KMnO4 = O2 + K2MnO4 + MnO

KMnO_4 potassium permanganate ⟶ O_2 oxygen + K_2MnO_4 potassium manganate + MnO manganese monoxide

Balance the chemical equation algebraically: KMnO_4 ⟶ O_2 + K_2MnO_4 + MnO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 ⟶ c_2 O_2 + c_3 K_2MnO_4 + 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_3 + c_4 O: | 4 c_1 = 2 c_2 + 4 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 = 3/2 c_3 = 1 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 4 c_2 = 3 c_3 = 2 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 KMnO_4 ⟶ 3 O_2 + 2 K_2MnO_4 + 2 MnO

⟶ + +

potassium permanganate ⟶ oxygen + potassium manganate + manganese monoxide

Construct the equilibrium constant, K, expression for: KMnO_4 ⟶ O_2 + K_2MnO_4 + 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 ⟶ 3 O_2 + 2 K_2MnO_4 + 2 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 | 3 | 3 K_2MnO_4 | 2 | 2 MnO | 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 | 4 | -4 | ([KMnO4])^(-4) O_2 | 3 | 3 | ([O2])^3 K_2MnO_4 | 2 | 2 | ([K2MnO4])^2 MnO | 2 | 2 | ([MnO])^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])^(-4) ([O2])^3 ([K2MnO4])^2 ([MnO])^2 = (([O2])^3 ([K2MnO4])^2 ([MnO])^2)/([KMnO4])^4

Construct the rate of reaction expression for: KMnO_4 ⟶ O_2 + K_2MnO_4 + 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 ⟶ 3 O_2 + 2 K_2MnO_4 + 2 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 | 3 | 3 K_2MnO_4 | 2 | 2 MnO | 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 | 4 | -4 | -1/4 (Δ[KMnO4])/(Δt) O_2 | 3 | 3 | 1/3 (Δ[O2])/(Δt) K_2MnO_4 | 2 | 2 | 1/2 (Δ[K2MnO4])/(Δt) MnO | 2 | 2 | 1/2 (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) = 1/3 (Δ[O2])/(Δt) = 1/2 (Δ[K2MnO4])/(Δt) = 1/2 (Δ[MnO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium permanganate | oxygen | potassium manganate | manganese monoxide formula | KMnO_4 | O_2 | K_2MnO_4 | MnO name | potassium permanganate | oxygen | potassium manganate | manganese monoxide IUPAC name | potassium permanganate | molecular oxygen | dipotassium dioxido-dioxomanganese | oxomanganese

| potassium permanganate | oxygen | potassium manganate | manganese monoxide molar mass | 158.03 g/mol | 31.998 g/mol | 197.13 g/mol | 70.937 g/mol phase | solid (at STP) | gas (at STP) | solid (at STP) | solid (at STP) melting point | 240 °C | -218 °C | 190 °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 | | | decomposes | insoluble surface tension | | 0.01347 N/m | | dynamic viscosity | | 2.055×10^-5 Pa s (at 25 °C) | | odor | odorless | odorless | |