KOH + KMnO4 + CH3CH2CH2OH = H2O + K2MnO4 + CH3CH2COOK

KOH potassium hydroxide + KMnO_4 potassium permanganate + CH_3CH_2CH_2OH N-propanol ⟶ H_2O water + K_2MnO_4 potassium manganate + CH3CH2COOK

Balance the chemical equation algebraically: KOH + KMnO_4 + CH_3CH_2CH_2OH ⟶ H_2O + K_2MnO_4 + CH3CH2COOK Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 KMnO_4 + c_3 CH_3CH_2CH_2OH ⟶ c_4 H_2O + c_5 K_2MnO_4 + c_6 CH3CH2COOK Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Mn and C: H: | c_1 + 8 c_3 = 2 c_4 + 5 c_6 K: | c_1 + c_2 = 2 c_5 + c_6 O: | c_1 + 4 c_2 + c_3 = c_4 + 4 c_5 + 2 c_6 Mn: | c_2 = c_5 C: | 3 c_3 = 3 c_6 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 = 5 c_2 = 4 c_3 = 1 c_4 = 4 c_5 = 4 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 KOH + 4 KMnO_4 + CH_3CH_2CH_2OH ⟶ 4 H_2O + 4 K_2MnO_4 + CH3CH2COOK

+ + ⟶ + + CH3CH2COOK

potassium hydroxide + potassium permanganate + N-propanol ⟶ water + potassium manganate + CH3CH2COOK

Construct the equilibrium constant, K, expression for: KOH + KMnO_4 + CH_3CH_2CH_2OH ⟶ H_2O + K_2MnO_4 + CH3CH2COOK 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: 5 KOH + 4 KMnO_4 + CH_3CH_2CH_2OH ⟶ 4 H_2O + 4 K_2MnO_4 + CH3CH2COOK 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 KOH | 5 | -5 KMnO_4 | 4 | -4 CH_3CH_2CH_2OH | 1 | -1 H_2O | 4 | 4 K_2MnO_4 | 4 | 4 CH3CH2COOK | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 5 | -5 | ([KOH])^(-5) KMnO_4 | 4 | -4 | ([KMnO4])^(-4) CH_3CH_2CH_2OH | 1 | -1 | ([CH3CH2CH2OH])^(-1) H_2O | 4 | 4 | ([H2O])^4 K_2MnO_4 | 4 | 4 | ([K2MnO4])^4 CH3CH2COOK | 1 | 1 | [CH3CH2COOK] 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 = ([KOH])^(-5) ([KMnO4])^(-4) ([CH3CH2CH2OH])^(-1) ([H2O])^4 ([K2MnO4])^4 [CH3CH2COOK] = (([H2O])^4 ([K2MnO4])^4 [CH3CH2COOK])/(([KOH])^5 ([KMnO4])^4 [CH3CH2CH2OH])

Construct the rate of reaction expression for: KOH + KMnO_4 + CH_3CH_2CH_2OH ⟶ H_2O + K_2MnO_4 + CH3CH2COOK 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: 5 KOH + 4 KMnO_4 + CH_3CH_2CH_2OH ⟶ 4 H_2O + 4 K_2MnO_4 + CH3CH2COOK 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 KOH | 5 | -5 KMnO_4 | 4 | -4 CH_3CH_2CH_2OH | 1 | -1 H_2O | 4 | 4 K_2MnO_4 | 4 | 4 CH3CH2COOK | 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 KOH | 5 | -5 | -1/5 (Δ[KOH])/(Δt) KMnO_4 | 4 | -4 | -1/4 (Δ[KMnO4])/(Δt) CH_3CH_2CH_2OH | 1 | -1 | -(Δ[CH3CH2CH2OH])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) K_2MnO_4 | 4 | 4 | 1/4 (Δ[K2MnO4])/(Δt) CH3CH2COOK | 1 | 1 | (Δ[CH3CH2COOK])/(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 = -1/5 (Δ[KOH])/(Δt) = -1/4 (Δ[KMnO4])/(Δt) = -(Δ[CH3CH2CH2OH])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/4 (Δ[K2MnO4])/(Δt) = (Δ[CH3CH2COOK])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | potassium permanganate | N-propanol | water | potassium manganate | CH3CH2COOK formula | KOH | KMnO_4 | CH_3CH_2CH_2OH | H_2O | K_2MnO_4 | CH3CH2COOK Hill formula | HKO | KMnO_4 | C_3H_8O | H_2O | K_2MnO_4 | C3H5KO2 name | potassium hydroxide | potassium permanganate | N-propanol | water | potassium manganate | IUPAC name | potassium hydroxide | potassium permanganate | propan-1-ol | water | dipotassium dioxido-dioxomanganese |