H2O + FeCl3 + K2CO3 = CO2 + KCl + Fe(OH)3

H_2O water + FeCl_3 iron(III) chloride + K_2CO_3 pearl ash ⟶ CO_2 carbon dioxide + KCl potassium chloride + Fe(OH)_3 iron(III) hydroxide

Balance the chemical equation algebraically: H_2O + FeCl_3 + K_2CO_3 ⟶ CO_2 + KCl + Fe(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 FeCl_3 + c_3 K_2CO_3 ⟶ c_4 CO_2 + c_5 KCl + c_6 Fe(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl, Fe, C and K: H: | 2 c_1 = 3 c_6 O: | c_1 + 3 c_3 = 2 c_4 + 3 c_6 Cl: | 3 c_2 = c_5 Fe: | c_2 = c_6 C: | c_3 = c_4 K: | 2 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_1 = 3/2 c_2 = 1 c_3 = 3/2 c_4 = 3/2 c_5 = 3 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 3 c_5 = 6 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 2 FeCl_3 + 3 K_2CO_3 ⟶ 3 CO_2 + 6 KCl + 2 Fe(OH)_3

+ + ⟶ + +

water + iron(III) chloride + pearl ash ⟶ carbon dioxide + potassium chloride + iron(III) hydroxide

Construct the equilibrium constant, K, expression for: H_2O + FeCl_3 + K_2CO_3 ⟶ CO_2 + KCl + 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: 3 H_2O + 2 FeCl_3 + 3 K_2CO_3 ⟶ 3 CO_2 + 6 KCl + 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 | 3 | -3 FeCl_3 | 2 | -2 K_2CO_3 | 3 | -3 CO_2 | 3 | 3 KCl | 6 | 6 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 | 3 | -3 | ([H2O])^(-3) FeCl_3 | 2 | -2 | ([FeCl3])^(-2) K_2CO_3 | 3 | -3 | ([K2CO3])^(-3) CO_2 | 3 | 3 | ([CO2])^3 KCl | 6 | 6 | ([KCl])^6 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])^(-3) ([FeCl3])^(-2) ([K2CO3])^(-3) ([CO2])^3 ([KCl])^6 ([Fe(OH)3])^2 = (([CO2])^3 ([KCl])^6 ([Fe(OH)3])^2)/(([H2O])^3 ([FeCl3])^2 ([K2CO3])^3)

Construct the rate of reaction expression for: H_2O + FeCl_3 + K_2CO_3 ⟶ CO_2 + KCl + 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: 3 H_2O + 2 FeCl_3 + 3 K_2CO_3 ⟶ 3 CO_2 + 6 KCl + 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 | 3 | -3 FeCl_3 | 2 | -2 K_2CO_3 | 3 | -3 CO_2 | 3 | 3 KCl | 6 | 6 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 | 3 | -3 | -1/3 (Δ[H2O])/(Δt) FeCl_3 | 2 | -2 | -1/2 (Δ[FeCl3])/(Δt) K_2CO_3 | 3 | -3 | -1/3 (Δ[K2CO3])/(Δt) CO_2 | 3 | 3 | 1/3 (Δ[CO2])/(Δt) KCl | 6 | 6 | 1/6 (Δ[KCl])/(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 = -1/3 (Δ[H2O])/(Δt) = -1/2 (Δ[FeCl3])/(Δt) = -1/3 (Δ[K2CO3])/(Δt) = 1/3 (Δ[CO2])/(Δt) = 1/6 (Δ[KCl])/(Δt) = 1/2 (Δ[Fe(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | iron(III) chloride | pearl ash | carbon dioxide | potassium chloride | iron(III) hydroxide formula | H_2O | FeCl_3 | K_2CO_3 | CO_2 | KCl | Fe(OH)_3 Hill formula | H_2O | Cl_3Fe | CK_2O_3 | CO_2 | ClK | FeH_3O_3 name | water | iron(III) chloride | pearl ash | carbon dioxide | potassium chloride | iron(III) hydroxide IUPAC name | water | trichloroiron | dipotassium carbonate | carbon dioxide | potassium chloride | ferric trihydroxide