KMnO4 + C2H2 = H2O + KOH + MnO2 + K2C2O4

KMnO_4 potassium permanganate + C_2H_2 acetylene ⟶ H_2O water + KOH potassium hydroxide + MnO_2 manganese dioxide + C_2K_2O_4 potassium oxalate

Balance the chemical equation algebraically: KMnO_4 + C_2H_2 ⟶ H_2O + KOH + MnO_2 + C_2K_2O_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 + c_2 C_2H_2 ⟶ c_3 H_2O + c_4 KOH + c_5 MnO_2 + c_6 C_2K_2O_4 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 = c_4 + 2 c_6 Mn: | c_1 = c_5 O: | 4 c_1 = c_3 + c_4 + 2 c_5 + 4 c_6 C: | 2 c_2 = 2 c_6 H: | 2 c_2 = 2 c_3 + c_4 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 = 4 c_2 = 3/2 c_3 = 1 c_4 = 1 c_5 = 4 c_6 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 8 c_2 = 3 c_3 = 2 c_4 = 2 c_5 = 8 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 KMnO_4 + 3 C_2H_2 ⟶ 2 H_2O + 2 KOH + 8 MnO_2 + 3 C_2K_2O_4

+ ⟶ + + +

potassium permanganate + acetylene ⟶ water + potassium hydroxide + manganese dioxide + potassium oxalate

Construct the equilibrium constant, K, expression for: KMnO_4 + C_2H_2 ⟶ H_2O + KOH + MnO_2 + C_2K_2O_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: 8 KMnO_4 + 3 C_2H_2 ⟶ 2 H_2O + 2 KOH + 8 MnO_2 + 3 C_2K_2O_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 KMnO_4 | 8 | -8 C_2H_2 | 3 | -3 H_2O | 2 | 2 KOH | 2 | 2 MnO_2 | 8 | 8 C_2K_2O_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KMnO_4 | 8 | -8 | ([KMnO4])^(-8) C_2H_2 | 3 | -3 | ([C2H2])^(-3) H_2O | 2 | 2 | ([H2O])^2 KOH | 2 | 2 | ([KOH])^2 MnO_2 | 8 | 8 | ([MnO2])^8 C_2K_2O_4 | 3 | 3 | ([C2K2O4])^3 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])^(-8) ([C2H2])^(-3) ([H2O])^2 ([KOH])^2 ([MnO2])^8 ([C2K2O4])^3 = (([H2O])^2 ([KOH])^2 ([MnO2])^8 ([C2K2O4])^3)/(([KMnO4])^8 ([C2H2])^3)

Construct the rate of reaction expression for: KMnO_4 + C_2H_2 ⟶ H_2O + KOH + MnO_2 + C_2K_2O_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: 8 KMnO_4 + 3 C_2H_2 ⟶ 2 H_2O + 2 KOH + 8 MnO_2 + 3 C_2K_2O_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 KMnO_4 | 8 | -8 C_2H_2 | 3 | -3 H_2O | 2 | 2 KOH | 2 | 2 MnO_2 | 8 | 8 C_2K_2O_4 | 3 | 3 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 | 8 | -8 | -1/8 (Δ[KMnO4])/(Δt) C_2H_2 | 3 | -3 | -1/3 (Δ[C2H2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) KOH | 2 | 2 | 1/2 (Δ[KOH])/(Δt) MnO_2 | 8 | 8 | 1/8 (Δ[MnO2])/(Δt) C_2K_2O_4 | 3 | 3 | 1/3 (Δ[C2K2O4])/(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 = -1/8 (Δ[KMnO4])/(Δt) = -1/3 (Δ[C2H2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[KOH])/(Δt) = 1/8 (Δ[MnO2])/(Δt) = 1/3 (Δ[C2K2O4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium permanganate | acetylene | water | potassium hydroxide | manganese dioxide | potassium oxalate formula | KMnO_4 | C_2H_2 | H_2O | KOH | MnO_2 | C_2K_2O_4 Hill formula | KMnO_4 | C_2H_2 | H_2O | HKO | MnO_2 | C_2K_2O_4 name | potassium permanganate | acetylene | water | potassium hydroxide | manganese dioxide | potassium oxalate IUPAC name | potassium permanganate | acetylene | water | potassium hydroxide | dioxomanganese | dipotassium oxalate