KMnO4 + H2O2 = H2O + O2 + MnO2 + K2MnO4

KMnO_4 potassium permanganate + H_2O_2 hydrogen peroxide ⟶ H_2O water + O_2 oxygen + MnO_2 manganese dioxide + K_2MnO_4 potassium manganate

Balance the chemical equation algebraically: KMnO_4 + H_2O_2 ⟶ H_2O + O_2 + MnO_2 + K_2MnO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 + c_2 H_2O_2 ⟶ c_3 H_2O + c_4 O_2 + c_5 MnO_2 + c_6 K_2MnO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for K, Mn, O and H: K: | c_1 = 2 c_6 Mn: | c_1 = c_5 + c_6 O: | 4 c_1 + 2 c_2 = c_3 + 2 c_4 + 2 c_5 + 4 c_6 H: | 2 c_2 = 2 c_3 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 = 2 c_3 = c_2 c_4 = c_2/2 + 1 c_5 = 1 c_6 = 1 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_2 = 2 and solve for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 2 c_4 = 2 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KMnO_4 + 2 H_2O_2 ⟶ 2 H_2O + 2 O_2 + MnO_2 + K_2MnO_4

+ ⟶ + + +

potassium permanganate + hydrogen peroxide ⟶ water + oxygen + manganese dioxide + potassium manganate

Construct the equilibrium constant, K, expression for: KMnO_4 + H_2O_2 ⟶ H_2O + O_2 + MnO_2 + K_2MnO_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: 2 KMnO_4 + 2 H_2O_2 ⟶ 2 H_2O + 2 O_2 + MnO_2 + K_2MnO_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 KMnO_4 | 2 | -2 H_2O_2 | 2 | -2 H_2O | 2 | 2 O_2 | 2 | 2 MnO_2 | 1 | 1 K_2MnO_4 | 1 | 1 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) H_2O_2 | 2 | -2 | ([H2O2])^(-2) H_2O | 2 | 2 | ([H2O])^2 O_2 | 2 | 2 | ([O2])^2 MnO_2 | 1 | 1 | [MnO2] K_2MnO_4 | 1 | 1 | [K2MnO4] 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) ([H2O2])^(-2) ([H2O])^2 ([O2])^2 [MnO2] [K2MnO4] = (([H2O])^2 ([O2])^2 [MnO2] [K2MnO4])/(([KMnO4])^2 ([H2O2])^2)

Construct the rate of reaction expression for: KMnO_4 + H_2O_2 ⟶ H_2O + O_2 + MnO_2 + K_2MnO_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: 2 KMnO_4 + 2 H_2O_2 ⟶ 2 H_2O + 2 O_2 + MnO_2 + K_2MnO_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 KMnO_4 | 2 | -2 H_2O_2 | 2 | -2 H_2O | 2 | 2 O_2 | 2 | 2 MnO_2 | 1 | 1 K_2MnO_4 | 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 KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) H_2O_2 | 2 | -2 | -1/2 (Δ[H2O2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) O_2 | 2 | 2 | 1/2 (Δ[O2])/(Δt) MnO_2 | 1 | 1 | (Δ[MnO2])/(Δt) K_2MnO_4 | 1 | 1 | (Δ[K2MnO4])/(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) = -1/2 (Δ[H2O2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[O2])/(Δt) = (Δ[MnO2])/(Δt) = (Δ[K2MnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium permanganate | hydrogen peroxide | water | oxygen | manganese dioxide | potassium manganate formula | KMnO_4 | H_2O_2 | H_2O | O_2 | MnO_2 | K_2MnO_4 name | potassium permanganate | hydrogen peroxide | water | oxygen | manganese dioxide | potassium manganate IUPAC name | potassium permanganate | hydrogen peroxide | water | molecular oxygen | dioxomanganese | dipotassium dioxido-dioxomanganese

| potassium permanganate | hydrogen peroxide | water | oxygen | manganese dioxide | potassium manganate molar mass | 158.03 g/mol | 34.014 g/mol | 18.015 g/mol | 31.998 g/mol | 86.936 g/mol | 197.13 g/mol phase | solid (at STP) | liquid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) | solid (at STP) melting point | 240 °C | -0.43 °C | 0 °C | -218 °C | 535 °C | 190 °C boiling point | | 150.2 °C | 99.9839 °C | -183 °C | | density | 1 g/cm^3 | 1.44 g/cm^3 | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 5.03 g/cm^3 | solubility in water | | miscible | | | insoluble | decomposes surface tension | | 0.0804 N/m | 0.0728 N/m | 0.01347 N/m | | dynamic viscosity | | 0.001249 Pa s (at 20 °C) | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | | odor | odorless | | odorless | odorless | |