H2SO4 + KClO3 + Na2SO3 = H2O + Cl2 + K2SO4 + Na2SO4

H_2SO_4 sulfuric acid + KClO_3 potassium chlorate + Na_2SO_3 sodium sulfite ⟶ H_2O water + Cl_2 chlorine + K_2SO_4 potassium sulfate + Na_2SO_4 sodium sulfate

Balance the chemical equation algebraically: H_2SO_4 + KClO_3 + Na_2SO_3 ⟶ H_2O + Cl_2 + K_2SO_4 + Na_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KClO_3 + c_3 Na_2SO_3 ⟶ c_4 H_2O + c_5 Cl_2 + c_6 K_2SO_4 + c_7 Na_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 Na: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 3 c_2 + 3 c_3 = c_4 + 4 c_6 + 4 c_7 S: | c_1 + c_3 = c_6 + c_7 Cl: | c_2 = 2 c_5 K: | c_2 = 2 c_6 Na: | 2 c_3 = 2 c_7 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 5 c_4 = 1 c_5 = 1 c_6 = 1 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2SO_4 + 2 KClO_3 + 5 Na_2SO_3 ⟶ H_2O + Cl_2 + K_2SO_4 + 5 Na_2SO_4

+ + ⟶ + + +

sulfuric acid + potassium chlorate + sodium sulfite ⟶ water + chlorine + potassium sulfate + sodium sulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + KClO_3 + Na_2SO_3 ⟶ H_2O + Cl_2 + K_2SO_4 + Na_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: H_2SO_4 + 2 KClO_3 + 5 Na_2SO_3 ⟶ H_2O + Cl_2 + K_2SO_4 + 5 Na_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 | 1 | -1 KClO_3 | 2 | -2 Na_2SO_3 | 5 | -5 H_2O | 1 | 1 Cl_2 | 1 | 1 K_2SO_4 | 1 | 1 Na_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 | 1 | -1 | ([H2SO4])^(-1) KClO_3 | 2 | -2 | ([KClO3])^(-2) Na_2SO_3 | 5 | -5 | ([Na2SO3])^(-5) H_2O | 1 | 1 | [H2O] Cl_2 | 1 | 1 | [Cl2] K_2SO_4 | 1 | 1 | [K2SO4] Na_2SO_4 | 5 | 5 | ([Na2SO4])^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])^(-1) ([KClO3])^(-2) ([Na2SO3])^(-5) [H2O] [Cl2] [K2SO4] ([Na2SO4])^5 = ([H2O] [Cl2] [K2SO4] ([Na2SO4])^5)/([H2SO4] ([KClO3])^2 ([Na2SO3])^5)

Construct the rate of reaction expression for: H_2SO_4 + KClO_3 + Na_2SO_3 ⟶ H_2O + Cl_2 + K_2SO_4 + Na_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: H_2SO_4 + 2 KClO_3 + 5 Na_2SO_3 ⟶ H_2O + Cl_2 + K_2SO_4 + 5 Na_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 | 1 | -1 KClO_3 | 2 | -2 Na_2SO_3 | 5 | -5 H_2O | 1 | 1 Cl_2 | 1 | 1 K_2SO_4 | 1 | 1 Na_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 | 1 | -1 | -(Δ[H2SO4])/(Δt) KClO_3 | 2 | -2 | -1/2 (Δ[KClO3])/(Δt) Na_2SO_3 | 5 | -5 | -1/5 (Δ[Na2SO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) Cl_2 | 1 | 1 | (Δ[Cl2])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) Na_2SO_4 | 5 | 5 | 1/5 (Δ[Na2SO4])/(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 = -(Δ[H2SO4])/(Δt) = -1/2 (Δ[KClO3])/(Δt) = -1/5 (Δ[Na2SO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[Cl2])/(Δt) = (Δ[K2SO4])/(Δt) = 1/5 (Δ[Na2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | potassium chlorate | sodium sulfite | water | chlorine | potassium sulfate | sodium sulfate formula | H_2SO_4 | KClO_3 | Na_2SO_3 | H_2O | Cl_2 | K_2SO_4 | Na_2SO_4 Hill formula | H_2O_4S | ClKO_3 | Na_2O_3S | H_2O | Cl_2 | K_2O_4S | Na_2O_4S name | sulfuric acid | potassium chlorate | sodium sulfite | water | chlorine | potassium sulfate | sodium sulfate IUPAC name | sulfuric acid | potassium chlorate | disodium sulfite | water | molecular chlorine | dipotassium sulfate | disodium sulfate