H2SO4 + KMnO4 + C4H9OH = H2O + CO2 + K2SO4 + MnSO4 + C3H6O

H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + CH_3(CH_2)_3OH 1-butanol ⟶ H_2O water + CO_2 carbon dioxide + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + CH_3COCH_3 acetone

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + CH_3(CH_2)_3OH ⟶ H_2O + CO_2 + K_2SO_4 + MnSO_4 + CH_3COCH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 CH_3(CH_2)_3OH ⟶ c_4 H_2O + c_5 CO_2 + c_6 K_2SO_4 + c_7 MnSO_4 + c_8 CH_3COCH_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and C: H: | 2 c_1 + 10 c_3 = 2 c_4 + 6 c_8 O: | 4 c_1 + 4 c_2 + c_3 = c_4 + 2 c_5 + 4 c_6 + 4 c_7 + c_8 S: | c_1 = c_6 + c_7 K: | c_2 = 2 c_6 Mn: | c_2 = c_7 C: | 4 c_3 = c_5 + 3 c_8 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_8 = 1 and solve the system of equations for the remaining coefficients: c_2 = (2 c_1)/3 c_3 = (5 c_1)/36 + 2/3 c_4 = (61 c_1)/36 + 1/3 c_5 = (5 c_1)/9 - 1/3 c_6 = c_1/3 c_7 = (2 c_1)/3 c_8 = 1 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_2 = (2 c_1)/3 c_3 = (5 c_1)/36 + 2 c_4 = (61 c_1)/36 + 1 c_5 = (5 c_1)/9 - 1 c_6 = c_1/3 c_7 = (2 c_1)/3 c_8 = 3 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 36 and solve for the remaining coefficients: c_1 = 36 c_2 = 24 c_3 = 7 c_4 = 62 c_5 = 19 c_6 = 12 c_7 = 24 c_8 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 36 H_2SO_4 + 24 KMnO_4 + 7 CH_3(CH_2)_3OH ⟶ 62 H_2O + 19 CO_2 + 12 K_2SO_4 + 24 MnSO_4 + 3 CH_3COCH_3

+ + ⟶ + + + +

sulfuric acid + potassium permanganate + 1-butanol ⟶ water + carbon dioxide + potassium sulfate + manganese(II) sulfate + acetone

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + CH_3(CH_2)_3OH ⟶ H_2O + CO_2 + K_2SO_4 + MnSO_4 + CH_3COCH_3 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: 36 H_2SO_4 + 24 KMnO_4 + 7 CH_3(CH_2)_3OH ⟶ 62 H_2O + 19 CO_2 + 12 K_2SO_4 + 24 MnSO_4 + 3 CH_3COCH_3 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_2SO_4 | 36 | -36 KMnO_4 | 24 | -24 CH_3(CH_2)_3OH | 7 | -7 H_2O | 62 | 62 CO_2 | 19 | 19 K_2SO_4 | 12 | 12 MnSO_4 | 24 | 24 CH_3COCH_3 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 36 | -36 | ([H2SO4])^(-36) KMnO_4 | 24 | -24 | ([KMnO4])^(-24) CH_3(CH_2)_3OH | 7 | -7 | ([CH3(CH2)3OH])^(-7) H_2O | 62 | 62 | ([H2O])^62 CO_2 | 19 | 19 | ([CO2])^19 K_2SO_4 | 12 | 12 | ([K2SO4])^12 MnSO_4 | 24 | 24 | ([MnSO4])^24 CH_3COCH_3 | 3 | 3 | ([CH3COCH3])^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 = ([H2SO4])^(-36) ([KMnO4])^(-24) ([CH3(CH2)3OH])^(-7) ([H2O])^62 ([CO2])^19 ([K2SO4])^12 ([MnSO4])^24 ([CH3COCH3])^3 = (([H2O])^62 ([CO2])^19 ([K2SO4])^12 ([MnSO4])^24 ([CH3COCH3])^3)/(([H2SO4])^36 ([KMnO4])^24 ([CH3(CH2)3OH])^7)

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + CH_3(CH_2)_3OH ⟶ H_2O + CO_2 + K_2SO_4 + MnSO_4 + CH_3COCH_3 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: 36 H_2SO_4 + 24 KMnO_4 + 7 CH_3(CH_2)_3OH ⟶ 62 H_2O + 19 CO_2 + 12 K_2SO_4 + 24 MnSO_4 + 3 CH_3COCH_3 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_2SO_4 | 36 | -36 KMnO_4 | 24 | -24 CH_3(CH_2)_3OH | 7 | -7 H_2O | 62 | 62 CO_2 | 19 | 19 K_2SO_4 | 12 | 12 MnSO_4 | 24 | 24 CH_3COCH_3 | 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 H_2SO_4 | 36 | -36 | -1/36 (Δ[H2SO4])/(Δt) KMnO_4 | 24 | -24 | -1/24 (Δ[KMnO4])/(Δt) CH_3(CH_2)_3OH | 7 | -7 | -1/7 (Δ[CH3(CH2)3OH])/(Δt) H_2O | 62 | 62 | 1/62 (Δ[H2O])/(Δt) CO_2 | 19 | 19 | 1/19 (Δ[CO2])/(Δt) K_2SO_4 | 12 | 12 | 1/12 (Δ[K2SO4])/(Δt) MnSO_4 | 24 | 24 | 1/24 (Δ[MnSO4])/(Δt) CH_3COCH_3 | 3 | 3 | 1/3 (Δ[CH3COCH3])/(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 = -1/36 (Δ[H2SO4])/(Δt) = -1/24 (Δ[KMnO4])/(Δt) = -1/7 (Δ[CH3(CH2)3OH])/(Δt) = 1/62 (Δ[H2O])/(Δt) = 1/19 (Δ[CO2])/(Δt) = 1/12 (Δ[K2SO4])/(Δt) = 1/24 (Δ[MnSO4])/(Δt) = 1/3 (Δ[CH3COCH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | potassium permanganate | 1-butanol | water | carbon dioxide | potassium sulfate | manganese(II) sulfate | acetone formula | H_2SO_4 | KMnO_4 | CH_3(CH_2)_3OH | H_2O | CO_2 | K_2SO_4 | MnSO_4 | CH_3COCH_3 Hill formula | H_2O_4S | KMnO_4 | C_4H_10O | H_2O | CO_2 | K_2O_4S | MnSO_4 | C_3H_6O name | sulfuric acid | potassium permanganate | 1-butanol | water | carbon dioxide | potassium sulfate | manganese(II) sulfate | acetone IUPAC name | sulfuric acid | potassium permanganate | butan-1-ol | water | carbon dioxide | dipotassium sulfate | manganese(+2) cation sulfate | acetone