Fe(OH)3 + SO3 = H2O + Fe2(SO4)3

Fe(OH)_3 iron(III) hydroxide + SO_3 sulfur trioxide ⟶ H_2O water + Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate

Balance the chemical equation algebraically: Fe(OH)_3 + SO_3 ⟶ H_2O + Fe_2(SO_4)_3·xH_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Fe(OH)_3 + c_2 SO_3 ⟶ c_3 H_2O + c_4 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, H, O and S: Fe: | c_1 = 2 c_4 H: | 3 c_1 = 2 c_3 O: | 3 c_1 + 3 c_2 = c_3 + 12 c_4 S: | c_2 = 3 c_4 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 = 2 c_2 = 3 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Fe(OH)_3 + 3 SO_3 ⟶ 3 H_2O + Fe_2(SO_4)_3·xH_2O

+ ⟶ +

iron(III) hydroxide + sulfur trioxide ⟶ water + iron(III) sulfate hydrate

Construct the equilibrium constant, K, expression for: Fe(OH)_3 + SO_3 ⟶ 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 Fe(OH)_3 + 3 SO_3 ⟶ 3 H_2O + 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(OH)_3 | 2 | -2 SO_3 | 3 | -3 H_2O | 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(OH)_3 | 2 | -2 | ([Fe(OH)3])^(-2) SO_3 | 3 | -3 | ([SO3])^(-3) H_2O | 3 | 3 | ([H2O])^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 = ([Fe(OH)3])^(-2) ([SO3])^(-3) ([H2O])^3 [Fe2(SO4)3·xH2O] = (([H2O])^3 [Fe2(SO4)3·xH2O])/(([Fe(OH)3])^2 ([SO3])^3)

Construct the rate of reaction expression for: Fe(OH)_3 + SO_3 ⟶ 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 Fe(OH)_3 + 3 SO_3 ⟶ 3 H_2O + 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(OH)_3 | 2 | -2 SO_3 | 3 | -3 H_2O | 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(OH)_3 | 2 | -2 | -1/2 (Δ[Fe(OH)3])/(Δt) SO_3 | 3 | -3 | -1/3 (Δ[SO3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(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 = -1/2 (Δ[Fe(OH)3])/(Δt) = -1/3 (Δ[SO3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[Fe2(SO4)3·xH2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| iron(III) hydroxide | sulfur trioxide | water | iron(III) sulfate hydrate formula | Fe(OH)_3 | SO_3 | H_2O | Fe_2(SO_4)_3·xH_2O Hill formula | FeH_3O_3 | O_3S | H_2O | Fe_2O_12S_3 name | iron(III) hydroxide | sulfur trioxide | water | iron(III) sulfate hydrate IUPAC name | ferric trihydroxide | sulfur trioxide | water | diferric trisulfate

| iron(III) hydroxide | sulfur trioxide | water | iron(III) sulfate hydrate molar mass | 106.87 g/mol | 80.06 g/mol | 18.015 g/mol | 399.9 g/mol phase | | liquid (at STP) | liquid (at STP) | melting point | | 16.8 °C | 0 °C | boiling point | | 44.7 °C | 99.9839 °C | density | | 1.97 g/cm^3 | 1 g/cm^3 | solubility in water | | reacts | | slightly soluble surface tension | | | 0.0728 N/m | dynamic viscosity | | 0.00159 Pa s (at 30 °C) | 8.9×10^-4 Pa s (at 25 °C) | odor | | | odorless |