H2SO4 + KClO3 + NH4NO3 = H2O + Cl2 + K2SO4 + NO2 + (NH4)2SO4

H_2SO_4 sulfuric acid + KClO_3 potassium chlorate + NH_4NO_3 ammonium nitrate ⟶ H_2O water + Cl_2 chlorine + K_2SO_4 potassium sulfate + NO_2 nitrogen dioxide + (NH_4)_2SO_4 ammonium sulfate

Balance the chemical equation algebraically: H_2SO_4 + KClO_3 + NH_4NO_3 ⟶ H_2O + Cl_2 + K_2SO_4 + NO_2 + (NH_4)_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KClO_3 + c_3 NH_4NO_3 ⟶ c_4 H_2O + c_5 Cl_2 + c_6 K_2SO_4 + c_7 NO_2 + c_8 (NH_4)_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cl, K and N: H: | 2 c_1 + 4 c_3 = 2 c_4 + 8 c_8 O: | 4 c_1 + 3 c_2 + 3 c_3 = c_4 + 4 c_6 + 2 c_7 + 4 c_8 S: | c_1 = c_6 + c_8 Cl: | c_2 = 2 c_5 K: | c_2 = 2 c_6 N: | 2 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_2 = 2 c_3 = (7 c_1)/3 - 2/3 c_4 = (5 c_1)/3 + 8/3 c_5 = 1 c_6 = 1 c_7 = (8 c_1)/3 + 2/3 c_8 = c_1 - 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_2 = 4 c_3 = (7 c_1)/3 - 4/3 c_4 = (5 c_1)/3 + 16/3 c_5 = 2 c_6 = 2 c_7 = (8 c_1)/3 + 4/3 c_8 = c_1 - 2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 7 and solve for the remaining coefficients: c_1 = 7 c_2 = 4 c_3 = 15 c_4 = 17 c_5 = 2 c_6 = 2 c_7 = 20 c_8 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 H_2SO_4 + 4 KClO_3 + 15 NH_4NO_3 ⟶ 17 H_2O + 2 Cl_2 + 2 K_2SO_4 + 20 NO_2 + 5 (NH_4)_2SO_4

+ + ⟶ + + + +

sulfuric acid + potassium chlorate + ammonium nitrate ⟶ water + chlorine + potassium sulfate + nitrogen dioxide + ammonium sulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + KClO_3 + NH_4NO_3 ⟶ H_2O + Cl_2 + K_2SO_4 + NO_2 + (NH_4)_2SO_4 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: 7 H_2SO_4 + 4 KClO_3 + 15 NH_4NO_3 ⟶ 17 H_2O + 2 Cl_2 + 2 K_2SO_4 + 20 NO_2 + 5 (NH_4)_2SO_4 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 | 7 | -7 KClO_3 | 4 | -4 NH_4NO_3 | 15 | -15 H_2O | 17 | 17 Cl_2 | 2 | 2 K_2SO_4 | 2 | 2 NO_2 | 20 | 20 (NH_4)_2SO_4 | 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 | 7 | -7 | ([H2SO4])^(-7) KClO_3 | 4 | -4 | ([KClO3])^(-4) NH_4NO_3 | 15 | -15 | ([NH4NO3])^(-15) H_2O | 17 | 17 | ([H2O])^17 Cl_2 | 2 | 2 | ([Cl2])^2 K_2SO_4 | 2 | 2 | ([K2SO4])^2 NO_2 | 20 | 20 | ([NO2])^20 (NH_4)_2SO_4 | 5 | 5 | ([(NH4)2SO4])^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])^(-7) ([KClO3])^(-4) ([NH4NO3])^(-15) ([H2O])^17 ([Cl2])^2 ([K2SO4])^2 ([NO2])^20 ([(NH4)2SO4])^5 = (([H2O])^17 ([Cl2])^2 ([K2SO4])^2 ([NO2])^20 ([(NH4)2SO4])^5)/(([H2SO4])^7 ([KClO3])^4 ([NH4NO3])^15)

Construct the rate of reaction expression for: H_2SO_4 + KClO_3 + NH_4NO_3 ⟶ H_2O + Cl_2 + K_2SO_4 + NO_2 + (NH_4)_2SO_4 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: 7 H_2SO_4 + 4 KClO_3 + 15 NH_4NO_3 ⟶ 17 H_2O + 2 Cl_2 + 2 K_2SO_4 + 20 NO_2 + 5 (NH_4)_2SO_4 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 | 7 | -7 KClO_3 | 4 | -4 NH_4NO_3 | 15 | -15 H_2O | 17 | 17 Cl_2 | 2 | 2 K_2SO_4 | 2 | 2 NO_2 | 20 | 20 (NH_4)_2SO_4 | 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 | 7 | -7 | -1/7 (Δ[H2SO4])/(Δt) KClO_3 | 4 | -4 | -1/4 (Δ[KClO3])/(Δt) NH_4NO_3 | 15 | -15 | -1/15 (Δ[NH4NO3])/(Δt) H_2O | 17 | 17 | 1/17 (Δ[H2O])/(Δt) Cl_2 | 2 | 2 | 1/2 (Δ[Cl2])/(Δt) K_2SO_4 | 2 | 2 | 1/2 (Δ[K2SO4])/(Δt) NO_2 | 20 | 20 | 1/20 (Δ[NO2])/(Δt) (NH_4)_2SO_4 | 5 | 5 | 1/5 (Δ[(NH4)2SO4])/(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 = -1/7 (Δ[H2SO4])/(Δt) = -1/4 (Δ[KClO3])/(Δt) = -1/15 (Δ[NH4NO3])/(Δt) = 1/17 (Δ[H2O])/(Δt) = 1/2 (Δ[Cl2])/(Δt) = 1/2 (Δ[K2SO4])/(Δt) = 1/20 (Δ[NO2])/(Δt) = 1/5 (Δ[(NH4)2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | potassium chlorate | ammonium nitrate | water | chlorine | potassium sulfate | nitrogen dioxide | ammonium sulfate formula | H_2SO_4 | KClO_3 | NH_4NO_3 | H_2O | Cl_2 | K_2SO_4 | NO_2 | (NH_4)_2SO_4 Hill formula | H_2O_4S | ClKO_3 | H_4N_2O_3 | H_2O | Cl_2 | K_2O_4S | NO_2 | H_8N_2O_4S name | sulfuric acid | potassium chlorate | ammonium nitrate | water | chlorine | potassium sulfate | nitrogen dioxide | ammonium sulfate IUPAC name | sulfuric acid | potassium chlorate | | water | molecular chlorine | dipotassium sulfate | Nitrogen dioxide |