H2SO4 + KMnO4 + FeCl2 = H2O + K2SO4 + MnSO4 + FeCl3 + Fe2(SO4)3

H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + FeCl_2 iron(II) chloride ⟶ H_2O water + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + FeCl_3 iron(III) chloride + Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + FeCl_2 ⟶ H_2O + K_2SO_4 + MnSO_4 + FeCl_3 + Fe_2(SO_4)_3·xH_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 FeCl_2 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 MnSO_4 + c_7 FeCl_3 + c_8 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, K, Mn, Cl and Fe: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 4 c_6 + 12 c_8 S: | c_1 = c_5 + c_6 + 3 c_8 K: | c_2 = 2 c_5 Mn: | c_2 = c_6 Cl: | 2 c_3 = 3 c_7 Fe: | c_3 = c_7 + 2 c_8 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 2 c_3 = 10 c_4 = 8 c_5 = 1 c_6 = 2 c_7 = 20/3 c_8 = 5/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 24 c_2 = 6 c_3 = 30 c_4 = 24 c_5 = 3 c_6 = 6 c_7 = 20 c_8 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 24 H_2SO_4 + 6 KMnO_4 + 30 FeCl_2 ⟶ 24 H_2O + 3 K_2SO_4 + 6 MnSO_4 + 20 FeCl_3 + 5 Fe_2(SO_4)_3·xH_2O

+ + ⟶ + + + +

sulfuric acid + potassium permanganate + iron(II) chloride ⟶ water + potassium sulfate + manganese(II) sulfate + iron(III) chloride + iron(III) sulfate hydrate

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + FeCl_2 ⟶ H_2O + K_2SO_4 + MnSO_4 + FeCl_3 + 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: 24 H_2SO_4 + 6 KMnO_4 + 30 FeCl_2 ⟶ 24 H_2O + 3 K_2SO_4 + 6 MnSO_4 + 20 FeCl_3 + 5 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 | 24 | -24 KMnO_4 | 6 | -6 FeCl_2 | 30 | -30 H_2O | 24 | 24 K_2SO_4 | 3 | 3 MnSO_4 | 6 | 6 FeCl_3 | 20 | 20 Fe_2(SO_4)_3·xH_2O | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 24 | -24 | ([H2SO4])^(-24) KMnO_4 | 6 | -6 | ([KMnO4])^(-6) FeCl_2 | 30 | -30 | ([FeCl2])^(-30) H_2O | 24 | 24 | ([H2O])^24 K_2SO_4 | 3 | 3 | ([K2SO4])^3 MnSO_4 | 6 | 6 | ([MnSO4])^6 FeCl_3 | 20 | 20 | ([FeCl3])^20 Fe_2(SO_4)_3·xH_2O | 5 | 5 | ([Fe2(SO4)3·xH2O])^5 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])^(-24) ([KMnO4])^(-6) ([FeCl2])^(-30) ([H2O])^24 ([K2SO4])^3 ([MnSO4])^6 ([FeCl3])^20 ([Fe2(SO4)3·xH2O])^5 = (([H2O])^24 ([K2SO4])^3 ([MnSO4])^6 ([FeCl3])^20 ([Fe2(SO4)3·xH2O])^5)/(([H2SO4])^24 ([KMnO4])^6 ([FeCl2])^30)

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + FeCl_2 ⟶ H_2O + K_2SO_4 + MnSO_4 + FeCl_3 + 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: 24 H_2SO_4 + 6 KMnO_4 + 30 FeCl_2 ⟶ 24 H_2O + 3 K_2SO_4 + 6 MnSO_4 + 20 FeCl_3 + 5 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 | 24 | -24 KMnO_4 | 6 | -6 FeCl_2 | 30 | -30 H_2O | 24 | 24 K_2SO_4 | 3 | 3 MnSO_4 | 6 | 6 FeCl_3 | 20 | 20 Fe_2(SO_4)_3·xH_2O | 5 | 5 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 | 24 | -24 | -1/24 (Δ[H2SO4])/(Δt) KMnO_4 | 6 | -6 | -1/6 (Δ[KMnO4])/(Δt) FeCl_2 | 30 | -30 | -1/30 (Δ[FeCl2])/(Δt) H_2O | 24 | 24 | 1/24 (Δ[H2O])/(Δt) K_2SO_4 | 3 | 3 | 1/3 (Δ[K2SO4])/(Δt) MnSO_4 | 6 | 6 | 1/6 (Δ[MnSO4])/(Δt) FeCl_3 | 20 | 20 | 1/20 (Δ[FeCl3])/(Δt) Fe_2(SO_4)_3·xH_2O | 5 | 5 | 1/5 (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 = -1/24 (Δ[H2SO4])/(Δt) = -1/6 (Δ[KMnO4])/(Δt) = -1/30 (Δ[FeCl2])/(Δt) = 1/24 (Δ[H2O])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = 1/6 (Δ[MnSO4])/(Δt) = 1/20 (Δ[FeCl3])/(Δt) = 1/5 (Δ[Fe2(SO4)3·xH2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | potassium permanganate | iron(II) chloride | water | potassium sulfate | manganese(II) sulfate | iron(III) chloride | iron(III) sulfate hydrate formula | H_2SO_4 | KMnO_4 | FeCl_2 | H_2O | K_2SO_4 | MnSO_4 | FeCl_3 | Fe_2(SO_4)_3·xH_2O Hill formula | H_2O_4S | KMnO_4 | Cl_2Fe | H_2O | K_2O_4S | MnSO_4 | Cl_3Fe | Fe_2O_12S_3 name | sulfuric acid | potassium permanganate | iron(II) chloride | water | potassium sulfate | manganese(II) sulfate | iron(III) chloride | iron(III) sulfate hydrate IUPAC name | sulfuric acid | potassium permanganate | dichloroiron | water | dipotassium sulfate | manganese(+2) cation sulfate | trichloroiron | diferric trisulfate