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H2SO4 + KMnO4 + K4Fe(CN)6 = H2O + HNO3 + CO2 + MnSO4 + Fe2(SO4)3 + KHSO4

Input interpretation

H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + K4Fe(CN)6 ⟶ H_2O water + HNO_3 nitric acid + CO_2 carbon dioxide + MnSO_4 manganese(II) sulfate + Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate + KHSO_4 potassium bisulfate
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + K4Fe(CN)6 ⟶ H_2O water + HNO_3 nitric acid + CO_2 carbon dioxide + MnSO_4 manganese(II) sulfate + Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate + KHSO_4 potassium bisulfate

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + K4Fe(CN)6 ⟶ H_2O + HNO_3 + CO_2 + MnSO_4 + Fe_2(SO_4)_3·xH_2O + KHSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 K4Fe(CN)6 ⟶ c_4 H_2O + c_5 HNO_3 + c_6 CO_2 + c_7 MnSO_4 + c_8 Fe_2(SO_4)_3·xH_2O + c_9 KHSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn, Fe, C and N: H: | 2 c_1 = 2 c_4 + c_5 + c_9 O: | 4 c_1 + 4 c_2 = c_4 + 3 c_5 + 2 c_6 + 4 c_7 + 12 c_8 + 4 c_9 S: | c_1 = c_7 + 3 c_8 + c_9 K: | c_2 + 4 c_3 = c_9 Mn: | c_2 = c_7 Fe: | c_3 = 2 c_8 C: | 6 c_3 = c_6 N: | 6 c_3 = c_5 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_1 = 299/5 c_2 = 122/5 c_3 = 2 c_4 = 188/5 c_5 = 12 c_6 = 12 c_7 = 122/5 c_8 = 1 c_9 = 162/5 Multiply by the least common denominator, 5, to eliminate fractional coefficients: c_1 = 299 c_2 = 122 c_3 = 10 c_4 = 188 c_5 = 60 c_6 = 60 c_7 = 122 c_8 = 5 c_9 = 162 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 299 H_2SO_4 + 122 KMnO_4 + 10 K4Fe(CN)6 ⟶ 188 H_2O + 60 HNO_3 + 60 CO_2 + 122 MnSO_4 + 5 Fe_2(SO_4)_3·xH_2O + 162 KHSO_4
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + K4Fe(CN)6 ⟶ H_2O + HNO_3 + CO_2 + MnSO_4 + Fe_2(SO_4)_3·xH_2O + KHSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 K4Fe(CN)6 ⟶ c_4 H_2O + c_5 HNO_3 + c_6 CO_2 + c_7 MnSO_4 + c_8 Fe_2(SO_4)_3·xH_2O + c_9 KHSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn, Fe, C and N: H: | 2 c_1 = 2 c_4 + c_5 + c_9 O: | 4 c_1 + 4 c_2 = c_4 + 3 c_5 + 2 c_6 + 4 c_7 + 12 c_8 + 4 c_9 S: | c_1 = c_7 + 3 c_8 + c_9 K: | c_2 + 4 c_3 = c_9 Mn: | c_2 = c_7 Fe: | c_3 = 2 c_8 C: | 6 c_3 = c_6 N: | 6 c_3 = c_5 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_1 = 299/5 c_2 = 122/5 c_3 = 2 c_4 = 188/5 c_5 = 12 c_6 = 12 c_7 = 122/5 c_8 = 1 c_9 = 162/5 Multiply by the least common denominator, 5, to eliminate fractional coefficients: c_1 = 299 c_2 = 122 c_3 = 10 c_4 = 188 c_5 = 60 c_6 = 60 c_7 = 122 c_8 = 5 c_9 = 162 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 299 H_2SO_4 + 122 KMnO_4 + 10 K4Fe(CN)6 ⟶ 188 H_2O + 60 HNO_3 + 60 CO_2 + 122 MnSO_4 + 5 Fe_2(SO_4)_3·xH_2O + 162 KHSO_4

Structures

+ + K4Fe(CN)6 ⟶ + + + + +
+ + K4Fe(CN)6 ⟶ + + + + +

Names

sulfuric acid + potassium permanganate + K4Fe(CN)6 ⟶ water + nitric acid + carbon dioxide + manganese(II) sulfate + iron(III) sulfate hydrate + potassium bisulfate
sulfuric acid + potassium permanganate + K4Fe(CN)6 ⟶ water + nitric acid + carbon dioxide + manganese(II) sulfate + iron(III) sulfate hydrate + potassium bisulfate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + K4Fe(CN)6 ⟶ H_2O + HNO_3 + CO_2 + MnSO_4 + Fe_2(SO_4)_3·xH_2O + 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: 299 H_2SO_4 + 122 KMnO_4 + 10 K4Fe(CN)6 ⟶ 188 H_2O + 60 HNO_3 + 60 CO_2 + 122 MnSO_4 + 5 Fe_2(SO_4)_3·xH_2O + 162 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 | 299 | -299 KMnO_4 | 122 | -122 K4Fe(CN)6 | 10 | -10 H_2O | 188 | 188 HNO_3 | 60 | 60 CO_2 | 60 | 60 MnSO_4 | 122 | 122 Fe_2(SO_4)_3·xH_2O | 5 | 5 KHSO_4 | 162 | 162 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 299 | -299 | ([H2SO4])^(-299) KMnO_4 | 122 | -122 | ([KMnO4])^(-122) K4Fe(CN)6 | 10 | -10 | ([K4Fe(CN)6])^(-10) H_2O | 188 | 188 | ([H2O])^188 HNO_3 | 60 | 60 | ([HNO3])^60 CO_2 | 60 | 60 | ([CO2])^60 MnSO_4 | 122 | 122 | ([MnSO4])^122 Fe_2(SO_4)_3·xH_2O | 5 | 5 | ([Fe2(SO4)3·xH2O])^5 KHSO_4 | 162 | 162 | ([KHSO4])^162 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])^(-299) ([KMnO4])^(-122) ([K4Fe(CN)6])^(-10) ([H2O])^188 ([HNO3])^60 ([CO2])^60 ([MnSO4])^122 ([Fe2(SO4)3·xH2O])^5 ([KHSO4])^162 = (([H2O])^188 ([HNO3])^60 ([CO2])^60 ([MnSO4])^122 ([Fe2(SO4)3·xH2O])^5 ([KHSO4])^162)/(([H2SO4])^299 ([KMnO4])^122 ([K4Fe(CN)6])^10)
Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + K4Fe(CN)6 ⟶ H_2O + HNO_3 + CO_2 + MnSO_4 + Fe_2(SO_4)_3·xH_2O + 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: 299 H_2SO_4 + 122 KMnO_4 + 10 K4Fe(CN)6 ⟶ 188 H_2O + 60 HNO_3 + 60 CO_2 + 122 MnSO_4 + 5 Fe_2(SO_4)_3·xH_2O + 162 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 | 299 | -299 KMnO_4 | 122 | -122 K4Fe(CN)6 | 10 | -10 H_2O | 188 | 188 HNO_3 | 60 | 60 CO_2 | 60 | 60 MnSO_4 | 122 | 122 Fe_2(SO_4)_3·xH_2O | 5 | 5 KHSO_4 | 162 | 162 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 299 | -299 | ([H2SO4])^(-299) KMnO_4 | 122 | -122 | ([KMnO4])^(-122) K4Fe(CN)6 | 10 | -10 | ([K4Fe(CN)6])^(-10) H_2O | 188 | 188 | ([H2O])^188 HNO_3 | 60 | 60 | ([HNO3])^60 CO_2 | 60 | 60 | ([CO2])^60 MnSO_4 | 122 | 122 | ([MnSO4])^122 Fe_2(SO_4)_3·xH_2O | 5 | 5 | ([Fe2(SO4)3·xH2O])^5 KHSO_4 | 162 | 162 | ([KHSO4])^162 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])^(-299) ([KMnO4])^(-122) ([K4Fe(CN)6])^(-10) ([H2O])^188 ([HNO3])^60 ([CO2])^60 ([MnSO4])^122 ([Fe2(SO4)3·xH2O])^5 ([KHSO4])^162 = (([H2O])^188 ([HNO3])^60 ([CO2])^60 ([MnSO4])^122 ([Fe2(SO4)3·xH2O])^5 ([KHSO4])^162)/(([H2SO4])^299 ([KMnO4])^122 ([K4Fe(CN)6])^10)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + K4Fe(CN)6 ⟶ H_2O + HNO_3 + CO_2 + MnSO_4 + Fe_2(SO_4)_3·xH_2O + 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: 299 H_2SO_4 + 122 KMnO_4 + 10 K4Fe(CN)6 ⟶ 188 H_2O + 60 HNO_3 + 60 CO_2 + 122 MnSO_4 + 5 Fe_2(SO_4)_3·xH_2O + 162 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 | 299 | -299 KMnO_4 | 122 | -122 K4Fe(CN)6 | 10 | -10 H_2O | 188 | 188 HNO_3 | 60 | 60 CO_2 | 60 | 60 MnSO_4 | 122 | 122 Fe_2(SO_4)_3·xH_2O | 5 | 5 KHSO_4 | 162 | 162 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 | 299 | -299 | -1/299 (Δ[H2SO4])/(Δt) KMnO_4 | 122 | -122 | -1/122 (Δ[KMnO4])/(Δt) K4Fe(CN)6 | 10 | -10 | -1/10 (Δ[K4Fe(CN)6])/(Δt) H_2O | 188 | 188 | 1/188 (Δ[H2O])/(Δt) HNO_3 | 60 | 60 | 1/60 (Δ[HNO3])/(Δt) CO_2 | 60 | 60 | 1/60 (Δ[CO2])/(Δt) MnSO_4 | 122 | 122 | 1/122 (Δ[MnSO4])/(Δt) Fe_2(SO_4)_3·xH_2O | 5 | 5 | 1/5 (Δ[Fe2(SO4)3·xH2O])/(Δt) KHSO_4 | 162 | 162 | 1/162 (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 = -1/299 (Δ[H2SO4])/(Δt) = -1/122 (Δ[KMnO4])/(Δt) = -1/10 (Δ[K4Fe(CN)6])/(Δt) = 1/188 (Δ[H2O])/(Δt) = 1/60 (Δ[HNO3])/(Δt) = 1/60 (Δ[CO2])/(Δt) = 1/122 (Δ[MnSO4])/(Δt) = 1/5 (Δ[Fe2(SO4)3·xH2O])/(Δt) = 1/162 (Δ[KHSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + K4Fe(CN)6 ⟶ H_2O + HNO_3 + CO_2 + MnSO_4 + Fe_2(SO_4)_3·xH_2O + 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: 299 H_2SO_4 + 122 KMnO_4 + 10 K4Fe(CN)6 ⟶ 188 H_2O + 60 HNO_3 + 60 CO_2 + 122 MnSO_4 + 5 Fe_2(SO_4)_3·xH_2O + 162 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 | 299 | -299 KMnO_4 | 122 | -122 K4Fe(CN)6 | 10 | -10 H_2O | 188 | 188 HNO_3 | 60 | 60 CO_2 | 60 | 60 MnSO_4 | 122 | 122 Fe_2(SO_4)_3·xH_2O | 5 | 5 KHSO_4 | 162 | 162 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 | 299 | -299 | -1/299 (Δ[H2SO4])/(Δt) KMnO_4 | 122 | -122 | -1/122 (Δ[KMnO4])/(Δt) K4Fe(CN)6 | 10 | -10 | -1/10 (Δ[K4Fe(CN)6])/(Δt) H_2O | 188 | 188 | 1/188 (Δ[H2O])/(Δt) HNO_3 | 60 | 60 | 1/60 (Δ[HNO3])/(Δt) CO_2 | 60 | 60 | 1/60 (Δ[CO2])/(Δt) MnSO_4 | 122 | 122 | 1/122 (Δ[MnSO4])/(Δt) Fe_2(SO_4)_3·xH_2O | 5 | 5 | 1/5 (Δ[Fe2(SO4)3·xH2O])/(Δt) KHSO_4 | 162 | 162 | 1/162 (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 = -1/299 (Δ[H2SO4])/(Δt) = -1/122 (Δ[KMnO4])/(Δt) = -1/10 (Δ[K4Fe(CN)6])/(Δt) = 1/188 (Δ[H2O])/(Δt) = 1/60 (Δ[HNO3])/(Δt) = 1/60 (Δ[CO2])/(Δt) = 1/122 (Δ[MnSO4])/(Δt) = 1/5 (Δ[Fe2(SO4)3·xH2O])/(Δt) = 1/162 (Δ[KHSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | potassium permanganate | K4Fe(CN)6 | water | nitric acid | carbon dioxide | manganese(II) sulfate | iron(III) sulfate hydrate | potassium bisulfate formula | H_2SO_4 | KMnO_4 | K4Fe(CN)6 | H_2O | HNO_3 | CO_2 | MnSO_4 | Fe_2(SO_4)_3·xH_2O | KHSO_4 Hill formula | H_2O_4S | KMnO_4 | C6FeK4N6 | H_2O | HNO_3 | CO_2 | MnSO_4 | Fe_2O_12S_3 | HKO_4S name | sulfuric acid | potassium permanganate | | water | nitric acid | carbon dioxide | manganese(II) sulfate | iron(III) sulfate hydrate | potassium bisulfate IUPAC name | sulfuric acid | potassium permanganate | | water | nitric acid | carbon dioxide | manganese(+2) cation sulfate | diferric trisulfate | potassium hydrogen sulfate
| sulfuric acid | potassium permanganate | K4Fe(CN)6 | water | nitric acid | carbon dioxide | manganese(II) sulfate | iron(III) sulfate hydrate | potassium bisulfate formula | H_2SO_4 | KMnO_4 | K4Fe(CN)6 | H_2O | HNO_3 | CO_2 | MnSO_4 | Fe_2(SO_4)_3·xH_2O | KHSO_4 Hill formula | H_2O_4S | KMnO_4 | C6FeK4N6 | H_2O | HNO_3 | CO_2 | MnSO_4 | Fe_2O_12S_3 | HKO_4S name | sulfuric acid | potassium permanganate | | water | nitric acid | carbon dioxide | manganese(II) sulfate | iron(III) sulfate hydrate | potassium bisulfate IUPAC name | sulfuric acid | potassium permanganate | | water | nitric acid | carbon dioxide | manganese(+2) cation sulfate | diferric trisulfate | potassium hydrogen sulfate

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