H2O + KMnO4 + C4H9OH = CO2 + KOH + MnO2 + C3H9O

H_2O water + KMnO_4 potassium permanganate + CH_3(CH_2)_3OH 1-butanol ⟶ CO_2 carbon dioxide + KOH potassium hydroxide + MnO_2 manganese dioxide + C3H9O

Balance the chemical equation algebraically: H_2O + KMnO_4 + CH_3(CH_2)_3OH ⟶ CO_2 + KOH + MnO_2 + C3H9O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KMnO_4 + c_3 CH_3(CH_2)_3OH ⟶ c_4 CO_2 + c_5 KOH + c_6 MnO_2 + c_7 C3H9O Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K, Mn and C: H: | 2 c_1 + 10 c_3 = c_5 + 9 c_7 O: | c_1 + 4 c_2 + c_3 = 2 c_4 + c_5 + 2 c_6 + c_7 K: | c_2 = c_5 Mn: | c_2 = c_6 C: | 4 c_3 = c_4 + 3 c_7 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_2 = 1 c_3 = (19 c_1)/13 + 4/13 c_4 = (4 c_1)/13 + 7/13 c_5 = 1 c_6 = 1 c_7 = (24 c_1)/13 + 3/13 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_2 = 2 c_3 = (19 c_1)/13 + 8/13 c_4 = (4 c_1)/13 + 14/13 c_5 = 2 c_6 = 2 c_7 = (24 c_1)/13 + 6/13 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 3 and solve for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 5 c_4 = 2 c_5 = 2 c_6 = 2 c_7 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 2 KMnO_4 + 5 CH_3(CH_2)_3OH ⟶ 2 CO_2 + 2 KOH + 2 MnO_2 + 6 C3H9O

+ + ⟶ + + + C3H9O

water + potassium permanganate + 1-butanol ⟶ carbon dioxide + potassium hydroxide + manganese dioxide + C3H9O

Construct the equilibrium constant, K, expression for: H_2O + KMnO_4 + CH_3(CH_2)_3OH ⟶ CO_2 + KOH + MnO_2 + C3H9O 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: 3 H_2O + 2 KMnO_4 + 5 CH_3(CH_2)_3OH ⟶ 2 CO_2 + 2 KOH + 2 MnO_2 + 6 C3H9O 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 H_2O | 3 | -3 KMnO_4 | 2 | -2 CH_3(CH_2)_3OH | 5 | -5 CO_2 | 2 | 2 KOH | 2 | 2 MnO_2 | 2 | 2 C3H9O | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) CH_3(CH_2)_3OH | 5 | -5 | ([CH3(CH2)3OH])^(-5) CO_2 | 2 | 2 | ([CO2])^2 KOH | 2 | 2 | ([KOH])^2 MnO_2 | 2 | 2 | ([MnO2])^2 C3H9O | 6 | 6 | ([C3H9O])^6 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 = ([H2O])^(-3) ([KMnO4])^(-2) ([CH3(CH2)3OH])^(-5) ([CO2])^2 ([KOH])^2 ([MnO2])^2 ([C3H9O])^6 = (([CO2])^2 ([KOH])^2 ([MnO2])^2 ([C3H9O])^6)/(([H2O])^3 ([KMnO4])^2 ([CH3(CH2)3OH])^5)

Construct the rate of reaction expression for: H_2O + KMnO_4 + CH_3(CH_2)_3OH ⟶ CO_2 + KOH + MnO_2 + C3H9O 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: 3 H_2O + 2 KMnO_4 + 5 CH_3(CH_2)_3OH ⟶ 2 CO_2 + 2 KOH + 2 MnO_2 + 6 C3H9O 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 H_2O | 3 | -3 KMnO_4 | 2 | -2 CH_3(CH_2)_3OH | 5 | -5 CO_2 | 2 | 2 KOH | 2 | 2 MnO_2 | 2 | 2 C3H9O | 6 | 6 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 H_2O | 3 | -3 | -1/3 (Δ[H2O])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) CH_3(CH_2)_3OH | 5 | -5 | -1/5 (Δ[CH3(CH2)3OH])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) KOH | 2 | 2 | 1/2 (Δ[KOH])/(Δt) MnO_2 | 2 | 2 | 1/2 (Δ[MnO2])/(Δt) C3H9O | 6 | 6 | 1/6 (Δ[C3H9O])/(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 = -1/3 (Δ[H2O])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/5 (Δ[CH3(CH2)3OH])/(Δt) = 1/2 (Δ[CO2])/(Δt) = 1/2 (Δ[KOH])/(Δt) = 1/2 (Δ[MnO2])/(Δt) = 1/6 (Δ[C3H9O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | potassium permanganate | 1-butanol | carbon dioxide | potassium hydroxide | manganese dioxide | C3H9O formula | H_2O | KMnO_4 | CH_3(CH_2)_3OH | CO_2 | KOH | MnO_2 | C3H9O Hill formula | H_2O | KMnO_4 | C_4H_10O | CO_2 | HKO | MnO_2 | C3H9O name | water | potassium permanganate | 1-butanol | carbon dioxide | potassium hydroxide | manganese dioxide | IUPAC name | water | potassium permanganate | butan-1-ol | carbon dioxide | potassium hydroxide | dioxomanganese |