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KMnO4 + C6H5C2H5 = H2O + KOH + MnO2 + K2CO3 + C6H5COOH

Input interpretation

KMnO_4 potassium permanganate + C_6H_5C_2H_5 ethylbenzene ⟶ H_2O water + KOH potassium hydroxide + MnO_2 manganese dioxide + K_2CO_3 pearl ash + C_6H_5COOH benzoic acid
KMnO_4 potassium permanganate + C_6H_5C_2H_5 ethylbenzene ⟶ H_2O water + KOH potassium hydroxide + MnO_2 manganese dioxide + K_2CO_3 pearl ash + C_6H_5COOH benzoic acid

Balanced equation

Balance the chemical equation algebraically: KMnO_4 + C_6H_5C_2H_5 ⟶ H_2O + KOH + MnO_2 + K_2CO_3 + C_6H_5COOH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 + c_2 C_6H_5C_2H_5 ⟶ c_3 H_2O + c_4 KOH + c_5 MnO_2 + c_6 K_2CO_3 + c_7 C_6H_5COOH 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 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: | 10 c_2 = 2 c_3 + c_4 + 6 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 = c_1/2 - 1 c_4 = 18/5 - (2 c_1)/5 c_5 = c_1 c_6 = (7 c_1)/10 - 9/5 c_7 = 7/5 - c_1/10 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 4 and solve for the remaining coefficients: c_1 = 4 c_2 = 1 c_3 = 1 c_4 = 2 c_5 = 4 c_6 = 1 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 KMnO_4 + C_6H_5C_2H_5 ⟶ H_2O + 2 KOH + 4 MnO_2 + K_2CO_3 + C_6H_5COOH
Balance the chemical equation algebraically: KMnO_4 + C_6H_5C_2H_5 ⟶ H_2O + KOH + MnO_2 + K_2CO_3 + C_6H_5COOH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 + c_2 C_6H_5C_2H_5 ⟶ c_3 H_2O + c_4 KOH + c_5 MnO_2 + c_6 K_2CO_3 + c_7 C_6H_5COOH 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 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: | 10 c_2 = 2 c_3 + c_4 + 6 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 = c_1/2 - 1 c_4 = 18/5 - (2 c_1)/5 c_5 = c_1 c_6 = (7 c_1)/10 - 9/5 c_7 = 7/5 - c_1/10 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 4 and solve for the remaining coefficients: c_1 = 4 c_2 = 1 c_3 = 1 c_4 = 2 c_5 = 4 c_6 = 1 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 KMnO_4 + C_6H_5C_2H_5 ⟶ H_2O + 2 KOH + 4 MnO_2 + K_2CO_3 + C_6H_5COOH

Structures

+ ⟶ + + + +
+ ⟶ + + + +

Names

potassium permanganate + ethylbenzene ⟶ water + potassium hydroxide + manganese dioxide + pearl ash + benzoic acid
potassium permanganate + ethylbenzene ⟶ water + potassium hydroxide + manganese dioxide + pearl ash + benzoic acid

Equilibrium constant

Construct the equilibrium constant, K, expression for: KMnO_4 + C_6H_5C_2H_5 ⟶ H_2O + KOH + MnO_2 + K_2CO_3 + C_6H_5COOH 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: 4 KMnO_4 + C_6H_5C_2H_5 ⟶ H_2O + 2 KOH + 4 MnO_2 + K_2CO_3 + C_6H_5COOH 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 | 4 | -4 C_6H_5C_2H_5 | 1 | -1 H_2O | 1 | 1 KOH | 2 | 2 MnO_2 | 4 | 4 K_2CO_3 | 1 | 1 C_6H_5COOH | 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 | 4 | -4 | ([KMnO4])^(-4) C_6H_5C_2H_5 | 1 | -1 | ([C6H5C2H5])^(-1) H_2O | 1 | 1 | [H2O] KOH | 2 | 2 | ([KOH])^2 MnO_2 | 4 | 4 | ([MnO2])^4 K_2CO_3 | 1 | 1 | [K2CO3] C_6H_5COOH | 1 | 1 | [C6H5COOH] 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])^(-4) ([C6H5C2H5])^(-1) [H2O] ([KOH])^2 ([MnO2])^4 [K2CO3] [C6H5COOH] = ([H2O] ([KOH])^2 ([MnO2])^4 [K2CO3] [C6H5COOH])/(([KMnO4])^4 [C6H5C2H5])
Construct the equilibrium constant, K, expression for: KMnO_4 + C_6H_5C_2H_5 ⟶ H_2O + KOH + MnO_2 + K_2CO_3 + C_6H_5COOH 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: 4 KMnO_4 + C_6H_5C_2H_5 ⟶ H_2O + 2 KOH + 4 MnO_2 + K_2CO_3 + C_6H_5COOH 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 | 4 | -4 C_6H_5C_2H_5 | 1 | -1 H_2O | 1 | 1 KOH | 2 | 2 MnO_2 | 4 | 4 K_2CO_3 | 1 | 1 C_6H_5COOH | 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 | 4 | -4 | ([KMnO4])^(-4) C_6H_5C_2H_5 | 1 | -1 | ([C6H5C2H5])^(-1) H_2O | 1 | 1 | [H2O] KOH | 2 | 2 | ([KOH])^2 MnO_2 | 4 | 4 | ([MnO2])^4 K_2CO_3 | 1 | 1 | [K2CO3] C_6H_5COOH | 1 | 1 | [C6H5COOH] 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])^(-4) ([C6H5C2H5])^(-1) [H2O] ([KOH])^2 ([MnO2])^4 [K2CO3] [C6H5COOH] = ([H2O] ([KOH])^2 ([MnO2])^4 [K2CO3] [C6H5COOH])/(([KMnO4])^4 [C6H5C2H5])

Rate of reaction

Construct the rate of reaction expression for: KMnO_4 + C_6H_5C_2H_5 ⟶ H_2O + KOH + MnO_2 + K_2CO_3 + C_6H_5COOH 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: 4 KMnO_4 + C_6H_5C_2H_5 ⟶ H_2O + 2 KOH + 4 MnO_2 + K_2CO_3 + C_6H_5COOH 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 | 4 | -4 C_6H_5C_2H_5 | 1 | -1 H_2O | 1 | 1 KOH | 2 | 2 MnO_2 | 4 | 4 K_2CO_3 | 1 | 1 C_6H_5COOH | 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 | 4 | -4 | -1/4 (Δ[KMnO4])/(Δt) C_6H_5C_2H_5 | 1 | -1 | -(Δ[C6H5C2H5])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) KOH | 2 | 2 | 1/2 (Δ[KOH])/(Δt) MnO_2 | 4 | 4 | 1/4 (Δ[MnO2])/(Δt) K_2CO_3 | 1 | 1 | (Δ[K2CO3])/(Δt) C_6H_5COOH | 1 | 1 | (Δ[C6H5COOH])/(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 = -1/4 (Δ[KMnO4])/(Δt) = -(Δ[C6H5C2H5])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[KOH])/(Δt) = 1/4 (Δ[MnO2])/(Δt) = (Δ[K2CO3])/(Δt) = (Δ[C6H5COOH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: KMnO_4 + C_6H_5C_2H_5 ⟶ H_2O + KOH + MnO_2 + K_2CO_3 + C_6H_5COOH 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: 4 KMnO_4 + C_6H_5C_2H_5 ⟶ H_2O + 2 KOH + 4 MnO_2 + K_2CO_3 + C_6H_5COOH 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 | 4 | -4 C_6H_5C_2H_5 | 1 | -1 H_2O | 1 | 1 KOH | 2 | 2 MnO_2 | 4 | 4 K_2CO_3 | 1 | 1 C_6H_5COOH | 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 | 4 | -4 | -1/4 (Δ[KMnO4])/(Δt) C_6H_5C_2H_5 | 1 | -1 | -(Δ[C6H5C2H5])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) KOH | 2 | 2 | 1/2 (Δ[KOH])/(Δt) MnO_2 | 4 | 4 | 1/4 (Δ[MnO2])/(Δt) K_2CO_3 | 1 | 1 | (Δ[K2CO3])/(Δt) C_6H_5COOH | 1 | 1 | (Δ[C6H5COOH])/(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 = -1/4 (Δ[KMnO4])/(Δt) = -(Δ[C6H5C2H5])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[KOH])/(Δt) = 1/4 (Δ[MnO2])/(Δt) = (Δ[K2CO3])/(Δt) = (Δ[C6H5COOH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| potassium permanganate | ethylbenzene | water | potassium hydroxide | manganese dioxide | pearl ash | benzoic acid formula | KMnO_4 | C_6H_5C_2H_5 | H_2O | KOH | MnO_2 | K_2CO_3 | C_6H_5COOH Hill formula | KMnO_4 | C_8H_10 | H_2O | HKO | MnO_2 | CK_2O_3 | C_7H_6O_2 name | potassium permanganate | ethylbenzene | water | potassium hydroxide | manganese dioxide | pearl ash | benzoic acid IUPAC name | potassium permanganate | ethylbenzene | water | potassium hydroxide | dioxomanganese | dipotassium carbonate | benzoic acid
| potassium permanganate | ethylbenzene | water | potassium hydroxide | manganese dioxide | pearl ash | benzoic acid formula | KMnO_4 | C_6H_5C_2H_5 | H_2O | KOH | MnO_2 | K_2CO_3 | C_6H_5COOH Hill formula | KMnO_4 | C_8H_10 | H_2O | HKO | MnO_2 | CK_2O_3 | C_7H_6O_2 name | potassium permanganate | ethylbenzene | water | potassium hydroxide | manganese dioxide | pearl ash | benzoic acid IUPAC name | potassium permanganate | ethylbenzene | water | potassium hydroxide | dioxomanganese | dipotassium carbonate | benzoic acid

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