H2O2 + FeSO4 = H2O + O2 + Fe2O3 + Fe2(SO4)3

H_2O_2 hydrogen peroxide + FeSO_4 duretter ⟶ H_2O water + O_2 oxygen + Fe_2O_3 iron(III) oxide + Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate

Balance the chemical equation algebraically: H_2O_2 + FeSO_4 ⟶ H_2O + O_2 + Fe_2O_3 + Fe_2(SO_4)_3·xH_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O_2 + c_2 FeSO_4 ⟶ c_3 H_2O + c_4 O_2 + c_5 Fe_2O_3 + c_6 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, Fe and S: H: | 2 c_1 = 2 c_3 O: | 2 c_1 + 4 c_2 = c_3 + 2 c_4 + 3 c_5 + 12 c_6 Fe: | c_2 = 2 c_5 + 2 c_6 S: | c_2 = 3 c_6 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_2 = 2 c_1 - 4 c_3 = c_1 c_4 = 1 c_5 = c_1/3 - 2/3 c_6 = (2 c_1)/3 - 4/3 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 5 and solve for the remaining coefficients: c_1 = 5 c_2 = 6 c_3 = 5 c_4 = 1 c_5 = 1 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 H_2O_2 + 6 FeSO_4 ⟶ 5 H_2O + O_2 + Fe_2O_3 + 2 Fe_2(SO_4)_3·xH_2O

+ ⟶ + + +

hydrogen peroxide + duretter ⟶ water + oxygen + iron(III) oxide + iron(III) sulfate hydrate

Construct the equilibrium constant, K, expression for: H_2O_2 + FeSO_4 ⟶ H_2O + O_2 + Fe_2O_3 + 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: 5 H_2O_2 + 6 FeSO_4 ⟶ 5 H_2O + O_2 + Fe_2O_3 + 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_2O_2 | 5 | -5 FeSO_4 | 6 | -6 H_2O | 5 | 5 O_2 | 1 | 1 Fe_2O_3 | 1 | 1 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_2O_2 | 5 | -5 | ([H2O2])^(-5) FeSO_4 | 6 | -6 | ([FeSO4])^(-6) H_2O | 5 | 5 | ([H2O])^5 O_2 | 1 | 1 | [O2] Fe_2O_3 | 1 | 1 | [Fe2O3] 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 = ([H2O2])^(-5) ([FeSO4])^(-6) ([H2O])^5 [O2] [Fe2O3] ([Fe2(SO4)3·xH2O])^2 = (([H2O])^5 [O2] [Fe2O3] ([Fe2(SO4)3·xH2O])^2)/(([H2O2])^5 ([FeSO4])^6)

Construct the rate of reaction expression for: H_2O_2 + FeSO_4 ⟶ H_2O + O_2 + Fe_2O_3 + 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: 5 H_2O_2 + 6 FeSO_4 ⟶ 5 H_2O + O_2 + Fe_2O_3 + 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_2O_2 | 5 | -5 FeSO_4 | 6 | -6 H_2O | 5 | 5 O_2 | 1 | 1 Fe_2O_3 | 1 | 1 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_2O_2 | 5 | -5 | -1/5 (Δ[H2O2])/(Δt) FeSO_4 | 6 | -6 | -1/6 (Δ[FeSO4])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) Fe_2O_3 | 1 | 1 | (Δ[Fe2O3])/(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 = -1/5 (Δ[H2O2])/(Δt) = -1/6 (Δ[FeSO4])/(Δt) = 1/5 (Δ[H2O])/(Δt) = (Δ[O2])/(Δt) = (Δ[Fe2O3])/(Δt) = 1/2 (Δ[Fe2(SO4)3·xH2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen peroxide | duretter | water | oxygen | iron(III) oxide | iron(III) sulfate hydrate formula | H_2O_2 | FeSO_4 | H_2O | O_2 | Fe_2O_3 | Fe_2(SO_4)_3·xH_2O Hill formula | H_2O_2 | FeO_4S | H_2O | O_2 | Fe_2O_3 | Fe_2O_12S_3 name | hydrogen peroxide | duretter | water | oxygen | iron(III) oxide | iron(III) sulfate hydrate IUPAC name | hydrogen peroxide | iron(+2) cation sulfate | water | molecular oxygen | | diferric trisulfate

| hydrogen peroxide | duretter | water | oxygen | iron(III) oxide | iron(III) sulfate hydrate molar mass | 34.014 g/mol | 151.9 g/mol | 18.015 g/mol | 31.998 g/mol | 159.69 g/mol | 399.9 g/mol phase | liquid (at STP) | | liquid (at STP) | gas (at STP) | solid (at STP) | melting point | -0.43 °C | | 0 °C | -218 °C | 1565 °C | boiling point | 150.2 °C | | 99.9839 °C | -183 °C | | density | 1.44 g/cm^3 | 2.841 g/cm^3 | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 5.26 g/cm^3 | solubility in water | miscible | | | | insoluble | slightly soluble surface tension | 0.0804 N/m | | 0.0728 N/m | 0.01347 N/m | | dynamic viscosity | 0.001249 Pa s (at 20 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | | odor | | | odorless | odorless | odorless |