KMnO4 + C6H5(CH3) = H2O + KOH + MnO2 + C6H5COOK

KMnO_4 potassium permanganate + C_6H_5CH_3 toluene ⟶ H_2O water + KOH potassium hydroxide + MnO_2 manganese dioxide + C_6H_5COOK potassium benzoate

Balance the chemical equation algebraically: KMnO_4 + C_6H_5CH_3 ⟶ H_2O + KOH + MnO_2 + C_6H_5COOK Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 + c_2 C_6H_5CH_3 ⟶ c_3 H_2O + c_4 KOH + c_5 MnO_2 + c_6 C_6H_5COOK 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 + c_6 Mn: | c_1 = c_5 O: | 4 c_1 = c_3 + c_4 + 2 c_5 + 2 c_6 C: | 7 c_2 = 7 c_6 H: | 8 c_2 = 2 c_3 + c_4 + 5 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KMnO_4 + C_6H_5CH_3 ⟶ H_2O + KOH + 2 MnO_2 + C_6H_5COOK

+ ⟶ + + +

potassium permanganate + toluene ⟶ water + potassium hydroxide + manganese dioxide + potassium benzoate

Construct the equilibrium constant, K, expression for: KMnO_4 + C_6H_5CH_3 ⟶ H_2O + KOH + MnO_2 + C_6H_5COOK 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 + C_6H_5CH_3 ⟶ H_2O + KOH + 2 MnO_2 + C_6H_5COOK 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 C_6H_5CH_3 | 1 | -1 H_2O | 1 | 1 KOH | 1 | 1 MnO_2 | 2 | 2 C_6H_5COOK | 1 | 1 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) C_6H_5CH_3 | 1 | -1 | ([C6H5CH3])^(-1) H_2O | 1 | 1 | [H2O] KOH | 1 | 1 | [KOH] MnO_2 | 2 | 2 | ([MnO2])^2 C_6H_5COOK | 1 | 1 | [C6H5COOK] 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) ([C6H5CH3])^(-1) [H2O] [KOH] ([MnO2])^2 [C6H5COOK] = ([H2O] [KOH] ([MnO2])^2 [C6H5COOK])/(([KMnO4])^2 [C6H5CH3])

Construct the rate of reaction expression for: KMnO_4 + C_6H_5CH_3 ⟶ H_2O + KOH + MnO_2 + C_6H_5COOK 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 + C_6H_5CH_3 ⟶ H_2O + KOH + 2 MnO_2 + C_6H_5COOK 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 C_6H_5CH_3 | 1 | -1 H_2O | 1 | 1 KOH | 1 | 1 MnO_2 | 2 | 2 C_6H_5COOK | 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 KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) C_6H_5CH_3 | 1 | -1 | -(Δ[C6H5CH3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) KOH | 1 | 1 | (Δ[KOH])/(Δt) MnO_2 | 2 | 2 | 1/2 (Δ[MnO2])/(Δt) C_6H_5COOK | 1 | 1 | (Δ[C6H5COOK])/(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[C6H5CH3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[KOH])/(Δt) = 1/2 (Δ[MnO2])/(Δt) = (Δ[C6H5COOK])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium permanganate | toluene | water | potassium hydroxide | manganese dioxide | potassium benzoate formula | KMnO_4 | C_6H_5CH_3 | H_2O | KOH | MnO_2 | C_6H_5COOK Hill formula | KMnO_4 | C_7H_8 | H_2O | HKO | MnO_2 | C_7H_5KO_2 name | potassium permanganate | toluene | water | potassium hydroxide | manganese dioxide | potassium benzoate IUPAC name | potassium permanganate | methylbenzene | water | potassium hydroxide | dioxomanganese | potassium benzoate

| potassium permanganate | toluene | water | potassium hydroxide | manganese dioxide | potassium benzoate molar mass | 158.03 g/mol | 92.14 g/mol | 18.015 g/mol | 56.105 g/mol | 86.936 g/mol | 160.21 g/mol phase | solid (at STP) | liquid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) | melting point | 240 °C | -93 °C | 0 °C | 406 °C | 535 °C | boiling point | | 110.5 °C | 99.9839 °C | 1327 °C | | density | 1 g/cm^3 | 0.865 g/cm^3 | 1 g/cm^3 | 2.044 g/cm^3 | 5.03 g/cm^3 | solubility in water | | | | soluble | insoluble | surface tension | | 0.02971 N/m | 0.0728 N/m | | | dynamic viscosity | | 5.6×10^-4 Pa s (at 25 °C) | 8.9×10^-4 Pa s (at 25 °C) | 0.001 Pa s (at 550 °C) | | odor | odorless | sweet | benzene | odorless | | |