H2SO4 + KClO3 + Fe(OH)2 = H2O + KCl + Fe2(SO4)3

H_2SO_4 sulfuric acid + KClO_3 potassium chlorate + Fe(OH)_2 iron(II) hydroxide ⟶ H_2O water + KCl potassium chloride + Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate

Balance the chemical equation algebraically: H_2SO_4 + KClO_3 + Fe(OH)_2 ⟶ H_2O + KCl + Fe_2(SO_4)_3·xH_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KClO_3 + c_3 Fe(OH)_2 ⟶ c_4 H_2O + c_5 KCl + c_6 Fe_2(SO_4)_3·xH_2O Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cl, K and Fe: H: | 2 c_1 + 2 c_3 = 2 c_4 O: | 4 c_1 + 3 c_2 + 2 c_3 = c_4 + 12 c_6 S: | c_1 = 3 c_6 Cl: | c_2 = c_5 K: | c_2 = c_5 Fe: | c_3 = 2 c_6 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 = 9 c_2 = 1 c_3 = 6 c_4 = 15 c_5 = 1 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 9 H_2SO_4 + KClO_3 + 6 Fe(OH)_2 ⟶ 15 H_2O + KCl + 3 Fe_2(SO_4)_3·xH_2O

+ + ⟶ + +

sulfuric acid + potassium chlorate + iron(II) hydroxide ⟶ water + potassium chloride + iron(III) sulfate hydrate

Construct the equilibrium constant, K, expression for: H_2SO_4 + KClO_3 + Fe(OH)_2 ⟶ H_2O + KCl + Fe_2(SO_4)_3·xH_2O 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: 9 H_2SO_4 + KClO_3 + 6 Fe(OH)_2 ⟶ 15 H_2O + KCl + 3 Fe_2(SO_4)_3·xH_2O 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_2SO_4 | 9 | -9 KClO_3 | 1 | -1 Fe(OH)_2 | 6 | -6 H_2O | 15 | 15 KCl | 1 | 1 Fe_2(SO_4)_3·xH_2O | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 9 | -9 | ([H2SO4])^(-9) KClO_3 | 1 | -1 | ([KClO3])^(-1) Fe(OH)_2 | 6 | -6 | ([Fe(OH)2])^(-6) H_2O | 15 | 15 | ([H2O])^15 KCl | 1 | 1 | [KCl] Fe_2(SO_4)_3·xH_2O | 3 | 3 | ([Fe2(SO4)3·xH2O])^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 = ([H2SO4])^(-9) ([KClO3])^(-1) ([Fe(OH)2])^(-6) ([H2O])^15 [KCl] ([Fe2(SO4)3·xH2O])^3 = (([H2O])^15 [KCl] ([Fe2(SO4)3·xH2O])^3)/(([H2SO4])^9 [KClO3] ([Fe(OH)2])^6)

Construct the rate of reaction expression for: H_2SO_4 + KClO_3 + Fe(OH)_2 ⟶ H_2O + KCl + Fe_2(SO_4)_3·xH_2O 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: 9 H_2SO_4 + KClO_3 + 6 Fe(OH)_2 ⟶ 15 H_2O + KCl + 3 Fe_2(SO_4)_3·xH_2O 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_2SO_4 | 9 | -9 KClO_3 | 1 | -1 Fe(OH)_2 | 6 | -6 H_2O | 15 | 15 KCl | 1 | 1 Fe_2(SO_4)_3·xH_2O | 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_2SO_4 | 9 | -9 | -1/9 (Δ[H2SO4])/(Δt) KClO_3 | 1 | -1 | -(Δ[KClO3])/(Δt) Fe(OH)_2 | 6 | -6 | -1/6 (Δ[Fe(OH)2])/(Δt) H_2O | 15 | 15 | 1/15 (Δ[H2O])/(Δt) KCl | 1 | 1 | (Δ[KCl])/(Δt) Fe_2(SO_4)_3·xH_2O | 3 | 3 | 1/3 (Δ[Fe2(SO4)3·xH2O])/(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 = -1/9 (Δ[H2SO4])/(Δt) = -(Δ[KClO3])/(Δt) = -1/6 (Δ[Fe(OH)2])/(Δt) = 1/15 (Δ[H2O])/(Δt) = (Δ[KCl])/(Δt) = 1/3 (Δ[Fe2(SO4)3·xH2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | potassium chlorate | iron(II) hydroxide | water | potassium chloride | iron(III) sulfate hydrate formula | H_2SO_4 | KClO_3 | Fe(OH)_2 | H_2O | KCl | Fe_2(SO_4)_3·xH_2O Hill formula | H_2O_4S | ClKO_3 | FeH_2O_2 | H_2O | ClK | Fe_2O_12S_3 name | sulfuric acid | potassium chlorate | iron(II) hydroxide | water | potassium chloride | iron(III) sulfate hydrate IUPAC name | sulfuric acid | potassium chlorate | ferrous dihydroxide | water | potassium chloride | diferric trisulfate

| sulfuric acid | potassium chlorate | iron(II) hydroxide | water | potassium chloride | iron(III) sulfate hydrate molar mass | 98.07 g/mol | 122.5 g/mol | 89.86 g/mol | 18.015 g/mol | 74.55 g/mol | 399.9 g/mol phase | liquid (at STP) | solid (at STP) | | liquid (at STP) | solid (at STP) | melting point | 10.371 °C | 356 °C | | 0 °C | 770 °C | boiling point | 279.6 °C | | | 99.9839 °C | 1420 °C | density | 1.8305 g/cm^3 | 2.34 g/cm^3 | | 1 g/cm^3 | 1.98 g/cm^3 | solubility in water | very soluble | soluble | | | soluble | slightly soluble surface tension | 0.0735 N/m | | | 0.0728 N/m | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | odorless | | | odorless | odorless |