Fe2(SO4)3 + NH4OH = Fe(OH)3 + (NH4)2SO4

Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate + NH_4OH ammonium hydroxide ⟶ Fe(OH)_3 iron(III) hydroxide + (NH_4)_2SO_4 ammonium sulfate

Balance the chemical equation algebraically: Fe_2(SO_4)_3·xH_2O + NH_4OH ⟶ Fe(OH)_3 + (NH_4)_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Fe_2(SO_4)_3·xH_2O + c_2 NH_4OH ⟶ c_3 Fe(OH)_3 + c_4 (NH_4)_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Fe, O, S, H and N: Fe: | 2 c_1 = c_3 O: | 12 c_1 + c_2 = 3 c_3 + 4 c_4 S: | 3 c_1 = c_4 H: | 5 c_2 = 3 c_3 + 8 c_4 N: | c_2 = 2 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 6 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Fe_2(SO_4)_3·xH_2O + 6 NH_4OH ⟶ 2 Fe(OH)_3 + 3 (NH_4)_2SO_4

+ ⟶ +

iron(III) sulfate hydrate + ammonium hydroxide ⟶ iron(III) hydroxide + ammonium sulfate

Construct the equilibrium constant, K, expression for: Fe_2(SO_4)_3·xH_2O + NH_4OH ⟶ Fe(OH)_3 + (NH_4)_2SO_4 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_2(SO_4)_3·xH_2O + 6 NH_4OH ⟶ 2 Fe(OH)_3 + 3 (NH_4)_2SO_4 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_2(SO_4)_3·xH_2O | 1 | -1 NH_4OH | 6 | -6 Fe(OH)_3 | 2 | 2 (NH_4)_2SO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Fe_2(SO_4)_3·xH_2O | 1 | -1 | ([Fe2(SO4)3·xH2O])^(-1) NH_4OH | 6 | -6 | ([NH4OH])^(-6) Fe(OH)_3 | 2 | 2 | ([Fe(OH)3])^2 (NH_4)_2SO_4 | 3 | 3 | ([(NH4)2SO4])^3 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 = ([Fe2(SO4)3·xH2O])^(-1) ([NH4OH])^(-6) ([Fe(OH)3])^2 ([(NH4)2SO4])^3 = (([Fe(OH)3])^2 ([(NH4)2SO4])^3)/([Fe2(SO4)3·xH2O] ([NH4OH])^6)

Construct the rate of reaction expression for: Fe_2(SO_4)_3·xH_2O + NH_4OH ⟶ Fe(OH)_3 + (NH_4)_2SO_4 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_2(SO_4)_3·xH_2O + 6 NH_4OH ⟶ 2 Fe(OH)_3 + 3 (NH_4)_2SO_4 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_2(SO_4)_3·xH_2O | 1 | -1 NH_4OH | 6 | -6 Fe(OH)_3 | 2 | 2 (NH_4)_2SO_4 | 3 | 3 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_2(SO_4)_3·xH_2O | 1 | -1 | -(Δ[Fe2(SO4)3·xH2O])/(Δt) NH_4OH | 6 | -6 | -1/6 (Δ[NH4OH])/(Δt) Fe(OH)_3 | 2 | 2 | 1/2 (Δ[Fe(OH)3])/(Δt) (NH_4)_2SO_4 | 3 | 3 | 1/3 (Δ[(NH4)2SO4])/(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[Fe2(SO4)3·xH2O])/(Δt) = -1/6 (Δ[NH4OH])/(Δt) = 1/2 (Δ[Fe(OH)3])/(Δt) = 1/3 (Δ[(NH4)2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| iron(III) sulfate hydrate | ammonium hydroxide | iron(III) hydroxide | ammonium sulfate formula | Fe_2(SO_4)_3·xH_2O | NH_4OH | Fe(OH)_3 | (NH_4)_2SO_4 Hill formula | Fe_2O_12S_3 | H_5NO | FeH_3O_3 | H_8N_2O_4S name | iron(III) sulfate hydrate | ammonium hydroxide | iron(III) hydroxide | ammonium sulfate IUPAC name | diferric trisulfate | ammonium hydroxide | ferric trihydroxide |

| iron(III) sulfate hydrate | ammonium hydroxide | iron(III) hydroxide | ammonium sulfate molar mass | 399.9 g/mol | 35.046 g/mol | 106.87 g/mol | 132.1 g/mol phase | | aqueous (at STP) | | solid (at STP) melting point | | -57.5 °C | | 280 °C boiling point | | 36 °C | | density | | 0.9 g/cm^3 | | 1.77 g/cm^3 solubility in water | slightly soluble | very soluble | | odor | | | | odorless