MnO2 + H2O2 = H2O + MnO3

MnO_2 manganese dioxide + H_2O_2 hydrogen peroxide ⟶ H_2O water + MnO3

Balance the chemical equation algebraically: MnO_2 + H_2O_2 ⟶ H_2O + MnO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MnO_2 + c_2 H_2O_2 ⟶ c_3 H_2O + c_4 MnO3 Set the number of atoms in the reactants equal to the number of atoms in the products for Mn, O and H: Mn: | c_1 = c_4 O: | 2 c_1 + 2 c_2 = c_3 + 3 c_4 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | MnO_2 + H_2O_2 ⟶ H_2O + MnO3

+ ⟶ + MnO3

manganese dioxide + hydrogen peroxide ⟶ water + MnO3

Construct the equilibrium constant, K, expression for: MnO_2 + H_2O_2 ⟶ H_2O + MnO3 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: MnO_2 + H_2O_2 ⟶ H_2O + MnO3 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 MnO_2 | 1 | -1 H_2O_2 | 1 | -1 H_2O | 1 | 1 MnO3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression MnO_2 | 1 | -1 | ([MnO2])^(-1) H_2O_2 | 1 | -1 | ([H2O2])^(-1) H_2O | 1 | 1 | [H2O] MnO3 | 1 | 1 | [MnO3] 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 = ([MnO2])^(-1) ([H2O2])^(-1) [H2O] [MnO3] = ([H2O] [MnO3])/([MnO2] [H2O2])

Construct the rate of reaction expression for: MnO_2 + H_2O_2 ⟶ H_2O + MnO3 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: MnO_2 + H_2O_2 ⟶ H_2O + MnO3 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 MnO_2 | 1 | -1 H_2O_2 | 1 | -1 H_2O | 1 | 1 MnO3 | 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 MnO_2 | 1 | -1 | -(Δ[MnO2])/(Δt) H_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) MnO3 | 1 | 1 | (Δ[MnO3])/(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 = -(Δ[MnO2])/(Δt) = -(Δ[H2O2])/(Δt) = (Δ[H2O])/(Δt) = (Δ[MnO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| manganese dioxide | hydrogen peroxide | water | MnO3 formula | MnO_2 | H_2O_2 | H_2O | MnO3 name | manganese dioxide | hydrogen peroxide | water | IUPAC name | dioxomanganese | hydrogen peroxide | water |

| manganese dioxide | hydrogen peroxide | water | MnO3 molar mass | 86.936 g/mol | 34.014 g/mol | 18.015 g/mol | 102.94 g/mol phase | solid (at STP) | liquid (at STP) | liquid (at STP) | melting point | 535 °C | -0.43 °C | 0 °C | boiling point | | 150.2 °C | 99.9839 °C | density | 5.03 g/cm^3 | 1.44 g/cm^3 | 1 g/cm^3 | solubility in water | insoluble | miscible | | surface tension | | 0.0804 N/m | 0.0728 N/m | dynamic viscosity | | 0.001249 Pa s (at 20 °C) | 8.9×10^-4 Pa s (at 25 °C) | odor | | | odorless |