Fe(OH)3 = H2O + Fe2O3

Fe(OH)_3 (iron(III) hydroxide) ⟶ H_2O (water) + Fe_2O_3 (iron(III) oxide)

Balance the chemical equation algebraically: Fe(OH)_3 ⟶ H_2O + Fe_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Fe(OH)_3 ⟶ c_2 H_2O + c_3 Fe_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Fe, H and O: Fe: | c_1 = 2 c_3 H: | 3 c_1 = 2 c_2 O: | 3 c_1 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 3 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Fe(OH)_3 ⟶ 3 H_2O + Fe_2O_3

⟶ +

iron(III) hydroxide ⟶ water + iron(III) oxide

Construct the equilibrium constant, K, expression for: Fe(OH)_3 ⟶ H_2O + Fe_2O_3 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 H_2O + Fe_2O_3 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 H_2O | 3 | 3 Fe_2O_3 | 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) H_2O | 3 | 3 | ([H2O])^3 Fe_2O_3 | 1 | 1 | [Fe2O3] 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) ([H2O])^3 [Fe2O3] = (([H2O])^3 [Fe2O3])/([Fe(OH)3])^2

Construct the rate of reaction expression for: Fe(OH)_3 ⟶ H_2O + Fe_2O_3 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 H_2O + Fe_2O_3 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 H_2O | 3 | 3 Fe_2O_3 | 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) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) Fe_2O_3 | 1 | 1 | (Δ[Fe2O3])/(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[H2O])/(Δt) = (Δ[Fe2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| iron(III) hydroxide | water | iron(III) oxide formula | Fe(OH)_3 | H_2O | Fe_2O_3 Hill formula | FeH_3O_3 | H_2O | Fe_2O_3 name | iron(III) hydroxide | water | iron(III) oxide IUPAC name | ferric trihydroxide | water |

| iron(III) hydroxide | water | iron(III) oxide molar mass | 106.87 g/mol | 18.015 g/mol | 159.69 g/mol phase | | liquid (at STP) | solid (at STP) melting point | | 0 °C | 1565 °C boiling point | | 99.9839 °C | density | | 1 g/cm^3 | 5.26 g/cm^3 solubility in water | | | insoluble surface tension | | 0.0728 N/m | dynamic viscosity | | 8.9×10^-4 Pa s (at 25 °C) | odor | | odorless | odorless