H2O + KI + K2MnO4 = KOH + I2 + MnO2

H_2O water + KI potassium iodide + K_2MnO_4 potassium manganate ⟶ KOH potassium hydroxide + I_2 iodine + MnO_2 manganese dioxide

Balance the chemical equation algebraically: H_2O + KI + K_2MnO_4 ⟶ KOH + I_2 + MnO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KI + c_3 K_2MnO_4 ⟶ c_4 KOH + c_5 I_2 + c_6 MnO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, I, K and Mn: H: | 2 c_1 = c_4 O: | c_1 + 4 c_3 = c_4 + 2 c_6 I: | c_2 = 2 c_5 K: | c_2 + 2 c_3 = c_4 Mn: | 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 = 2 c_2 = 2 c_3 = 1 c_4 = 4 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 2 KI + K_2MnO_4 ⟶ 4 KOH + I_2 + MnO_2

+ + ⟶ + +

water + potassium iodide + potassium manganate ⟶ potassium hydroxide + iodine + manganese dioxide

Construct the equilibrium constant, K, expression for: H_2O + KI + K_2MnO_4 ⟶ KOH + I_2 + MnO_2 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: 2 H_2O + 2 KI + K_2MnO_4 ⟶ 4 KOH + I_2 + MnO_2 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_2O | 2 | -2 KI | 2 | -2 K_2MnO_4 | 1 | -1 KOH | 4 | 4 I_2 | 1 | 1 MnO_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) KI | 2 | -2 | ([KI])^(-2) K_2MnO_4 | 1 | -1 | ([K2MnO4])^(-1) KOH | 4 | 4 | ([KOH])^4 I_2 | 1 | 1 | [I2] MnO_2 | 1 | 1 | [MnO2] 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 = ([H2O])^(-2) ([KI])^(-2) ([K2MnO4])^(-1) ([KOH])^4 [I2] [MnO2] = (([KOH])^4 [I2] [MnO2])/(([H2O])^2 ([KI])^2 [K2MnO4])

Construct the rate of reaction expression for: H_2O + KI + K_2MnO_4 ⟶ KOH + I_2 + MnO_2 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: 2 H_2O + 2 KI + K_2MnO_4 ⟶ 4 KOH + I_2 + MnO_2 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_2O | 2 | -2 KI | 2 | -2 K_2MnO_4 | 1 | -1 KOH | 4 | 4 I_2 | 1 | 1 MnO_2 | 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_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) KI | 2 | -2 | -1/2 (Δ[KI])/(Δt) K_2MnO_4 | 1 | -1 | -(Δ[K2MnO4])/(Δt) KOH | 4 | 4 | 1/4 (Δ[KOH])/(Δt) I_2 | 1 | 1 | (Δ[I2])/(Δt) MnO_2 | 1 | 1 | (Δ[MnO2])/(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 = -1/2 (Δ[H2O])/(Δt) = -1/2 (Δ[KI])/(Δt) = -(Δ[K2MnO4])/(Δt) = 1/4 (Δ[KOH])/(Δt) = (Δ[I2])/(Δt) = (Δ[MnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | potassium iodide | potassium manganate | potassium hydroxide | iodine | manganese dioxide formula | H_2O | KI | K_2MnO_4 | KOH | I_2 | MnO_2 Hill formula | H_2O | IK | K_2MnO_4 | HKO | I_2 | MnO_2 name | water | potassium iodide | potassium manganate | potassium hydroxide | iodine | manganese dioxide IUPAC name | water | potassium iodide | dipotassium dioxido-dioxomanganese | potassium hydroxide | molecular iodine | dioxomanganese

| water | potassium iodide | potassium manganate | potassium hydroxide | iodine | manganese dioxide molar mass | 18.015 g/mol | 166.0028 g/mol | 197.13 g/mol | 56.105 g/mol | 253.80894 g/mol | 86.936 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 0 °C | 681 °C | 190 °C | 406 °C | 113 °C | 535 °C boiling point | 99.9839 °C | 1330 °C | | 1327 °C | 184 °C | density | 1 g/cm^3 | 3.123 g/cm^3 | | 2.044 g/cm^3 | 4.94 g/cm^3 | 5.03 g/cm^3 solubility in water | | | decomposes | soluble | | insoluble surface tension | 0.0728 N/m | | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 0.0010227 Pa s (at 732.9 °C) | | 0.001 Pa s (at 550 °C) | 0.00227 Pa s (at 116 °C) | odor | odorless | | | | |