KMnO4 + C8H8 = H2O + KOH + MnO2 + K2CO3 + C7H5O2K

KMnO_4 potassium permanganate + C_6H_5CH=CH_2 styrene ⟶ H_2O water + KOH potassium hydroxide + MnO_2 manganese dioxide + K_2CO_3 pearl ash + C_6H_5COOK potassium benzoate

Balance the chemical equation algebraically: KMnO_4 + C_6H_5CH=CH_2 ⟶ H_2O + KOH + MnO_2 + K_2CO_3 + C_6H_5COOK Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 + c_2 C_6H_5CH=CH_2 ⟶ c_3 H_2O + c_4 KOH + c_5 MnO_2 + c_6 K_2CO_3 + c_7 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 + 2 c_6 + c_7 Mn: | c_1 = c_5 O: | 4 c_1 = c_3 + c_4 + 2 c_5 + 3 c_6 + 2 c_7 C: | 8 c_2 = c_6 + 7 c_7 H: | 8 c_2 = 2 c_3 + c_4 + 5 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_4 = 1 and solve the system of equations for the remaining coefficients: c_2 = (9 c_1)/40 + 3/4 c_3 = (2 c_1)/5 c_4 = 1 c_5 = c_1 c_6 = (2 c_1)/5 - 1 c_7 = c_1/5 + 1 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 10 and solve for the remaining coefficients: c_1 = 10 c_2 = 3 c_3 = 4 c_4 = 1 c_5 = 10 c_6 = 3 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 KMnO_4 + 3 C_6H_5CH=CH_2 ⟶ 4 H_2O + KOH + 10 MnO_2 + 3 K_2CO_3 + 3 C_6H_5COOK

+ ⟶ + + + +

potassium permanganate + styrene ⟶ water + potassium hydroxide + manganese dioxide + pearl ash + potassium benzoate

Construct the equilibrium constant, K, expression for: KMnO_4 + C_6H_5CH=CH_2 ⟶ H_2O + KOH + MnO_2 + K_2CO_3 + 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: 10 KMnO_4 + 3 C_6H_5CH=CH_2 ⟶ 4 H_2O + KOH + 10 MnO_2 + 3 K_2CO_3 + 3 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 | 10 | -10 C_6H_5CH=CH_2 | 3 | -3 H_2O | 4 | 4 KOH | 1 | 1 MnO_2 | 10 | 10 K_2CO_3 | 3 | 3 C_6H_5COOK | 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 | 10 | -10 | ([KMnO4])^(-10) C_6H_5CH=CH_2 | 3 | -3 | ([C6H5CH=CH2])^(-3) H_2O | 4 | 4 | ([H2O])^4 KOH | 1 | 1 | [KOH] MnO_2 | 10 | 10 | ([MnO2])^10 K_2CO_3 | 3 | 3 | ([K2CO3])^3 C_6H_5COOK | 3 | 3 | ([C6H5COOK])^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])^(-10) ([C6H5CH=CH2])^(-3) ([H2O])^4 [KOH] ([MnO2])^10 ([K2CO3])^3 ([C6H5COOK])^3 = (([H2O])^4 [KOH] ([MnO2])^10 ([K2CO3])^3 ([C6H5COOK])^3)/(([KMnO4])^10 ([C6H5CH=CH2])^3)

Construct the rate of reaction expression for: KMnO_4 + C_6H_5CH=CH_2 ⟶ H_2O + KOH + MnO_2 + K_2CO_3 + 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: 10 KMnO_4 + 3 C_6H_5CH=CH_2 ⟶ 4 H_2O + KOH + 10 MnO_2 + 3 K_2CO_3 + 3 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 | 10 | -10 C_6H_5CH=CH_2 | 3 | -3 H_2O | 4 | 4 KOH | 1 | 1 MnO_2 | 10 | 10 K_2CO_3 | 3 | 3 C_6H_5COOK | 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 | 10 | -10 | -1/10 (Δ[KMnO4])/(Δt) C_6H_5CH=CH_2 | 3 | -3 | -1/3 (Δ[C6H5CH=CH2])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) KOH | 1 | 1 | (Δ[KOH])/(Δt) MnO_2 | 10 | 10 | 1/10 (Δ[MnO2])/(Δt) K_2CO_3 | 3 | 3 | 1/3 (Δ[K2CO3])/(Δt) C_6H_5COOK | 3 | 3 | 1/3 (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 = -1/10 (Δ[KMnO4])/(Δt) = -1/3 (Δ[C6H5CH=CH2])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[KOH])/(Δt) = 1/10 (Δ[MnO2])/(Δt) = 1/3 (Δ[K2CO3])/(Δt) = 1/3 (Δ[C6H5COOK])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium permanganate | styrene | water | potassium hydroxide | manganese dioxide | pearl ash | potassium benzoate formula | KMnO_4 | C_6H_5CH=CH_2 | H_2O | KOH | MnO_2 | K_2CO_3 | C_6H_5COOK Hill formula | KMnO_4 | C_8H_8 | H_2O | HKO | MnO_2 | CK_2O_3 | C_7H_5KO_2 name | potassium permanganate | styrene | water | potassium hydroxide | manganese dioxide | pearl ash | potassium benzoate IUPAC name | potassium permanganate | vinylbenzene | water | potassium hydroxide | dioxomanganese | dipotassium carbonate | potassium benzoate