Fe2O3 + SO3 = Fe2(SO4)3

Fe_2O_3 iron(III) oxide + SO_3 sulfur trioxide ⟶ Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate

Balance the chemical equation algebraically: Fe_2O_3 + SO_3 ⟶ Fe_2(SO_4)_3·xH_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Fe_2O_3 + c_2 SO_3 ⟶ c_3 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 Fe, O and S: Fe: | 2 c_1 = 2 c_3 O: | 3 c_1 + 3 c_2 = 12 c_3 S: | c_2 = 3 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 = 3 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Fe_2O_3 + 3 SO_3 ⟶ Fe_2(SO_4)_3·xH_2O

+ ⟶

iron(III) oxide + sulfur trioxide ⟶ iron(III) sulfate hydrate

Construct the equilibrium constant, K, expression for: Fe_2O_3 + SO_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: Fe_2O_3 + 3 SO_3 ⟶ 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 Fe_2O_3 | 1 | -1 SO_3 | 3 | -3 Fe_2(SO_4)_3·xH_2O | 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) SO_3 | 3 | -3 | ([SO3])^(-3) Fe_2(SO_4)_3·xH_2O | 1 | 1 | [Fe2(SO4)3·xH2O] 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) ([SO3])^(-3) [Fe2(SO4)3·xH2O] = ([Fe2(SO4)3·xH2O])/([Fe2O3] ([SO3])^3)

Construct the rate of reaction expression for: Fe_2O_3 + SO_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: Fe_2O_3 + 3 SO_3 ⟶ 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 Fe_2O_3 | 1 | -1 SO_3 | 3 | -3 Fe_2(SO_4)_3·xH_2O | 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) SO_3 | 3 | -3 | -1/3 (Δ[SO3])/(Δt) Fe_2(SO_4)_3·xH_2O | 1 | 1 | (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 = -(Δ[Fe2O3])/(Δt) = -1/3 (Δ[SO3])/(Δt) = (Δ[Fe2(SO4)3·xH2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| iron(III) oxide | sulfur trioxide | iron(III) sulfate hydrate formula | Fe_2O_3 | SO_3 | Fe_2(SO_4)_3·xH_2O Hill formula | Fe_2O_3 | O_3S | Fe_2O_12S_3 name | iron(III) oxide | sulfur trioxide | iron(III) sulfate hydrate IUPAC name | | sulfur trioxide | diferric trisulfate

| iron(III) oxide | sulfur trioxide | iron(III) sulfate hydrate molar mass | 159.69 g/mol | 80.06 g/mol | 399.9 g/mol phase | solid (at STP) | liquid (at STP) | melting point | 1565 °C | 16.8 °C | boiling point | | 44.7 °C | density | 5.26 g/cm^3 | 1.97 g/cm^3 | solubility in water | insoluble | reacts | slightly soluble dynamic viscosity | | 0.00159 Pa s (at 30 °C) | odor | odorless | |