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H2SO4 + KMnO4 + C8H12 = H2O + CO2 + K2SO4 + MnSO4 + C7H10O6

Input interpretation

H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + C_6H_9CH=CH_2 4-vinylcyclohexene ⟶ H_2O water + CO_2 carbon dioxide + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + C_7H_10O_6 3-dehydroquinic acid
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + C_6H_9CH=CH_2 4-vinylcyclohexene ⟶ H_2O water + CO_2 carbon dioxide + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + C_7H_10O_6 3-dehydroquinic acid

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + C_6H_9CH=CH_2 ⟶ H_2O + CO_2 + K_2SO_4 + MnSO_4 + C_7H_10O_6 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 C_6H_9CH=CH_2 ⟶ c_4 H_2O + c_5 CO_2 + c_6 K_2SO_4 + c_7 MnSO_4 + c_8 C_7H_10O_6 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 + 12 c_3 = 2 c_4 + 10 c_8 O: | 4 c_1 + 4 c_2 = c_4 + 2 c_5 + 4 c_6 + 4 c_7 + 6 c_8 S: | c_1 = c_6 + c_7 K: | c_2 = 2 c_6 Mn: | c_2 = c_7 C: | 8 c_3 = c_5 + 7 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)/66 + 13/22 c_4 = (16 c_1)/11 - 16/11 c_5 = (20 c_1)/33 - 25/11 c_6 = c_1/3 c_7 = (2 c_1)/3 c_8 = 1 Multiply by the least common denominator, 22, to eliminate fractional coefficients: c_2 = (2 c_1)/3 c_3 = (5 c_1)/66 + 13 c_4 = (16 c_1)/11 - 32 c_5 = (20 c_1)/33 - 50 c_6 = c_1/3 c_7 = (2 c_1)/3 c_8 = 22 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 132 and solve for the remaining coefficients: c_1 = 132 c_2 = 88 c_3 = 23 c_4 = 160 c_5 = 30 c_6 = 44 c_7 = 88 c_8 = 22 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 132 H_2SO_4 + 88 KMnO_4 + 23 C_6H_9CH=CH_2 ⟶ 160 H_2O + 30 CO_2 + 44 K_2SO_4 + 88 MnSO_4 + 22 C_7H_10O_6
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + C_6H_9CH=CH_2 ⟶ H_2O + CO_2 + K_2SO_4 + MnSO_4 + C_7H_10O_6 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 C_6H_9CH=CH_2 ⟶ c_4 H_2O + c_5 CO_2 + c_6 K_2SO_4 + c_7 MnSO_4 + c_8 C_7H_10O_6 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 + 12 c_3 = 2 c_4 + 10 c_8 O: | 4 c_1 + 4 c_2 = c_4 + 2 c_5 + 4 c_6 + 4 c_7 + 6 c_8 S: | c_1 = c_6 + c_7 K: | c_2 = 2 c_6 Mn: | c_2 = c_7 C: | 8 c_3 = c_5 + 7 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)/66 + 13/22 c_4 = (16 c_1)/11 - 16/11 c_5 = (20 c_1)/33 - 25/11 c_6 = c_1/3 c_7 = (2 c_1)/3 c_8 = 1 Multiply by the least common denominator, 22, to eliminate fractional coefficients: c_2 = (2 c_1)/3 c_3 = (5 c_1)/66 + 13 c_4 = (16 c_1)/11 - 32 c_5 = (20 c_1)/33 - 50 c_6 = c_1/3 c_7 = (2 c_1)/3 c_8 = 22 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 132 and solve for the remaining coefficients: c_1 = 132 c_2 = 88 c_3 = 23 c_4 = 160 c_5 = 30 c_6 = 44 c_7 = 88 c_8 = 22 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 132 H_2SO_4 + 88 KMnO_4 + 23 C_6H_9CH=CH_2 ⟶ 160 H_2O + 30 CO_2 + 44 K_2SO_4 + 88 MnSO_4 + 22 C_7H_10O_6

Structures

+ + ⟶ + + + +
+ + ⟶ + + + +

Names

sulfuric acid + potassium permanganate + 4-vinylcyclohexene ⟶ water + carbon dioxide + potassium sulfate + manganese(II) sulfate + 3-dehydroquinic acid
sulfuric acid + potassium permanganate + 4-vinylcyclohexene ⟶ water + carbon dioxide + potassium sulfate + manganese(II) sulfate + 3-dehydroquinic acid

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + C_6H_9CH=CH_2 ⟶ H_2O + CO_2 + K_2SO_4 + MnSO_4 + C_7H_10O_6 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: 132 H_2SO_4 + 88 KMnO_4 + 23 C_6H_9CH=CH_2 ⟶ 160 H_2O + 30 CO_2 + 44 K_2SO_4 + 88 MnSO_4 + 22 C_7H_10O_6 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 | 132 | -132 KMnO_4 | 88 | -88 C_6H_9CH=CH_2 | 23 | -23 H_2O | 160 | 160 CO_2 | 30 | 30 K_2SO_4 | 44 | 44 MnSO_4 | 88 | 88 C_7H_10O_6 | 22 | 22 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 132 | -132 | ([H2SO4])^(-132) KMnO_4 | 88 | -88 | ([KMnO4])^(-88) C_6H_9CH=CH_2 | 23 | -23 | ([C6H9CH=CH2])^(-23) H_2O | 160 | 160 | ([H2O])^160 CO_2 | 30 | 30 | ([CO2])^30 K_2SO_4 | 44 | 44 | ([K2SO4])^44 MnSO_4 | 88 | 88 | ([MnSO4])^88 C_7H_10O_6 | 22 | 22 | ([C7H10O6])^22 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])^(-132) ([KMnO4])^(-88) ([C6H9CH=CH2])^(-23) ([H2O])^160 ([CO2])^30 ([K2SO4])^44 ([MnSO4])^88 ([C7H10O6])^22 = (([H2O])^160 ([CO2])^30 ([K2SO4])^44 ([MnSO4])^88 ([C7H10O6])^22)/(([H2SO4])^132 ([KMnO4])^88 ([C6H9CH=CH2])^23)
Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + C_6H_9CH=CH_2 ⟶ H_2O + CO_2 + K_2SO_4 + MnSO_4 + C_7H_10O_6 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: 132 H_2SO_4 + 88 KMnO_4 + 23 C_6H_9CH=CH_2 ⟶ 160 H_2O + 30 CO_2 + 44 K_2SO_4 + 88 MnSO_4 + 22 C_7H_10O_6 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 | 132 | -132 KMnO_4 | 88 | -88 C_6H_9CH=CH_2 | 23 | -23 H_2O | 160 | 160 CO_2 | 30 | 30 K_2SO_4 | 44 | 44 MnSO_4 | 88 | 88 C_7H_10O_6 | 22 | 22 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 132 | -132 | ([H2SO4])^(-132) KMnO_4 | 88 | -88 | ([KMnO4])^(-88) C_6H_9CH=CH_2 | 23 | -23 | ([C6H9CH=CH2])^(-23) H_2O | 160 | 160 | ([H2O])^160 CO_2 | 30 | 30 | ([CO2])^30 K_2SO_4 | 44 | 44 | ([K2SO4])^44 MnSO_4 | 88 | 88 | ([MnSO4])^88 C_7H_10O_6 | 22 | 22 | ([C7H10O6])^22 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])^(-132) ([KMnO4])^(-88) ([C6H9CH=CH2])^(-23) ([H2O])^160 ([CO2])^30 ([K2SO4])^44 ([MnSO4])^88 ([C7H10O6])^22 = (([H2O])^160 ([CO2])^30 ([K2SO4])^44 ([MnSO4])^88 ([C7H10O6])^22)/(([H2SO4])^132 ([KMnO4])^88 ([C6H9CH=CH2])^23)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + C_6H_9CH=CH_2 ⟶ H_2O + CO_2 + K_2SO_4 + MnSO_4 + C_7H_10O_6 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: 132 H_2SO_4 + 88 KMnO_4 + 23 C_6H_9CH=CH_2 ⟶ 160 H_2O + 30 CO_2 + 44 K_2SO_4 + 88 MnSO_4 + 22 C_7H_10O_6 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 | 132 | -132 KMnO_4 | 88 | -88 C_6H_9CH=CH_2 | 23 | -23 H_2O | 160 | 160 CO_2 | 30 | 30 K_2SO_4 | 44 | 44 MnSO_4 | 88 | 88 C_7H_10O_6 | 22 | 22 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 | 132 | -132 | -1/132 (Δ[H2SO4])/(Δt) KMnO_4 | 88 | -88 | -1/88 (Δ[KMnO4])/(Δt) C_6H_9CH=CH_2 | 23 | -23 | -1/23 (Δ[C6H9CH=CH2])/(Δt) H_2O | 160 | 160 | 1/160 (Δ[H2O])/(Δt) CO_2 | 30 | 30 | 1/30 (Δ[CO2])/(Δt) K_2SO_4 | 44 | 44 | 1/44 (Δ[K2SO4])/(Δt) MnSO_4 | 88 | 88 | 1/88 (Δ[MnSO4])/(Δt) C_7H_10O_6 | 22 | 22 | 1/22 (Δ[C7H10O6])/(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 = -1/132 (Δ[H2SO4])/(Δt) = -1/88 (Δ[KMnO4])/(Δt) = -1/23 (Δ[C6H9CH=CH2])/(Δt) = 1/160 (Δ[H2O])/(Δt) = 1/30 (Δ[CO2])/(Δt) = 1/44 (Δ[K2SO4])/(Δt) = 1/88 (Δ[MnSO4])/(Δt) = 1/22 (Δ[C7H10O6])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + C_6H_9CH=CH_2 ⟶ H_2O + CO_2 + K_2SO_4 + MnSO_4 + C_7H_10O_6 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: 132 H_2SO_4 + 88 KMnO_4 + 23 C_6H_9CH=CH_2 ⟶ 160 H_2O + 30 CO_2 + 44 K_2SO_4 + 88 MnSO_4 + 22 C_7H_10O_6 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 | 132 | -132 KMnO_4 | 88 | -88 C_6H_9CH=CH_2 | 23 | -23 H_2O | 160 | 160 CO_2 | 30 | 30 K_2SO_4 | 44 | 44 MnSO_4 | 88 | 88 C_7H_10O_6 | 22 | 22 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 | 132 | -132 | -1/132 (Δ[H2SO4])/(Δt) KMnO_4 | 88 | -88 | -1/88 (Δ[KMnO4])/(Δt) C_6H_9CH=CH_2 | 23 | -23 | -1/23 (Δ[C6H9CH=CH2])/(Δt) H_2O | 160 | 160 | 1/160 (Δ[H2O])/(Δt) CO_2 | 30 | 30 | 1/30 (Δ[CO2])/(Δt) K_2SO_4 | 44 | 44 | 1/44 (Δ[K2SO4])/(Δt) MnSO_4 | 88 | 88 | 1/88 (Δ[MnSO4])/(Δt) C_7H_10O_6 | 22 | 22 | 1/22 (Δ[C7H10O6])/(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 = -1/132 (Δ[H2SO4])/(Δt) = -1/88 (Δ[KMnO4])/(Δt) = -1/23 (Δ[C6H9CH=CH2])/(Δt) = 1/160 (Δ[H2O])/(Δt) = 1/30 (Δ[CO2])/(Δt) = 1/44 (Δ[K2SO4])/(Δt) = 1/88 (Δ[MnSO4])/(Δt) = 1/22 (Δ[C7H10O6])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | potassium permanganate | 4-vinylcyclohexene | water | carbon dioxide | potassium sulfate | manganese(II) sulfate | 3-dehydroquinic acid formula | H_2SO_4 | KMnO_4 | C_6H_9CH=CH_2 | H_2O | CO_2 | K_2SO_4 | MnSO_4 | C_7H_10O_6 Hill formula | H_2O_4S | KMnO_4 | C_8H_12 | H_2O | CO_2 | K_2O_4S | MnSO_4 | C_7H_10O_6 name | sulfuric acid | potassium permanganate | 4-vinylcyclohexene | water | carbon dioxide | potassium sulfate | manganese(II) sulfate | 3-dehydroquinic acid IUPAC name | sulfuric acid | potassium permanganate | 4-vinylcyclohexene | water | carbon dioxide | dipotassium sulfate | manganese(+2) cation sulfate | (1R, 3R, 4S)-1, 3, 4-trihydroxy-5-oxocyclohexane-1-carboxylic acid
| sulfuric acid | potassium permanganate | 4-vinylcyclohexene | water | carbon dioxide | potassium sulfate | manganese(II) sulfate | 3-dehydroquinic acid formula | H_2SO_4 | KMnO_4 | C_6H_9CH=CH_2 | H_2O | CO_2 | K_2SO_4 | MnSO_4 | C_7H_10O_6 Hill formula | H_2O_4S | KMnO_4 | C_8H_12 | H_2O | CO_2 | K_2O_4S | MnSO_4 | C_7H_10O_6 name | sulfuric acid | potassium permanganate | 4-vinylcyclohexene | water | carbon dioxide | potassium sulfate | manganese(II) sulfate | 3-dehydroquinic acid IUPAC name | sulfuric acid | potassium permanganate | 4-vinylcyclohexene | water | carbon dioxide | dipotassium sulfate | manganese(+2) cation sulfate | (1R, 3R, 4S)-1, 3, 4-trihydroxy-5-oxocyclohexane-1-carboxylic acid

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