H2SO4 + KMnO4 + CuI = H2O + K2SO4 + I2 + CuSO4 + MnSO4

H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + CuI cuprous iodide ⟶ H_2O water + K_2SO_4 potassium sulfate + I_2 iodine + CuSO_4 copper(II) sulfate + MnSO_4 manganese(II) sulfate

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + CuI ⟶ H_2O + K_2SO_4 + I_2 + CuSO_4 + MnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 CuI ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 I_2 + c_7 CuSO_4 + c_8 MnSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn, Cu and I: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 4 c_7 + 4 c_8 S: | c_1 = c_5 + c_7 + c_8 K: | c_2 = 2 c_5 Mn: | c_2 = c_8 Cu: | c_3 = c_7 I: | 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 = 8 c_2 = 2 c_3 = 5 c_4 = 8 c_5 = 1 c_6 = 5/2 c_7 = 5 c_8 = 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 16 c_2 = 4 c_3 = 10 c_4 = 16 c_5 = 2 c_6 = 5 c_7 = 10 c_8 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 H_2SO_4 + 4 KMnO_4 + 10 CuI ⟶ 16 H_2O + 2 K_2SO_4 + 5 I_2 + 10 CuSO_4 + 4 MnSO_4

sulfuric acid + potassium permanganate + cuprous iodide ⟶ water + potassium sulfate + iodine + copper(II) sulfate + manganese(II) sulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + CuI ⟶ H_2O + K_2SO_4 + I_2 + CuSO_4 + MnSO_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: 16 H_2SO_4 + 4 KMnO_4 + 10 CuI ⟶ 16 H_2O + 2 K_2SO_4 + 5 I_2 + 10 CuSO_4 + 4 MnSO_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 | 16 | -16 KMnO_4 | 4 | -4 CuI | 10 | -10 H_2O | 16 | 16 K_2SO_4 | 2 | 2 I_2 | 5 | 5 CuSO_4 | 10 | 10 MnSO_4 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 16 | -16 | ([H2SO4])^(-16) KMnO_4 | 4 | -4 | ([KMnO4])^(-4) CuI | 10 | -10 | ([CuI])^(-10) H_2O | 16 | 16 | ([H2O])^16 K_2SO_4 | 2 | 2 | ([K2SO4])^2 I_2 | 5 | 5 | ([I2])^5 CuSO_4 | 10 | 10 | ([CuSO4])^10 MnSO_4 | 4 | 4 | ([MnSO4])^4 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])^(-16) ([KMnO4])^(-4) ([CuI])^(-10) ([H2O])^16 ([K2SO4])^2 ([I2])^5 ([CuSO4])^10 ([MnSO4])^4 = (([H2O])^16 ([K2SO4])^2 ([I2])^5 ([CuSO4])^10 ([MnSO4])^4)/(([H2SO4])^16 ([KMnO4])^4 ([CuI])^10)

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + CuI ⟶ H_2O + K_2SO_4 + I_2 + CuSO_4 + MnSO_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: 16 H_2SO_4 + 4 KMnO_4 + 10 CuI ⟶ 16 H_2O + 2 K_2SO_4 + 5 I_2 + 10 CuSO_4 + 4 MnSO_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 | 16 | -16 KMnO_4 | 4 | -4 CuI | 10 | -10 H_2O | 16 | 16 K_2SO_4 | 2 | 2 I_2 | 5 | 5 CuSO_4 | 10 | 10 MnSO_4 | 4 | 4 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 | 16 | -16 | -1/16 (Δ[H2SO4])/(Δt) KMnO_4 | 4 | -4 | -1/4 (Δ[KMnO4])/(Δt) CuI | 10 | -10 | -1/10 (Δ[CuI])/(Δt) H_2O | 16 | 16 | 1/16 (Δ[H2O])/(Δt) K_2SO_4 | 2 | 2 | 1/2 (Δ[K2SO4])/(Δt) I_2 | 5 | 5 | 1/5 (Δ[I2])/(Δt) CuSO_4 | 10 | 10 | 1/10 (Δ[CuSO4])/(Δt) MnSO_4 | 4 | 4 | 1/4 (Δ[MnSO4])/(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 = -1/16 (Δ[H2SO4])/(Δt) = -1/4 (Δ[KMnO4])/(Δt) = -1/10 (Δ[CuI])/(Δt) = 1/16 (Δ[H2O])/(Δt) = 1/2 (Δ[K2SO4])/(Δt) = 1/5 (Δ[I2])/(Δt) = 1/10 (Δ[CuSO4])/(Δt) = 1/4 (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | potassium permanganate | cuprous iodide | water | potassium sulfate | iodine | copper(II) sulfate | manganese(II) sulfate formula | H_2SO_4 | KMnO_4 | CuI | H_2O | K_2SO_4 | I_2 | CuSO_4 | MnSO_4 Hill formula | H_2O_4S | KMnO_4 | CuI | H_2O | K_2O_4S | I_2 | CuO_4S | MnSO_4 name | sulfuric acid | potassium permanganate | cuprous iodide | water | potassium sulfate | iodine | copper(II) sulfate | manganese(II) sulfate IUPAC name | sulfuric acid | potassium permanganate | cuprous iodide | water | dipotassium sulfate | molecular iodine | copper sulfate | manganese(+2) cation sulfate