KMnO4 = O2 + K2O + MnO

KMnO_4 potassium permanganate ⟶ O_2 oxygen + K_2O potassium oxide + MnO manganese monoxide

Balance the chemical equation algebraically: KMnO_4 ⟶ O_2 + K_2O + MnO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 ⟶ c_2 O_2 + c_3 K_2O + c_4 MnO Set the number of atoms in the reactants equal to the number of atoms in the products for K, Mn and O: K: | c_1 = 2 c_3 Mn: | c_1 = c_4 O: | 4 c_1 = 2 c_2 + c_3 + c_4 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 = 5/2 c_3 = 1 c_4 = 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 4 c_2 = 5 c_3 = 2 c_4 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 KMnO_4 ⟶ 5 O_2 + 2 K_2O + 4 MnO

⟶ + +

potassium permanganate ⟶ oxygen + potassium oxide + manganese monoxide

Construct the equilibrium constant, K, expression for: KMnO_4 ⟶ O_2 + K_2O + MnO 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: 4 KMnO_4 ⟶ 5 O_2 + 2 K_2O + 4 MnO 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 | 4 | -4 O_2 | 5 | 5 K_2O | 2 | 2 MnO | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KMnO_4 | 4 | -4 | ([KMnO4])^(-4) O_2 | 5 | 5 | ([O2])^5 K_2O | 2 | 2 | ([K2O])^2 MnO | 4 | 4 | ([MnO])^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 = ([KMnO4])^(-4) ([O2])^5 ([K2O])^2 ([MnO])^4 = (([O2])^5 ([K2O])^2 ([MnO])^4)/([KMnO4])^4

Construct the rate of reaction expression for: KMnO_4 ⟶ O_2 + K_2O + MnO 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: 4 KMnO_4 ⟶ 5 O_2 + 2 K_2O + 4 MnO 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 | 4 | -4 O_2 | 5 | 5 K_2O | 2 | 2 MnO | 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 KMnO_4 | 4 | -4 | -1/4 (Δ[KMnO4])/(Δt) O_2 | 5 | 5 | 1/5 (Δ[O2])/(Δt) K_2O | 2 | 2 | 1/2 (Δ[K2O])/(Δt) MnO | 4 | 4 | 1/4 (Δ[MnO])/(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 = -1/4 (Δ[KMnO4])/(Δt) = 1/5 (Δ[O2])/(Δt) = 1/2 (Δ[K2O])/(Δt) = 1/4 (Δ[MnO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium permanganate | oxygen | potassium oxide | manganese monoxide formula | KMnO_4 | O_2 | K_2O | MnO name | potassium permanganate | oxygen | potassium oxide | manganese monoxide IUPAC name | potassium permanganate | molecular oxygen | dipotassium oxygen(2-) | oxomanganese

| potassium permanganate | oxygen | potassium oxide | manganese monoxide molar mass | 158.03 g/mol | 31.998 g/mol | 94.196 g/mol | 70.937 g/mol phase | solid (at STP) | gas (at STP) | | solid (at STP) melting point | 240 °C | -218 °C | | 1840 °C boiling point | | -183 °C | | density | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | | 5.45 g/cm^3 solubility in water | | | | insoluble surface tension | | 0.01347 N/m | | dynamic viscosity | | 2.055×10^-5 Pa s (at 25 °C) | | odor | odorless | odorless | |