NaOH + MnSO4 + H2O2 = H2O + Na2SO4 + MnO2

NaOH sodium hydroxide + MnSO_4 manganese(II) sulfate + H_2O_2 hydrogen peroxide ⟶ H_2O water + Na_2SO_4 sodium sulfate + MnO_2 manganese dioxide

Balance the chemical equation algebraically: NaOH + MnSO_4 + H_2O_2 ⟶ H_2O + Na_2SO_4 + MnO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 MnSO_4 + c_3 H_2O_2 ⟶ c_4 H_2O + c_5 Na_2SO_4 + c_6 MnO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Mn and S: H: | c_1 + 2 c_3 = 2 c_4 Na: | c_1 = 2 c_5 O: | c_1 + 4 c_2 + 2 c_3 = c_4 + 4 c_5 + 2 c_6 Mn: | c_2 = c_6 S: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + MnSO_4 + H_2O_2 ⟶ 2 H_2O + Na_2SO_4 + MnO_2

+ + ⟶ + +

sodium hydroxide + manganese(II) sulfate + hydrogen peroxide ⟶ water + sodium sulfate + manganese dioxide

Construct the equilibrium constant, K, expression for: NaOH + MnSO_4 + H_2O_2 ⟶ H_2O + Na_2SO_4 + MnO_2 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 NaOH + MnSO_4 + H_2O_2 ⟶ 2 H_2O + Na_2SO_4 + MnO_2 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 NaOH | 2 | -2 MnSO_4 | 1 | -1 H_2O_2 | 1 | -1 H_2O | 2 | 2 Na_2SO_4 | 1 | 1 MnO_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 2 | -2 | ([NaOH])^(-2) MnSO_4 | 1 | -1 | ([MnSO4])^(-1) H_2O_2 | 1 | -1 | ([H2O2])^(-1) H_2O | 2 | 2 | ([H2O])^2 Na_2SO_4 | 1 | 1 | [Na2SO4] MnO_2 | 1 | 1 | [MnO2] 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 = ([NaOH])^(-2) ([MnSO4])^(-1) ([H2O2])^(-1) ([H2O])^2 [Na2SO4] [MnO2] = (([H2O])^2 [Na2SO4] [MnO2])/(([NaOH])^2 [MnSO4] [H2O2])

Construct the rate of reaction expression for: NaOH + MnSO_4 + H_2O_2 ⟶ H_2O + Na_2SO_4 + MnO_2 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 NaOH + MnSO_4 + H_2O_2 ⟶ 2 H_2O + Na_2SO_4 + MnO_2 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 NaOH | 2 | -2 MnSO_4 | 1 | -1 H_2O_2 | 1 | -1 H_2O | 2 | 2 Na_2SO_4 | 1 | 1 MnO_2 | 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 NaOH | 2 | -2 | -1/2 (Δ[NaOH])/(Δt) MnSO_4 | 1 | -1 | -(Δ[MnSO4])/(Δt) H_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) Na_2SO_4 | 1 | 1 | (Δ[Na2SO4])/(Δt) MnO_2 | 1 | 1 | (Δ[MnO2])/(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[NaOH])/(Δt) = -(Δ[MnSO4])/(Δt) = -(Δ[H2O2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[Na2SO4])/(Δt) = (Δ[MnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | manganese(II) sulfate | hydrogen peroxide | water | sodium sulfate | manganese dioxide formula | NaOH | MnSO_4 | H_2O_2 | H_2O | Na_2SO_4 | MnO_2 Hill formula | HNaO | MnSO_4 | H_2O_2 | H_2O | Na_2O_4S | MnO_2 name | sodium hydroxide | manganese(II) sulfate | hydrogen peroxide | water | sodium sulfate | manganese dioxide IUPAC name | sodium hydroxide | manganese(+2) cation sulfate | hydrogen peroxide | water | disodium sulfate | dioxomanganese