O2])^(-5) FeS | 3 | -3 | ([FeS])^(-3) SO_2 | 3 | 3 | ([SO2])^3 FeO·Fe_2O_3 | 1 | 1 | [FeO·Fe2O3] 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 = ([O2])^(-5) ([FeS])^(-3) ([SO2])^3 [FeO·Fe2O3] = (([SO2])^3 [FeO·Fe2O3])/(([O2])^5 ([FeS])^3)

Construct the rate of reaction expression for: O_2 + FeS ⟶ 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: 5 O_2 + 3 FeS ⟶ 3 SO_2 + 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 O_2 | 5 | -5 FeS | 3 | -3 SO_2 | 3 | 3 FeO·Fe_2O_3 | 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 O_2 | 5 | -5 | -1/5 (Δ[O2])/(Δt) FeS | 3 | -3 | -1/3 (Δ[FeS])/(Δt) SO_2 | 3 | 3 | 1/3 (Δ[SO2])/(Δt) FeO·Fe_2O_3 | 1 | 1 | (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 = -1/5 (Δ[O2])/(Δt) = -1/3 (Δ[FeS])/(Δt) = 1/3 (Δ[SO2])/(Δt) = (Δ[FeO·Fe2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | ferrous sulfide | sulfur dioxide | iron(II, III) oxide formula | O_2 | FeS | SO_2 | FeO·Fe_2O_3 Hill formula | O_2 | FeS | O_2S | Fe_3O_4 name | oxygen | ferrous sulfide | sulfur dioxide | iron(II, III) oxide IUPAC name | molecular oxygen | | sulfur dioxide |

| oxygen | ferrous sulfide | sulfur dioxide | iron(II, III) oxide molar mass | 31.998 g/mol | 87.9 g/mol | 64.06 g/mol | 231.53 g/mol phase | gas (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | -218 °C | 1195 °C | -73 °C | 1538 °C boiling point | -183 °C | | -10 °C | density | 0.001429 g/cm^3 (at 0 °C) | 4.84 g/cm^3 | 0.002619 g/cm^3 (at 25 °C) | 5 g/cm^3 solubility in water | | insoluble | | surface tension | 0.01347 N/m | | 0.02859 N/m | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | 0.00343 Pa s (at 1250 °C) | 1.282×10^-5 Pa s (at 25 °C) | odor | odorless | | |