Input interpretation
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + H_2O_2 hydrogen peroxide ⟶ H_2O water + O_2 oxygen + MnSO_4 manganese(II) sulfate + KHSO_4 potassium bisulfate
Balanced equation
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + H_2O_2 ⟶ H_2O + O_2 + MnSO_4 + KHSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 H_2O_2 ⟶ c_4 H_2O + c_5 O_2 + c_6 MnSO_4 + c_7 KHSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K and Mn: H: | 2 c_1 + 2 c_3 = 2 c_4 + c_7 O: | 4 c_1 + 4 c_2 + 2 c_3 = c_4 + 2 c_5 + 4 c_6 + 4 c_7 S: | c_1 = c_6 + c_7 K: | c_2 = c_7 Mn: | c_2 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_2 = c_1/2 c_3 = 1 c_4 = (3 c_1)/4 + 1 c_5 = (5 c_1)/8 + 1/2 c_6 = c_1/2 c_7 = c_1/2 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 = 2 c_3 = 1 c_4 = 4 c_5 = 3 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2SO_4 + 2 KMnO_4 + H_2O_2 ⟶ 4 H_2O + 3 O_2 + 2 MnSO_4 + 2 KHSO_4
Structures
+ + ⟶ + + +
Names
sulfuric acid + potassium permanganate + hydrogen peroxide ⟶ water + oxygen + manganese(II) sulfate + potassium bisulfate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + H_2O_2 ⟶ H_2O + O_2 + MnSO_4 + KHSO_4 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 H_2SO_4 + 2 KMnO_4 + H_2O_2 ⟶ 4 H_2O + 3 O_2 + 2 MnSO_4 + 2 KHSO_4 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 | 4 | -4 KMnO_4 | 2 | -2 H_2O_2 | 1 | -1 H_2O | 4 | 4 O_2 | 3 | 3 MnSO_4 | 2 | 2 KHSO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 4 | -4 | ([H2SO4])^(-4) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) H_2O_2 | 1 | -1 | ([H2O2])^(-1) H_2O | 4 | 4 | ([H2O])^4 O_2 | 3 | 3 | ([O2])^3 MnSO_4 | 2 | 2 | ([MnSO4])^2 KHSO_4 | 2 | 2 | ([KHSO4])^2 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])^(-4) ([KMnO4])^(-2) ([H2O2])^(-1) ([H2O])^4 ([O2])^3 ([MnSO4])^2 ([KHSO4])^2 = (([H2O])^4 ([O2])^3 ([MnSO4])^2 ([KHSO4])^2)/(([H2SO4])^4 ([KMnO4])^2 [H2O2])](../image_source/07ae61d9321010c0a56679c5aad9d282.png)
Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + H_2O_2 ⟶ H_2O + O_2 + MnSO_4 + KHSO_4 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 H_2SO_4 + 2 KMnO_4 + H_2O_2 ⟶ 4 H_2O + 3 O_2 + 2 MnSO_4 + 2 KHSO_4 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 | 4 | -4 KMnO_4 | 2 | -2 H_2O_2 | 1 | -1 H_2O | 4 | 4 O_2 | 3 | 3 MnSO_4 | 2 | 2 KHSO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 4 | -4 | ([H2SO4])^(-4) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) H_2O_2 | 1 | -1 | ([H2O2])^(-1) H_2O | 4 | 4 | ([H2O])^4 O_2 | 3 | 3 | ([O2])^3 MnSO_4 | 2 | 2 | ([MnSO4])^2 KHSO_4 | 2 | 2 | ([KHSO4])^2 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])^(-4) ([KMnO4])^(-2) ([H2O2])^(-1) ([H2O])^4 ([O2])^3 ([MnSO4])^2 ([KHSO4])^2 = (([H2O])^4 ([O2])^3 ([MnSO4])^2 ([KHSO4])^2)/(([H2SO4])^4 ([KMnO4])^2 [H2O2])
Rate of reaction
![Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + H_2O_2 ⟶ H_2O + O_2 + MnSO_4 + KHSO_4 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 H_2SO_4 + 2 KMnO_4 + H_2O_2 ⟶ 4 H_2O + 3 O_2 + 2 MnSO_4 + 2 KHSO_4 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 | 4 | -4 KMnO_4 | 2 | -2 H_2O_2 | 1 | -1 H_2O | 4 | 4 O_2 | 3 | 3 MnSO_4 | 2 | 2 KHSO_4 | 2 | 2 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 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) H_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) O_2 | 3 | 3 | 1/3 (Δ[O2])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) KHSO_4 | 2 | 2 | 1/2 (Δ[KHSO4])/(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[H2SO4])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -(Δ[H2O2])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/3 (Δ[O2])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = 1/2 (Δ[KHSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/56552741250038362ee5a941754841e1.png)
Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + H_2O_2 ⟶ H_2O + O_2 + MnSO_4 + KHSO_4 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 H_2SO_4 + 2 KMnO_4 + H_2O_2 ⟶ 4 H_2O + 3 O_2 + 2 MnSO_4 + 2 KHSO_4 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 | 4 | -4 KMnO_4 | 2 | -2 H_2O_2 | 1 | -1 H_2O | 4 | 4 O_2 | 3 | 3 MnSO_4 | 2 | 2 KHSO_4 | 2 | 2 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 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) H_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) O_2 | 3 | 3 | 1/3 (Δ[O2])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) KHSO_4 | 2 | 2 | 1/2 (Δ[KHSO4])/(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[H2SO4])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -(Δ[H2O2])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/3 (Δ[O2])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = 1/2 (Δ[KHSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sulfuric acid | potassium permanganate | hydrogen peroxide | water | oxygen | manganese(II) sulfate | potassium bisulfate formula | H_2SO_4 | KMnO_4 | H_2O_2 | H_2O | O_2 | MnSO_4 | KHSO_4 Hill formula | H_2O_4S | KMnO_4 | H_2O_2 | H_2O | O_2 | MnSO_4 | HKO_4S name | sulfuric acid | potassium permanganate | hydrogen peroxide | water | oxygen | manganese(II) sulfate | potassium bisulfate IUPAC name | sulfuric acid | potassium permanganate | hydrogen peroxide | water | molecular oxygen | manganese(+2) cation sulfate | potassium hydrogen sulfate