KMnO4 + HI = H2O + I2 + KI + MnI2

KMnO_4 potassium permanganate + HI hydrogen iodide ⟶ H_2O water + I_2 iodine + KI potassium iodide + MnI_2 manganese(II) iodide

Balance the chemical equation algebraically: KMnO_4 + HI ⟶ H_2O + I_2 + KI + MnI_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 + c_2 HI ⟶ c_3 H_2O + c_4 I_2 + c_5 KI + c_6 MnI_2 Set the number of atoms in the reactants equal to the number of atoms in the products for K, Mn, O, H and I: K: | c_1 = c_5 Mn: | c_1 = c_6 O: | 4 c_1 = c_3 H: | c_2 = 2 c_3 I: | c_2 = 2 c_4 + c_5 + 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 8 c_3 = 4 c_4 = 5/2 c_5 = 1 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 16 c_3 = 8 c_4 = 5 c_5 = 2 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KMnO_4 + 16 HI ⟶ 8 H_2O + 5 I_2 + 2 KI + 2 MnI_2

+ ⟶ + + +

potassium permanganate + hydrogen iodide ⟶ water + iodine + potassium iodide + manganese(II) iodide

Construct the equilibrium constant, K, expression for: KMnO_4 + HI ⟶ H_2O + I_2 + KI + MnI_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 KMnO_4 + 16 HI ⟶ 8 H_2O + 5 I_2 + 2 KI + 2 MnI_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 KMnO_4 | 2 | -2 HI | 16 | -16 H_2O | 8 | 8 I_2 | 5 | 5 KI | 2 | 2 MnI_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KMnO_4 | 2 | -2 | ([KMnO4])^(-2) HI | 16 | -16 | ([HI])^(-16) H_2O | 8 | 8 | ([H2O])^8 I_2 | 5 | 5 | ([I2])^5 KI | 2 | 2 | ([KI])^2 MnI_2 | 2 | 2 | ([MnI2])^2 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 = ([KMnO4])^(-2) ([HI])^(-16) ([H2O])^8 ([I2])^5 ([KI])^2 ([MnI2])^2 = (([H2O])^8 ([I2])^5 ([KI])^2 ([MnI2])^2)/(([KMnO4])^2 ([HI])^16)

Construct the rate of reaction expression for: KMnO_4 + HI ⟶ H_2O + I_2 + KI + MnI_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 KMnO_4 + 16 HI ⟶ 8 H_2O + 5 I_2 + 2 KI + 2 MnI_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 KMnO_4 | 2 | -2 HI | 16 | -16 H_2O | 8 | 8 I_2 | 5 | 5 KI | 2 | 2 MnI_2 | 2 | 2 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 KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) HI | 16 | -16 | -1/16 (Δ[HI])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) I_2 | 5 | 5 | 1/5 (Δ[I2])/(Δt) KI | 2 | 2 | 1/2 (Δ[KI])/(Δt) MnI_2 | 2 | 2 | 1/2 (Δ[MnI2])/(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[KMnO4])/(Δt) = -1/16 (Δ[HI])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/5 (Δ[I2])/(Δt) = 1/2 (Δ[KI])/(Δt) = 1/2 (Δ[MnI2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium permanganate | hydrogen iodide | water | iodine | potassium iodide | manganese(II) iodide formula | KMnO_4 | HI | H_2O | I_2 | KI | MnI_2 Hill formula | KMnO_4 | HI | H_2O | I_2 | IK | I_2Mn name | potassium permanganate | hydrogen iodide | water | iodine | potassium iodide | manganese(II) iodide IUPAC name | potassium permanganate | hydrogen iodide | water | molecular iodine | potassium iodide | manganous diiodide

| potassium permanganate | hydrogen iodide | water | iodine | potassium iodide | manganese(II) iodide molar mass | 158.03 g/mol | 127.912 g/mol | 18.015 g/mol | 253.80894 g/mol | 166.0028 g/mol | 308.74698 g/mol phase | solid (at STP) | gas (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 240 °C | -50.76 °C | 0 °C | 113 °C | 681 °C | 80 °C boiling point | | -35.55 °C | 99.9839 °C | 184 °C | 1330 °C | density | 1 g/cm^3 | 0.005228 g/cm^3 (at 25 °C) | 1 g/cm^3 | 4.94 g/cm^3 | 3.123 g/cm^3 | 5.01 g/cm^3 solubility in water | | very soluble | | | | soluble surface tension | | | 0.0728 N/m | | | dynamic viscosity | | 0.001321 Pa s (at -39 °C) | 8.9×10^-4 Pa s (at 25 °C) | 0.00227 Pa s (at 116 °C) | 0.0010227 Pa s (at 732.9 °C) | odor | odorless | | odorless | | |