KOH + MnO2 + O3 = H2O + KMnO4

KOH potassium hydroxide + MnO_2 manganese dioxide + O_3 ozone ⟶ H_2O water + KMnO_4 potassium permanganate

Balance the chemical equation algebraically: KOH + MnO_2 + O_3 ⟶ H_2O + KMnO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 MnO_2 + c_3 O_3 ⟶ c_4 H_2O + c_5 KMnO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O and Mn: H: | c_1 = 2 c_4 K: | c_1 = c_5 O: | c_1 + 2 c_2 + 3 c_3 = c_4 + 4 c_5 Mn: | c_2 = c_5 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 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KOH + 2 MnO_2 + O_3 ⟶ H_2O + 2 KMnO_4

+ + ⟶ +

potassium hydroxide + manganese dioxide + ozone ⟶ water + potassium permanganate

| potassium hydroxide | manganese dioxide | ozone | water | potassium permanganate molecular free energy | -379.4 kJ/mol | -465.1 kJ/mol | 163.2 kJ/mol | -237.1 kJ/mol | -737.6 kJ/mol total free energy | -758.8 kJ/mol | -930.2 kJ/mol | 163.2 kJ/mol | -237.1 kJ/mol | -1475 kJ/mol | G_initial = -1526 kJ/mol | | | G_final = -1712 kJ/mol | ΔG_rxn^0 | -1712 kJ/mol - -1526 kJ/mol = -186.5 kJ/mol (exergonic) | | | |

Construct the equilibrium constant, K, expression for: KOH + MnO_2 + O_3 ⟶ H_2O + KMnO_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 KOH + 2 MnO_2 + O_3 ⟶ H_2O + 2 KMnO_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 KOH | 2 | -2 MnO_2 | 2 | -2 O_3 | 1 | -1 H_2O | 1 | 1 KMnO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 2 | -2 | ([KOH])^(-2) MnO_2 | 2 | -2 | ([MnO2])^(-2) O_3 | 1 | -1 | ([O3])^(-1) H_2O | 1 | 1 | [H2O] KMnO_4 | 2 | 2 | ([KMnO4])^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 = ([KOH])^(-2) ([MnO2])^(-2) ([O3])^(-1) [H2O] ([KMnO4])^2 = ([H2O] ([KMnO4])^2)/(([KOH])^2 ([MnO2])^2 [O3])

Construct the rate of reaction expression for: KOH + MnO_2 + O_3 ⟶ H_2O + KMnO_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 KOH + 2 MnO_2 + O_3 ⟶ H_2O + 2 KMnO_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 KOH | 2 | -2 MnO_2 | 2 | -2 O_3 | 1 | -1 H_2O | 1 | 1 KMnO_4 | 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 KOH | 2 | -2 | -1/2 (Δ[KOH])/(Δt) MnO_2 | 2 | -2 | -1/2 (Δ[MnO2])/(Δt) O_3 | 1 | -1 | -(Δ[O3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) KMnO_4 | 2 | 2 | 1/2 (Δ[KMnO4])/(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[KOH])/(Δt) = -1/2 (Δ[MnO2])/(Δt) = -(Δ[O3])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[KMnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | manganese dioxide | ozone | water | potassium permanganate formula | KOH | MnO_2 | O_3 | H_2O | KMnO_4 Hill formula | HKO | MnO_2 | O_3 | H_2O | KMnO_4 name | potassium hydroxide | manganese dioxide | ozone | water | potassium permanganate IUPAC name | potassium hydroxide | dioxomanganese | ozone | water | potassium permanganate

| potassium hydroxide | manganese dioxide | ozone | water | potassium permanganate molar mass | 56.105 g/mol | 86.936 g/mol | 47.997 g/mol | 18.015 g/mol | 158.03 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | liquid (at STP) | solid (at STP) melting point | 406 °C | 535 °C | -192.2 °C | 0 °C | 240 °C boiling point | 1327 °C | | -111.9 °C | 99.9839 °C | density | 2.044 g/cm^3 | 5.03 g/cm^3 | 0.001962 g/cm^3 (at 25 °C) | 1 g/cm^3 | 1 g/cm^3 solubility in water | soluble | insoluble | | | surface tension | | | | 0.0728 N/m | dynamic viscosity | 0.001 Pa s (at 550 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | odor | | | | odorless | odorless