H2O + O2 + Fe = H2 + Fe(OH)3

H_2O water + O_2 oxygen + Fe iron ⟶ H_2 hydrogen + Fe(OH)_3 iron(III) hydroxide

Balance the chemical equation algebraically: H_2O + O_2 + Fe ⟶ H_2 + Fe(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 O_2 + c_3 Fe ⟶ c_4 H_2 + c_5 Fe(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and Fe: H: | 2 c_1 = 2 c_4 + 3 c_5 O: | c_1 + 2 c_2 = 3 c_5 Fe: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_2 = 1 c_3 = c_1/3 + 2/3 c_4 = c_1/2 - 1 c_5 = c_1/3 + 2/3 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 4 and solve for the remaining coefficients: c_1 = 4 c_2 = 1 c_3 = 2 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2O + O_2 + 2 Fe ⟶ H_2 + 2 Fe(OH)_3

+ + ⟶ +

water + oxygen + iron ⟶ hydrogen + iron(III) hydroxide

Construct the equilibrium constant, K, expression for: H_2O + O_2 + Fe ⟶ H_2 + Fe(OH)_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: 4 H_2O + O_2 + 2 Fe ⟶ H_2 + 2 Fe(OH)_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 H_2O | 4 | -4 O_2 | 1 | -1 Fe | 2 | -2 H_2 | 1 | 1 Fe(OH)_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 4 | -4 | ([H2O])^(-4) O_2 | 1 | -1 | ([O2])^(-1) Fe | 2 | -2 | ([Fe])^(-2) H_2 | 1 | 1 | [H2] Fe(OH)_3 | 2 | 2 | ([Fe(OH)3])^2 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])^(-4) ([O2])^(-1) ([Fe])^(-2) [H2] ([Fe(OH)3])^2 = ([H2] ([Fe(OH)3])^2)/(([H2O])^4 [O2] ([Fe])^2)

Construct the rate of reaction expression for: H_2O + O_2 + Fe ⟶ H_2 + Fe(OH)_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: 4 H_2O + O_2 + 2 Fe ⟶ H_2 + 2 Fe(OH)_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 H_2O | 4 | -4 O_2 | 1 | -1 Fe | 2 | -2 H_2 | 1 | 1 Fe(OH)_3 | 2 | 2 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 | 4 | -4 | -1/4 (Δ[H2O])/(Δt) O_2 | 1 | -1 | -(Δ[O2])/(Δt) Fe | 2 | -2 | -1/2 (Δ[Fe])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(Δt) Fe(OH)_3 | 2 | 2 | 1/2 (Δ[Fe(OH)3])/(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 = -1/4 (Δ[H2O])/(Δt) = -(Δ[O2])/(Δt) = -1/2 (Δ[Fe])/(Δt) = (Δ[H2])/(Δt) = 1/2 (Δ[Fe(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | oxygen | iron | hydrogen | iron(III) hydroxide formula | H_2O | O_2 | Fe | H_2 | Fe(OH)_3 Hill formula | H_2O | O_2 | Fe | H_2 | FeH_3O_3 name | water | oxygen | iron | hydrogen | iron(III) hydroxide IUPAC name | water | molecular oxygen | iron | molecular hydrogen | ferric trihydroxide

| water | oxygen | iron | hydrogen | iron(III) hydroxide molar mass | 18.015 g/mol | 31.998 g/mol | 55.845 g/mol | 2.016 g/mol | 106.87 g/mol phase | liquid (at STP) | gas (at STP) | solid (at STP) | gas (at STP) | melting point | 0 °C | -218 °C | 1535 °C | -259.2 °C | boiling point | 99.9839 °C | -183 °C | 2750 °C | -252.8 °C | density | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 7.874 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | solubility in water | | | insoluble | | surface tension | 0.0728 N/m | 0.01347 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | | 8.9×10^-6 Pa s (at 25 °C) | odor | odorless | odorless | | odorless |