O2 + NaOH + MnO2 = H2O + Na2MnO4

O_2 oxygen + NaOH sodium hydroxide + MnO_2 manganese dioxide ⟶ H_2O water + Na2MnO4

Balance the chemical equation algebraically: O_2 + NaOH + MnO_2 ⟶ H_2O + Na2MnO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 NaOH + c_3 MnO_2 ⟶ c_4 H_2O + c_5 Na2MnO4 Set the number of atoms in the reactants equal to the number of atoms in the products for O, H, Na and Mn: O: | 2 c_1 + c_2 + 2 c_3 = c_4 + 4 c_5 H: | c_2 = 2 c_4 Na: | c_2 = 2 c_5 Mn: | c_3 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 4 c_3 = 2 c_4 = 2 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | O_2 + 4 NaOH + 2 MnO_2 ⟶ 2 H_2O + 2 Na2MnO4

+ + ⟶ + Na2MnO4

oxygen + sodium hydroxide + manganese dioxide ⟶ water + Na2MnO4

Construct the equilibrium constant, K, expression for: O_2 + NaOH + MnO_2 ⟶ H_2O + Na2MnO4 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: O_2 + 4 NaOH + 2 MnO_2 ⟶ 2 H_2O + 2 Na2MnO4 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 O_2 | 1 | -1 NaOH | 4 | -4 MnO_2 | 2 | -2 H_2O | 2 | 2 Na2MnO4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 1 | -1 | ([O2])^(-1) NaOH | 4 | -4 | ([NaOH])^(-4) MnO_2 | 2 | -2 | ([MnO2])^(-2) H_2O | 2 | 2 | ([H2O])^2 Na2MnO4 | 2 | 2 | ([Na2MnO4])^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 = ([O2])^(-1) ([NaOH])^(-4) ([MnO2])^(-2) ([H2O])^2 ([Na2MnO4])^2 = (([H2O])^2 ([Na2MnO4])^2)/([O2] ([NaOH])^4 ([MnO2])^2)

Construct the rate of reaction expression for: O_2 + NaOH + MnO_2 ⟶ H_2O + Na2MnO4 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: O_2 + 4 NaOH + 2 MnO_2 ⟶ 2 H_2O + 2 Na2MnO4 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 O_2 | 1 | -1 NaOH | 4 | -4 MnO_2 | 2 | -2 H_2O | 2 | 2 Na2MnO4 | 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 O_2 | 1 | -1 | -(Δ[O2])/(Δt) NaOH | 4 | -4 | -1/4 (Δ[NaOH])/(Δt) MnO_2 | 2 | -2 | -1/2 (Δ[MnO2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) Na2MnO4 | 2 | 2 | 1/2 (Δ[Na2MnO4])/(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[O2])/(Δt) = -1/4 (Δ[NaOH])/(Δt) = -1/2 (Δ[MnO2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[Na2MnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | sodium hydroxide | manganese dioxide | water | Na2MnO4 formula | O_2 | NaOH | MnO_2 | H_2O | Na2MnO4 Hill formula | O_2 | HNaO | MnO_2 | H_2O | MnNa2O4 name | oxygen | sodium hydroxide | manganese dioxide | water | IUPAC name | molecular oxygen | sodium hydroxide | dioxomanganese | water |