H2O + NH3 + Fe2(SO4)3 = Fe(OH)3 + (NH4)2SO4

H_2O water + NH_3 ammonia + Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate ⟶ Fe(OH)_3 iron(III) hydroxide + (NH_4)_2SO_4 ammonium sulfate

Balance the chemical equation algebraically: H_2O + NH_3 + Fe_2(SO_4)_3·xH_2O ⟶ Fe(OH)_3 + (NH_4)_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NH_3 + c_3 Fe_2(SO_4)_3·xH_2O ⟶ c_4 Fe(OH)_3 + c_5 (NH_4)_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, N, Fe and S: H: | 2 c_1 + 3 c_2 = 3 c_4 + 8 c_5 O: | c_1 + 12 c_3 = 3 c_4 + 4 c_5 N: | c_2 = 2 c_5 Fe: | 2 c_3 = c_4 S: | 3 c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 6 c_3 = 1 c_4 = 2 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + 6 NH_3 + Fe_2(SO_4)_3·xH_2O ⟶ 2 Fe(OH)_3 + 3 (NH_4)_2SO_4

+ + ⟶ +

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

Construct the equilibrium constant, K, expression for: H_2O + NH_3 + Fe_2(SO_4)_3·xH_2O ⟶ 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: 6 H_2O + 6 NH_3 + Fe_2(SO_4)_3·xH_2O ⟶ 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 H_2O | 6 | -6 NH_3 | 6 | -6 Fe_2(SO_4)_3·xH_2O | 1 | -1 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 H_2O | 6 | -6 | ([H2O])^(-6) NH_3 | 6 | -6 | ([NH3])^(-6) Fe_2(SO_4)_3·xH_2O | 1 | -1 | ([Fe2(SO4)3·xH2O])^(-1) 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 = ([H2O])^(-6) ([NH3])^(-6) ([Fe2(SO4)3·xH2O])^(-1) ([Fe(OH)3])^2 ([(NH4)2SO4])^3 = (([Fe(OH)3])^2 ([(NH4)2SO4])^3)/(([H2O])^6 ([NH3])^6 [Fe2(SO4)3·xH2O])

Construct the rate of reaction expression for: H_2O + NH_3 + Fe_2(SO_4)_3·xH_2O ⟶ 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: 6 H_2O + 6 NH_3 + Fe_2(SO_4)_3·xH_2O ⟶ 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 H_2O | 6 | -6 NH_3 | 6 | -6 Fe_2(SO_4)_3·xH_2O | 1 | -1 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 H_2O | 6 | -6 | -1/6 (Δ[H2O])/(Δt) NH_3 | 6 | -6 | -1/6 (Δ[NH3])/(Δt) Fe_2(SO_4)_3·xH_2O | 1 | -1 | -(Δ[Fe2(SO4)3·xH2O])/(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 = -1/6 (Δ[H2O])/(Δt) = -1/6 (Δ[NH3])/(Δt) = -(Δ[Fe2(SO4)3·xH2O])/(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)

| water | ammonia | iron(III) sulfate hydrate | iron(III) hydroxide | ammonium sulfate formula | H_2O | NH_3 | Fe_2(SO_4)_3·xH_2O | Fe(OH)_3 | (NH_4)_2SO_4 Hill formula | H_2O | H_3N | Fe_2O_12S_3 | FeH_3O_3 | H_8N_2O_4S name | water | ammonia | iron(III) sulfate hydrate | iron(III) hydroxide | ammonium sulfate IUPAC name | water | ammonia | diferric trisulfate | ferric trihydroxide |

| water | ammonia | iron(III) sulfate hydrate | iron(III) hydroxide | ammonium sulfate molar mass | 18.015 g/mol | 17.031 g/mol | 399.9 g/mol | 106.87 g/mol | 132.1 g/mol phase | liquid (at STP) | gas (at STP) | | | solid (at STP) melting point | 0 °C | -77.73 °C | | | 280 °C boiling point | 99.9839 °C | -33.33 °C | | | density | 1 g/cm^3 | 6.96×10^-4 g/cm^3 (at 25 °C) | | | 1.77 g/cm^3 solubility in water | | | slightly soluble | | surface tension | 0.0728 N/m | 0.0234 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 1.009×10^-5 Pa s (at 25 °C) | | | odor | odorless | | | | odorless