H2SO4 + FeCl2 + KNO2 = H2O + K2SO4 + N2 + FeCl3 + Fe2(SO4)3

H_2SO_4 sulfuric acid + FeCl_2 iron(II) chloride + KNO_2 potassium nitrite ⟶ H_2O water + K_2SO_4 potassium sulfate + N_2 nitrogen + FeCl_3 iron(III) chloride + Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate

Balance the chemical equation algebraically: H_2SO_4 + FeCl_2 + KNO_2 ⟶ H_2O + K_2SO_4 + N_2 + 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 FeCl_2 + c_3 KNO_2 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 N_2 + 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, Cl, Fe, K and N: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 2 c_3 = c_4 + 4 c_5 + 12 c_8 S: | c_1 = c_5 + 3 c_8 Cl: | 2 c_2 = 3 c_7 Fe: | c_2 = c_7 + 2 c_8 K: | c_3 = 2 c_5 N: | 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 6 c_3 = 2 c_4 = 4 c_5 = 1 c_6 = 1 c_7 = 4 c_8 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2SO_4 + 6 FeCl_2 + 2 KNO_2 ⟶ 4 H_2O + K_2SO_4 + N_2 + 4 FeCl_3 + Fe_2(SO_4)_3·xH_2O

+ + ⟶ + + + +

sulfuric acid + iron(II) chloride + potassium nitrite ⟶ water + potassium sulfate + nitrogen + iron(III) chloride + iron(III) sulfate hydrate

Construct the equilibrium constant, K, expression for: H_2SO_4 + FeCl_2 + KNO_2 ⟶ H_2O + K_2SO_4 + N_2 + 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: 4 H_2SO_4 + 6 FeCl_2 + 2 KNO_2 ⟶ 4 H_2O + K_2SO_4 + N_2 + 4 FeCl_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 | 4 | -4 FeCl_2 | 6 | -6 KNO_2 | 2 | -2 H_2O | 4 | 4 K_2SO_4 | 1 | 1 N_2 | 1 | 1 FeCl_3 | 4 | 4 Fe_2(SO_4)_3·xH_2O | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 4 | -4 | ([H2SO4])^(-4) FeCl_2 | 6 | -6 | ([FeCl2])^(-6) KNO_2 | 2 | -2 | ([KNO2])^(-2) H_2O | 4 | 4 | ([H2O])^4 K_2SO_4 | 1 | 1 | [K2SO4] N_2 | 1 | 1 | [N2] FeCl_3 | 4 | 4 | ([FeCl3])^4 Fe_2(SO_4)_3·xH_2O | 1 | 1 | [Fe2(SO4)3·xH2O] 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])^(-4) ([FeCl2])^(-6) ([KNO2])^(-2) ([H2O])^4 [K2SO4] [N2] ([FeCl3])^4 [Fe2(SO4)3·xH2O] = (([H2O])^4 [K2SO4] [N2] ([FeCl3])^4 [Fe2(SO4)3·xH2O])/(([H2SO4])^4 ([FeCl2])^6 ([KNO2])^2)

Construct the rate of reaction expression for: H_2SO_4 + FeCl_2 + KNO_2 ⟶ H_2O + K_2SO_4 + N_2 + 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: 4 H_2SO_4 + 6 FeCl_2 + 2 KNO_2 ⟶ 4 H_2O + K_2SO_4 + N_2 + 4 FeCl_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 | 4 | -4 FeCl_2 | 6 | -6 KNO_2 | 2 | -2 H_2O | 4 | 4 K_2SO_4 | 1 | 1 N_2 | 1 | 1 FeCl_3 | 4 | 4 Fe_2(SO_4)_3·xH_2O | 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 H_2SO_4 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) FeCl_2 | 6 | -6 | -1/6 (Δ[FeCl2])/(Δt) KNO_2 | 2 | -2 | -1/2 (Δ[KNO2])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) N_2 | 1 | 1 | (Δ[N2])/(Δt) FeCl_3 | 4 | 4 | 1/4 (Δ[FeCl3])/(Δt) Fe_2(SO_4)_3·xH_2O | 1 | 1 | (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 = -1/4 (Δ[H2SO4])/(Δt) = -1/6 (Δ[FeCl2])/(Δt) = -1/2 (Δ[KNO2])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[N2])/(Δt) = 1/4 (Δ[FeCl3])/(Δt) = (Δ[Fe2(SO4)3·xH2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | iron(II) chloride | potassium nitrite | water | potassium sulfate | nitrogen | iron(III) chloride | iron(III) sulfate hydrate formula | H_2SO_4 | FeCl_2 | KNO_2 | H_2O | K_2SO_4 | N_2 | FeCl_3 | Fe_2(SO_4)_3·xH_2O Hill formula | H_2O_4S | Cl_2Fe | KNO_2 | H_2O | K_2O_4S | N_2 | Cl_3Fe | Fe_2O_12S_3 name | sulfuric acid | iron(II) chloride | potassium nitrite | water | potassium sulfate | nitrogen | iron(III) chloride | iron(III) sulfate hydrate IUPAC name | sulfuric acid | dichloroiron | potassium nitrite | water | dipotassium sulfate | molecular nitrogen | trichloroiron | diferric trisulfate