H2SO4 + O2 + FeSO2 = H2O + Fe2(SO4)3

H_2SO_4 sulfuric acid + O_2 oxygen + FeSO2 ⟶ H_2O water + Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate

Balance the chemical equation algebraically: H_2SO_4 + O_2 + FeSO2 ⟶ H_2O + Fe_2(SO_4)_3·xH_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 O_2 + c_3 FeSO2 ⟶ c_4 H_2O + c_5 Fe_2(SO_4)_3·xH_2O Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Fe: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 2 c_2 + 2 c_3 = c_4 + 12 c_5 S: | c_1 + c_3 = 3 c_5 Fe: | c_3 = 2 c_5 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 = 5/2 c_3 = 2 c_4 = 1 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 5 c_3 = 4 c_4 = 2 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + 5 O_2 + 4 FeSO2 ⟶ 2 H_2O + 2 Fe_2(SO_4)_3·xH_2O

+ + FeSO2 ⟶ +

sulfuric acid + oxygen + FeSO2 ⟶ water + iron(III) sulfate hydrate

Construct the equilibrium constant, K, expression for: H_2SO_4 + O_2 + FeSO2 ⟶ H_2O + Fe_2(SO_4)_3·xH_2O 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: 2 H_2SO_4 + 5 O_2 + 4 FeSO2 ⟶ 2 H_2O + 2 Fe_2(SO_4)_3·xH_2O 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 H_2SO_4 | 2 | -2 O_2 | 5 | -5 FeSO2 | 4 | -4 H_2O | 2 | 2 Fe_2(SO_4)_3·xH_2O | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 2 | -2 | ([H2SO4])^(-2) O_2 | 5 | -5 | ([O2])^(-5) FeSO2 | 4 | -4 | ([FeSO2])^(-4) H_2O | 2 | 2 | ([H2O])^2 Fe_2(SO_4)_3·xH_2O | 2 | 2 | ([Fe2(SO4)3·xH2O])^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 = ([H2SO4])^(-2) ([O2])^(-5) ([FeSO2])^(-4) ([H2O])^2 ([Fe2(SO4)3·xH2O])^2 = (([H2O])^2 ([Fe2(SO4)3·xH2O])^2)/(([H2SO4])^2 ([O2])^5 ([FeSO2])^4)

Construct the rate of reaction expression for: H_2SO_4 + O_2 + FeSO2 ⟶ H_2O + Fe_2(SO_4)_3·xH_2O 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: 2 H_2SO_4 + 5 O_2 + 4 FeSO2 ⟶ 2 H_2O + 2 Fe_2(SO_4)_3·xH_2O 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 H_2SO_4 | 2 | -2 O_2 | 5 | -5 FeSO2 | 4 | -4 H_2O | 2 | 2 Fe_2(SO_4)_3·xH_2O | 2 | 2 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 H_2SO_4 | 2 | -2 | -1/2 (Δ[H2SO4])/(Δt) O_2 | 5 | -5 | -1/5 (Δ[O2])/(Δt) FeSO2 | 4 | -4 | -1/4 (Δ[FeSO2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) Fe_2(SO_4)_3·xH_2O | 2 | 2 | 1/2 (Δ[Fe2(SO4)3·xH2O])/(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 = -1/2 (Δ[H2SO4])/(Δt) = -1/5 (Δ[O2])/(Δt) = -1/4 (Δ[FeSO2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[Fe2(SO4)3·xH2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | oxygen | FeSO2 | water | iron(III) sulfate hydrate formula | H_2SO_4 | O_2 | FeSO2 | H_2O | Fe_2(SO_4)_3·xH_2O Hill formula | H_2O_4S | O_2 | FeO2S | H_2O | Fe_2O_12S_3 name | sulfuric acid | oxygen | | water | iron(III) sulfate hydrate IUPAC name | sulfuric acid | molecular oxygen | | water | diferric trisulfate

| sulfuric acid | oxygen | FeSO2 | water | iron(III) sulfate hydrate molar mass | 98.07 g/mol | 31.998 g/mol | 119.9 g/mol | 18.015 g/mol | 399.9 g/mol phase | liquid (at STP) | gas (at STP) | | liquid (at STP) | melting point | 10.371 °C | -218 °C | | 0 °C | boiling point | 279.6 °C | -183 °C | | 99.9839 °C | density | 1.8305 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | | 1 g/cm^3 | solubility in water | very soluble | | | | slightly soluble surface tension | 0.0735 N/m | 0.01347 N/m | | 0.0728 N/m | dynamic viscosity | 0.021 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | odorless | | odorless |