Input interpretation
![H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + (CH_3)_2C=CH_2 isobutylene ⟶ H_2O water + CO_2 carbon dioxide + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + CH_3CH_2COOH propionic acid](../image_source/8cc6c96d43644316a39a86fc5f2e3450.png)
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + (CH_3)_2C=CH_2 isobutylene ⟶ H_2O water + CO_2 carbon dioxide + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + CH_3CH_2COOH propionic acid
Balanced equation
![Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + (CH_3)_2C=CH_2 ⟶ H_2O + CO_2 + K_2SO_4 + MnSO_4 + CH_3CH_2COOH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 (CH_3)_2C=CH_2 ⟶ c_4 H_2O + c_5 CO_2 + c_6 K_2SO_4 + c_7 MnSO_4 + c_8 CH_3CH_2COOH 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 + 8 c_3 = 2 c_4 + 6 c_8 O: | 4 c_1 + 4 c_2 = c_4 + 2 c_5 + 4 c_6 + 4 c_7 + 2 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_3 = 1 and solve the system of equations for the remaining coefficients: c_2 = (2 c_1)/3 c_3 = 1 c_4 = (12 c_1)/7 - 8/7 c_5 = (5 c_1)/7 - 8/7 c_6 = c_1/3 c_7 = (2 c_1)/3 c_8 = 12/7 - (5 c_1)/21 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 3 and solve for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 1 c_4 = 4 c_5 = 1 c_6 = 1 c_7 = 2 c_8 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + 2 KMnO_4 + (CH_3)_2C=CH_2 ⟶ 4 H_2O + CO_2 + K_2SO_4 + 2 MnSO_4 + CH_3CH_2COOH](../image_source/f62115bf554cbeba81eef988f4da362b.png)
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + (CH_3)_2C=CH_2 ⟶ H_2O + CO_2 + K_2SO_4 + MnSO_4 + CH_3CH_2COOH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 (CH_3)_2C=CH_2 ⟶ c_4 H_2O + c_5 CO_2 + c_6 K_2SO_4 + c_7 MnSO_4 + c_8 CH_3CH_2COOH 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 + 8 c_3 = 2 c_4 + 6 c_8 O: | 4 c_1 + 4 c_2 = c_4 + 2 c_5 + 4 c_6 + 4 c_7 + 2 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_3 = 1 and solve the system of equations for the remaining coefficients: c_2 = (2 c_1)/3 c_3 = 1 c_4 = (12 c_1)/7 - 8/7 c_5 = (5 c_1)/7 - 8/7 c_6 = c_1/3 c_7 = (2 c_1)/3 c_8 = 12/7 - (5 c_1)/21 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 3 and solve for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 1 c_4 = 4 c_5 = 1 c_6 = 1 c_7 = 2 c_8 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + 2 KMnO_4 + (CH_3)_2C=CH_2 ⟶ 4 H_2O + CO_2 + K_2SO_4 + 2 MnSO_4 + CH_3CH_2COOH
Structures
![+ + ⟶ + + + +](../image_source/0b68d7126b798618879e2f3be4e9430d.png)
+ + ⟶ + + + +
Names
![sulfuric acid + potassium permanganate + isobutylene ⟶ water + carbon dioxide + potassium sulfate + manganese(II) sulfate + propionic acid](../image_source/0ac77c80396c81f6550fae9b20d8cf8a.png)
sulfuric acid + potassium permanganate + isobutylene ⟶ water + carbon dioxide + potassium sulfate + manganese(II) sulfate + propionic acid
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + (CH_3)_2C=CH_2 ⟶ H_2O + CO_2 + K_2SO_4 + MnSO_4 + CH_3CH_2COOH 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: 3 H_2SO_4 + 2 KMnO_4 + (CH_3)_2C=CH_2 ⟶ 4 H_2O + CO_2 + K_2SO_4 + 2 MnSO_4 + CH_3CH_2COOH 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 | 3 | -3 KMnO_4 | 2 | -2 (CH_3)_2C=CH_2 | 1 | -1 H_2O | 4 | 4 CO_2 | 1 | 1 K_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 CH_3CH_2COOH | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 3 | -3 | ([H2SO4])^(-3) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) (CH_3)_2C=CH_2 | 1 | -1 | ([(CH3)2C=CH2])^(-1) H_2O | 4 | 4 | ([H2O])^4 CO_2 | 1 | 1 | [CO2] K_2SO_4 | 1 | 1 | [K2SO4] MnSO_4 | 2 | 2 | ([MnSO4])^2 CH_3CH_2COOH | 1 | 1 | [CH3CH2COOH] 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])^(-3) ([KMnO4])^(-2) ([(CH3)2C=CH2])^(-1) ([H2O])^4 [CO2] [K2SO4] ([MnSO4])^2 [CH3CH2COOH] = (([H2O])^4 [CO2] [K2SO4] ([MnSO4])^2 [CH3CH2COOH])/(([H2SO4])^3 ([KMnO4])^2 [(CH3)2C=CH2])](../image_source/8eea0083cc564b80b417030243b360a0.png)
Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + (CH_3)_2C=CH_2 ⟶ H_2O + CO_2 + K_2SO_4 + MnSO_4 + CH_3CH_2COOH 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: 3 H_2SO_4 + 2 KMnO_4 + (CH_3)_2C=CH_2 ⟶ 4 H_2O + CO_2 + K_2SO_4 + 2 MnSO_4 + CH_3CH_2COOH 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 | 3 | -3 KMnO_4 | 2 | -2 (CH_3)_2C=CH_2 | 1 | -1 H_2O | 4 | 4 CO_2 | 1 | 1 K_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 CH_3CH_2COOH | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 3 | -3 | ([H2SO4])^(-3) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) (CH_3)_2C=CH_2 | 1 | -1 | ([(CH3)2C=CH2])^(-1) H_2O | 4 | 4 | ([H2O])^4 CO_2 | 1 | 1 | [CO2] K_2SO_4 | 1 | 1 | [K2SO4] MnSO_4 | 2 | 2 | ([MnSO4])^2 CH_3CH_2COOH | 1 | 1 | [CH3CH2COOH] 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])^(-3) ([KMnO4])^(-2) ([(CH3)2C=CH2])^(-1) ([H2O])^4 [CO2] [K2SO4] ([MnSO4])^2 [CH3CH2COOH] = (([H2O])^4 [CO2] [K2SO4] ([MnSO4])^2 [CH3CH2COOH])/(([H2SO4])^3 ([KMnO4])^2 [(CH3)2C=CH2])
Rate of reaction
![Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + (CH_3)_2C=CH_2 ⟶ H_2O + CO_2 + K_2SO_4 + MnSO_4 + CH_3CH_2COOH 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: 3 H_2SO_4 + 2 KMnO_4 + (CH_3)_2C=CH_2 ⟶ 4 H_2O + CO_2 + K_2SO_4 + 2 MnSO_4 + CH_3CH_2COOH 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 | 3 | -3 KMnO_4 | 2 | -2 (CH_3)_2C=CH_2 | 1 | -1 H_2O | 4 | 4 CO_2 | 1 | 1 K_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 CH_3CH_2COOH | 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 H_2SO_4 | 3 | -3 | -1/3 (Δ[H2SO4])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) (CH_3)_2C=CH_2 | 1 | -1 | -(Δ[(CH3)2C=CH2])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) CH_3CH_2COOH | 1 | 1 | (Δ[CH3CH2COOH])/(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 = -1/3 (Δ[H2SO4])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -(Δ[(CH3)2C=CH2])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[CO2])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = (Δ[CH3CH2COOH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/4e84bae528ab257451fe31c52c54f70d.png)
Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + (CH_3)_2C=CH_2 ⟶ H_2O + CO_2 + K_2SO_4 + MnSO_4 + CH_3CH_2COOH 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: 3 H_2SO_4 + 2 KMnO_4 + (CH_3)_2C=CH_2 ⟶ 4 H_2O + CO_2 + K_2SO_4 + 2 MnSO_4 + CH_3CH_2COOH 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 | 3 | -3 KMnO_4 | 2 | -2 (CH_3)_2C=CH_2 | 1 | -1 H_2O | 4 | 4 CO_2 | 1 | 1 K_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 CH_3CH_2COOH | 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 H_2SO_4 | 3 | -3 | -1/3 (Δ[H2SO4])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) (CH_3)_2C=CH_2 | 1 | -1 | -(Δ[(CH3)2C=CH2])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) CH_3CH_2COOH | 1 | 1 | (Δ[CH3CH2COOH])/(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 = -1/3 (Δ[H2SO4])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -(Δ[(CH3)2C=CH2])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[CO2])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = (Δ[CH3CH2COOH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
![| sulfuric acid | potassium permanganate | isobutylene | water | carbon dioxide | potassium sulfate | manganese(II) sulfate | propionic acid formula | H_2SO_4 | KMnO_4 | (CH_3)_2C=CH_2 | H_2O | CO_2 | K_2SO_4 | MnSO_4 | CH_3CH_2COOH Hill formula | H_2O_4S | KMnO_4 | C_4H_8 | H_2O | CO_2 | K_2O_4S | MnSO_4 | C_3H_6O_2 name | sulfuric acid | potassium permanganate | isobutylene | water | carbon dioxide | potassium sulfate | manganese(II) sulfate | propionic acid IUPAC name | sulfuric acid | potassium permanganate | 2-methylprop-1-ene | water | carbon dioxide | dipotassium sulfate | manganese(+2) cation sulfate | propionic acid](../image_source/ea6475d23a41060717d4fa79b59887d2.png)
| sulfuric acid | potassium permanganate | isobutylene | water | carbon dioxide | potassium sulfate | manganese(II) sulfate | propionic acid formula | H_2SO_4 | KMnO_4 | (CH_3)_2C=CH_2 | H_2O | CO_2 | K_2SO_4 | MnSO_4 | CH_3CH_2COOH Hill formula | H_2O_4S | KMnO_4 | C_4H_8 | H_2O | CO_2 | K_2O_4S | MnSO_4 | C_3H_6O_2 name | sulfuric acid | potassium permanganate | isobutylene | water | carbon dioxide | potassium sulfate | manganese(II) sulfate | propionic acid IUPAC name | sulfuric acid | potassium permanganate | 2-methylprop-1-ene | water | carbon dioxide | dipotassium sulfate | manganese(+2) cation sulfate | propionic acid