KOH + KMnO4 + KI = H2O + K2MnO4 + KIO3

KOH potassium hydroxide + KMnO_4 potassium permanganate + KI potassium iodide ⟶ H_2O water + K_2MnO_4 potassium manganate + KIO_3 potassium iodate

Balance the chemical equation algebraically: KOH + KMnO_4 + KI ⟶ H_2O + K_2MnO_4 + KIO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 KMnO_4 + c_3 KI ⟶ c_4 H_2O + c_5 K_2MnO_4 + c_6 KIO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Mn and I: H: | c_1 = 2 c_4 K: | c_1 + c_2 + c_3 = 2 c_5 + c_6 O: | c_1 + 4 c_2 = c_4 + 4 c_5 + 3 c_6 Mn: | c_2 = c_5 I: | c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 6 c_3 = 1 c_4 = 3 c_5 = 6 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 KOH + 6 KMnO_4 + KI ⟶ 3 H_2O + 6 K_2MnO_4 + KIO_3

+ + ⟶ + +

potassium hydroxide + potassium permanganate + potassium iodide ⟶ water + potassium manganate + potassium iodate

Construct the equilibrium constant, K, expression for: KOH + KMnO_4 + KI ⟶ H_2O + K_2MnO_4 + KIO_3 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: 6 KOH + 6 KMnO_4 + KI ⟶ 3 H_2O + 6 K_2MnO_4 + KIO_3 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 KOH | 6 | -6 KMnO_4 | 6 | -6 KI | 1 | -1 H_2O | 3 | 3 K_2MnO_4 | 6 | 6 KIO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 6 | -6 | ([KOH])^(-6) KMnO_4 | 6 | -6 | ([KMnO4])^(-6) KI | 1 | -1 | ([KI])^(-1) H_2O | 3 | 3 | ([H2O])^3 K_2MnO_4 | 6 | 6 | ([K2MnO4])^6 KIO_3 | 1 | 1 | [KIO3] 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 = ([KOH])^(-6) ([KMnO4])^(-6) ([KI])^(-1) ([H2O])^3 ([K2MnO4])^6 [KIO3] = (([H2O])^3 ([K2MnO4])^6 [KIO3])/(([KOH])^6 ([KMnO4])^6 [KI])

Construct the rate of reaction expression for: KOH + KMnO_4 + KI ⟶ H_2O + K_2MnO_4 + KIO_3 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: 6 KOH + 6 KMnO_4 + KI ⟶ 3 H_2O + 6 K_2MnO_4 + KIO_3 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 KOH | 6 | -6 KMnO_4 | 6 | -6 KI | 1 | -1 H_2O | 3 | 3 K_2MnO_4 | 6 | 6 KIO_3 | 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 KOH | 6 | -6 | -1/6 (Δ[KOH])/(Δt) KMnO_4 | 6 | -6 | -1/6 (Δ[KMnO4])/(Δt) KI | 1 | -1 | -(Δ[KI])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) K_2MnO_4 | 6 | 6 | 1/6 (Δ[K2MnO4])/(Δt) KIO_3 | 1 | 1 | (Δ[KIO3])/(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 = -1/6 (Δ[KOH])/(Δt) = -1/6 (Δ[KMnO4])/(Δt) = -(Δ[KI])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/6 (Δ[K2MnO4])/(Δt) = (Δ[KIO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | potassium permanganate | potassium iodide | water | potassium manganate | potassium iodate formula | KOH | KMnO_4 | KI | H_2O | K_2MnO_4 | KIO_3 Hill formula | HKO | KMnO_4 | IK | H_2O | K_2MnO_4 | IKO_3 name | potassium hydroxide | potassium permanganate | potassium iodide | water | potassium manganate | potassium iodate IUPAC name | potassium hydroxide | potassium permanganate | potassium iodide | water | dipotassium dioxido-dioxomanganese | potassium iodate

| potassium hydroxide | potassium permanganate | potassium iodide | water | potassium manganate | potassium iodate molar mass | 56.105 g/mol | 158.03 g/mol | 166.0028 g/mol | 18.015 g/mol | 197.13 g/mol | 214 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 406 °C | 240 °C | 681 °C | 0 °C | 190 °C | 560 °C boiling point | 1327 °C | | 1330 °C | 99.9839 °C | | density | 2.044 g/cm^3 | 1 g/cm^3 | 3.123 g/cm^3 | 1 g/cm^3 | | 1.005 g/cm^3 solubility in water | soluble | | | | decomposes | surface tension | | | | 0.0728 N/m | | dynamic viscosity | 0.001 Pa s (at 550 °C) | | 0.0010227 Pa s (at 732.9 °C) | 8.9×10^-4 Pa s (at 25 °C) | | odor | | odorless | | odorless | |