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H2SO4 + KMnO4 + NO = H2O + MnSO4 + KNO3 + Mn(NO3)2

Input interpretation

H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + NO nitric oxide ⟶ H_2O water + MnSO_4 manganese(II) sulfate + KNO_3 potassium nitrate + Mn(NO_3)_2 manganese(II) nitrate
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + NO nitric oxide ⟶ H_2O water + MnSO_4 manganese(II) sulfate + KNO_3 potassium nitrate + Mn(NO_3)_2 manganese(II) nitrate

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + NO ⟶ H_2O + MnSO_4 + KNO_3 + Mn(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 NO ⟶ c_4 H_2O + c_5 MnSO_4 + c_6 KNO_3 + c_7 Mn(NO_3)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and N: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 + c_3 = c_4 + 4 c_5 + 3 c_6 + 6 c_7 S: | c_1 = c_5 K: | c_2 = c_6 Mn: | c_2 = c_5 + c_7 N: | c_3 = c_6 + 2 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_7 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 3 c_3 = 5 c_4 = 2 c_5 = 2 c_6 = 3 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + 3 KMnO_4 + 5 NO ⟶ 2 H_2O + 2 MnSO_4 + 3 KNO_3 + Mn(NO_3)_2
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + NO ⟶ H_2O + MnSO_4 + KNO_3 + Mn(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 NO ⟶ c_4 H_2O + c_5 MnSO_4 + c_6 KNO_3 + c_7 Mn(NO_3)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and N: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 + c_3 = c_4 + 4 c_5 + 3 c_6 + 6 c_7 S: | c_1 = c_5 K: | c_2 = c_6 Mn: | c_2 = c_5 + c_7 N: | c_3 = c_6 + 2 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_7 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 3 c_3 = 5 c_4 = 2 c_5 = 2 c_6 = 3 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + 3 KMnO_4 + 5 NO ⟶ 2 H_2O + 2 MnSO_4 + 3 KNO_3 + Mn(NO_3)_2

Structures

+ + ⟶ + + +
+ + ⟶ + + +

Names

sulfuric acid + potassium permanganate + nitric oxide ⟶ water + manganese(II) sulfate + potassium nitrate + manganese(II) nitrate
sulfuric acid + potassium permanganate + nitric oxide ⟶ water + manganese(II) sulfate + potassium nitrate + manganese(II) nitrate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + NO ⟶ H_2O + MnSO_4 + KNO_3 + Mn(NO_3)_2 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: 2 H_2SO_4 + 3 KMnO_4 + 5 NO ⟶ 2 H_2O + 2 MnSO_4 + 3 KNO_3 + Mn(NO_3)_2 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 | 2 | -2 KMnO_4 | 3 | -3 NO | 5 | -5 H_2O | 2 | 2 MnSO_4 | 2 | 2 KNO_3 | 3 | 3 Mn(NO_3)_2 | 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 | 2 | -2 | ([H2SO4])^(-2) KMnO_4 | 3 | -3 | ([KMnO4])^(-3) NO | 5 | -5 | ([NO])^(-5) H_2O | 2 | 2 | ([H2O])^2 MnSO_4 | 2 | 2 | ([MnSO4])^2 KNO_3 | 3 | 3 | ([KNO3])^3 Mn(NO_3)_2 | 1 | 1 | [Mn(NO3)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])^(-2) ([KMnO4])^(-3) ([NO])^(-5) ([H2O])^2 ([MnSO4])^2 ([KNO3])^3 [Mn(NO3)2] = (([H2O])^2 ([MnSO4])^2 ([KNO3])^3 [Mn(NO3)2])/(([H2SO4])^2 ([KMnO4])^3 ([NO])^5)
Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + NO ⟶ H_2O + MnSO_4 + KNO_3 + Mn(NO_3)_2 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: 2 H_2SO_4 + 3 KMnO_4 + 5 NO ⟶ 2 H_2O + 2 MnSO_4 + 3 KNO_3 + Mn(NO_3)_2 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 | 2 | -2 KMnO_4 | 3 | -3 NO | 5 | -5 H_2O | 2 | 2 MnSO_4 | 2 | 2 KNO_3 | 3 | 3 Mn(NO_3)_2 | 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 | 2 | -2 | ([H2SO4])^(-2) KMnO_4 | 3 | -3 | ([KMnO4])^(-3) NO | 5 | -5 | ([NO])^(-5) H_2O | 2 | 2 | ([H2O])^2 MnSO_4 | 2 | 2 | ([MnSO4])^2 KNO_3 | 3 | 3 | ([KNO3])^3 Mn(NO_3)_2 | 1 | 1 | [Mn(NO3)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])^(-2) ([KMnO4])^(-3) ([NO])^(-5) ([H2O])^2 ([MnSO4])^2 ([KNO3])^3 [Mn(NO3)2] = (([H2O])^2 ([MnSO4])^2 ([KNO3])^3 [Mn(NO3)2])/(([H2SO4])^2 ([KMnO4])^3 ([NO])^5)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + NO ⟶ H_2O + MnSO_4 + KNO_3 + Mn(NO_3)_2 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: 2 H_2SO_4 + 3 KMnO_4 + 5 NO ⟶ 2 H_2O + 2 MnSO_4 + 3 KNO_3 + Mn(NO_3)_2 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 | 2 | -2 KMnO_4 | 3 | -3 NO | 5 | -5 H_2O | 2 | 2 MnSO_4 | 2 | 2 KNO_3 | 3 | 3 Mn(NO_3)_2 | 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 | 2 | -2 | -1/2 (Δ[H2SO4])/(Δt) KMnO_4 | 3 | -3 | -1/3 (Δ[KMnO4])/(Δt) NO | 5 | -5 | -1/5 (Δ[NO])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) KNO_3 | 3 | 3 | 1/3 (Δ[KNO3])/(Δt) Mn(NO_3)_2 | 1 | 1 | (Δ[Mn(NO3)2])/(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 = -1/2 (Δ[H2SO4])/(Δt) = -1/3 (Δ[KMnO4])/(Δt) = -1/5 (Δ[NO])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = 1/3 (Δ[KNO3])/(Δt) = (Δ[Mn(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + NO ⟶ H_2O + MnSO_4 + KNO_3 + Mn(NO_3)_2 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: 2 H_2SO_4 + 3 KMnO_4 + 5 NO ⟶ 2 H_2O + 2 MnSO_4 + 3 KNO_3 + Mn(NO_3)_2 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 | 2 | -2 KMnO_4 | 3 | -3 NO | 5 | -5 H_2O | 2 | 2 MnSO_4 | 2 | 2 KNO_3 | 3 | 3 Mn(NO_3)_2 | 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 | 2 | -2 | -1/2 (Δ[H2SO4])/(Δt) KMnO_4 | 3 | -3 | -1/3 (Δ[KMnO4])/(Δt) NO | 5 | -5 | -1/5 (Δ[NO])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) KNO_3 | 3 | 3 | 1/3 (Δ[KNO3])/(Δt) Mn(NO_3)_2 | 1 | 1 | (Δ[Mn(NO3)2])/(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 = -1/2 (Δ[H2SO4])/(Δt) = -1/3 (Δ[KMnO4])/(Δt) = -1/5 (Δ[NO])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = 1/3 (Δ[KNO3])/(Δt) = (Δ[Mn(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | potassium permanganate | nitric oxide | water | manganese(II) sulfate | potassium nitrate | manganese(II) nitrate formula | H_2SO_4 | KMnO_4 | NO | H_2O | MnSO_4 | KNO_3 | Mn(NO_3)_2 Hill formula | H_2O_4S | KMnO_4 | NO | H_2O | MnSO_4 | KNO_3 | MnN_2O_6 name | sulfuric acid | potassium permanganate | nitric oxide | water | manganese(II) sulfate | potassium nitrate | manganese(II) nitrate IUPAC name | sulfuric acid | potassium permanganate | nitric oxide | water | manganese(+2) cation sulfate | potassium nitrate | manganese(2+) dinitrate
| sulfuric acid | potassium permanganate | nitric oxide | water | manganese(II) sulfate | potassium nitrate | manganese(II) nitrate formula | H_2SO_4 | KMnO_4 | NO | H_2O | MnSO_4 | KNO_3 | Mn(NO_3)_2 Hill formula | H_2O_4S | KMnO_4 | NO | H_2O | MnSO_4 | KNO_3 | MnN_2O_6 name | sulfuric acid | potassium permanganate | nitric oxide | water | manganese(II) sulfate | potassium nitrate | manganese(II) nitrate IUPAC name | sulfuric acid | potassium permanganate | nitric oxide | water | manganese(+2) cation sulfate | potassium nitrate | manganese(2+) dinitrate

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