H2SO4 + KI + K2O2 = H2O + K2SO4 + I2 + H2S

H_2SO_4 sulfuric acid + KI potassium iodide + K_2O_2 potassium peroxide ⟶ H_2O water + K_2SO_4 potassium sulfate + I_2 iodine + H_2S hydrogen sulfide

Balance the chemical equation algebraically: H_2SO_4 + KI + K_2O_2 ⟶ H_2O + K_2SO_4 + I_2 + H_2S Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KI + c_3 K_2O_2 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 I_2 + c_7 H_2S Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, I and K: H: | 2 c_1 = 2 c_4 + 2 c_7 O: | 4 c_1 + 2 c_3 = c_4 + 4 c_5 S: | c_1 = c_5 + c_7 I: | c_2 = 2 c_6 K: | c_2 + 2 c_3 = 2 c_5 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_3 = 1 and solve the system of equations for the remaining coefficients: c_2 = (8 c_1)/5 - 6/5 c_3 = 1 c_4 = (4 c_1)/5 + 2/5 c_5 = (4 c_1)/5 + 2/5 c_6 = (4 c_1)/5 - 3/5 c_7 = c_1/5 - 2/5 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 = 10 c_3 = 1 c_4 = 6 c_5 = 6 c_6 = 5 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 H_2SO_4 + 10 KI + K_2O_2 ⟶ 6 H_2O + 6 K_2SO_4 + 5 I_2 + H_2S

+ + ⟶ + + +

sulfuric acid + potassium iodide + potassium peroxide ⟶ water + potassium sulfate + iodine + hydrogen sulfide

Construct the equilibrium constant, K, expression for: H_2SO_4 + KI + K_2O_2 ⟶ H_2O + K_2SO_4 + I_2 + H_2S 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 + 10 KI + K_2O_2 ⟶ 6 H_2O + 6 K_2SO_4 + 5 I_2 + H_2S 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 KI | 10 | -10 K_2O_2 | 1 | -1 H_2O | 6 | 6 K_2SO_4 | 6 | 6 I_2 | 5 | 5 H_2S | 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 | 7 | -7 | ([H2SO4])^(-7) KI | 10 | -10 | ([KI])^(-10) K_2O_2 | 1 | -1 | ([K2O2])^(-1) H_2O | 6 | 6 | ([H2O])^6 K_2SO_4 | 6 | 6 | ([K2SO4])^6 I_2 | 5 | 5 | ([I2])^5 H_2S | 1 | 1 | [H2S] 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) ([KI])^(-10) ([K2O2])^(-1) ([H2O])^6 ([K2SO4])^6 ([I2])^5 [H2S] = (([H2O])^6 ([K2SO4])^6 ([I2])^5 [H2S])/(([H2SO4])^7 ([KI])^10 [K2O2])

Construct the rate of reaction expression for: H_2SO_4 + KI + K_2O_2 ⟶ H_2O + K_2SO_4 + I_2 + H_2S 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 + 10 KI + K_2O_2 ⟶ 6 H_2O + 6 K_2SO_4 + 5 I_2 + H_2S 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 KI | 10 | -10 K_2O_2 | 1 | -1 H_2O | 6 | 6 K_2SO_4 | 6 | 6 I_2 | 5 | 5 H_2S | 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 | 7 | -7 | -1/7 (Δ[H2SO4])/(Δt) KI | 10 | -10 | -1/10 (Δ[KI])/(Δt) K_2O_2 | 1 | -1 | -(Δ[K2O2])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) K_2SO_4 | 6 | 6 | 1/6 (Δ[K2SO4])/(Δt) I_2 | 5 | 5 | 1/5 (Δ[I2])/(Δt) H_2S | 1 | 1 | (Δ[H2S])/(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) = -1/10 (Δ[KI])/(Δt) = -(Δ[K2O2])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/6 (Δ[K2SO4])/(Δt) = 1/5 (Δ[I2])/(Δt) = (Δ[H2S])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | potassium iodide | potassium peroxide | water | potassium sulfate | iodine | hydrogen sulfide formula | H_2SO_4 | KI | K_2O_2 | H_2O | K_2SO_4 | I_2 | H_2S Hill formula | H_2O_4S | IK | K_2O_2 | H_2O | K_2O_4S | I_2 | H_2S name | sulfuric acid | potassium iodide | potassium peroxide | water | potassium sulfate | iodine | hydrogen sulfide IUPAC name | sulfuric acid | potassium iodide | dipotassium peroxide | water | dipotassium sulfate | molecular iodine | hydrogen sulfide