KMnO4 + H2C2O4 = H2O + CO2 + K2O + MnO3

KMnO_4 potassium permanganate + HO_2CCO_2H oxalic acid ⟶ H_2O water + CO_2 carbon dioxide + K_2O potassium oxide + MnO3

Balance the chemical equation algebraically: KMnO_4 + HO_2CCO_2H ⟶ H_2O + CO_2 + K_2O + MnO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 + c_2 HO_2CCO_2H ⟶ c_3 H_2O + c_4 CO_2 + c_5 K_2O + c_6 MnO3 Set the number of atoms in the reactants equal to the number of atoms in the products for K, Mn, O, C and H: K: | c_1 = 2 c_5 Mn: | c_1 = c_6 O: | 4 c_1 + 4 c_2 = c_3 + 2 c_4 + c_5 + 3 c_6 C: | 2 c_2 = 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_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 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KMnO_4 + HO_2CCO_2H ⟶ H_2O + 2 CO_2 + K_2O + 2 MnO3

+ ⟶ + + + MnO3

potassium permanganate + oxalic acid ⟶ water + carbon dioxide + potassium oxide + MnO3

Construct the equilibrium constant, K, expression for: KMnO_4 + HO_2CCO_2H ⟶ H_2O + CO_2 + K_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: 2 KMnO_4 + HO_2CCO_2H ⟶ H_2O + 2 CO_2 + K_2O + 2 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 KMnO_4 | 2 | -2 HO_2CCO_2H | 1 | -1 H_2O | 1 | 1 CO_2 | 2 | 2 K_2O | 1 | 1 MnO3 | 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 | 2 | -2 | ([KMnO4])^(-2) HO_2CCO_2H | 1 | -1 | ([HO2CCO2H])^(-1) H_2O | 1 | 1 | [H2O] CO_2 | 2 | 2 | ([CO2])^2 K_2O | 1 | 1 | [K2O] MnO3 | 2 | 2 | ([MnO3])^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])^(-2) ([HO2CCO2H])^(-1) [H2O] ([CO2])^2 [K2O] ([MnO3])^2 = ([H2O] ([CO2])^2 [K2O] ([MnO3])^2)/(([KMnO4])^2 [HO2CCO2H])

Construct the rate of reaction expression for: KMnO_4 + HO_2CCO_2H ⟶ H_2O + CO_2 + K_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: 2 KMnO_4 + HO_2CCO_2H ⟶ H_2O + 2 CO_2 + K_2O + 2 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 KMnO_4 | 2 | -2 HO_2CCO_2H | 1 | -1 H_2O | 1 | 1 CO_2 | 2 | 2 K_2O | 1 | 1 MnO3 | 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 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) HO_2CCO_2H | 1 | -1 | -(Δ[HO2CCO2H])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) K_2O | 1 | 1 | (Δ[K2O])/(Δt) MnO3 | 2 | 2 | 1/2 (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 = -1/2 (Δ[KMnO4])/(Δt) = -(Δ[HO2CCO2H])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[CO2])/(Δt) = (Δ[K2O])/(Δt) = 1/2 (Δ[MnO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium permanganate | oxalic acid | water | carbon dioxide | potassium oxide | MnO3 formula | KMnO_4 | HO_2CCO_2H | H_2O | CO_2 | K_2O | MnO3 Hill formula | KMnO_4 | C_2H_2O_4 | H_2O | CO_2 | K_2O | MnO3 name | potassium permanganate | oxalic acid | water | carbon dioxide | potassium oxide | IUPAC name | potassium permanganate | oxalic acid | water | carbon dioxide | dipotassium oxygen(2-) |