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H2SO4 + KMnO4 + Fe(SO4) = H2O + K2SO4 + Fe2(SO4)3 + Mn(SO4)2

Input interpretation

H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + FeSO_4·7H_2O ironate ⟶ H_2O water + K_2SO_4 potassium sulfate + Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate + Mn(SO4)2
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + FeSO_4·7H_2O ironate ⟶ H_2O water + K_2SO_4 potassium sulfate + Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate + Mn(SO4)2

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + FeSO_4·7H_2O ⟶ H_2O + K_2SO_4 + Fe_2(SO_4)_3·xH_2O + Mn(SO4)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 FeSO_4·7H_2O ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Fe_2(SO_4)_3·xH_2O + c_7 Mn(SO4)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 Fe: H: | 2 c_1 + 14 c_3 = 2 c_4 O: | 4 c_1 + 4 c_2 + 11 c_3 = c_4 + 4 c_5 + 12 c_6 + 8 c_7 S: | c_1 + c_3 = c_5 + 3 c_6 + 2 c_7 K: | c_2 = 2 c_5 Mn: | c_2 = c_7 Fe: | c_3 = 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 2 c_3 = 6 c_4 = 50 c_5 = 1 c_6 = 3 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 H_2SO_4 + 2 KMnO_4 + 6 FeSO_4·7H_2O ⟶ 50 H_2O + K_2SO_4 + 3 Fe_2(SO_4)_3·xH_2O + 2 Mn(SO4)2
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + FeSO_4·7H_2O ⟶ H_2O + K_2SO_4 + Fe_2(SO_4)_3·xH_2O + Mn(SO4)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 FeSO_4·7H_2O ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Fe_2(SO_4)_3·xH_2O + c_7 Mn(SO4)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 Fe: H: | 2 c_1 + 14 c_3 = 2 c_4 O: | 4 c_1 + 4 c_2 + 11 c_3 = c_4 + 4 c_5 + 12 c_6 + 8 c_7 S: | c_1 + c_3 = c_5 + 3 c_6 + 2 c_7 K: | c_2 = 2 c_5 Mn: | c_2 = c_7 Fe: | c_3 = 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 2 c_3 = 6 c_4 = 50 c_5 = 1 c_6 = 3 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 H_2SO_4 + 2 KMnO_4 + 6 FeSO_4·7H_2O ⟶ 50 H_2O + K_2SO_4 + 3 Fe_2(SO_4)_3·xH_2O + 2 Mn(SO4)2

Structures

+ + ⟶ + + + Mn(SO4)2
+ + ⟶ + + + Mn(SO4)2

Names

sulfuric acid + potassium permanganate + ironate ⟶ water + potassium sulfate + iron(III) sulfate hydrate + Mn(SO4)2
sulfuric acid + potassium permanganate + ironate ⟶ water + potassium sulfate + iron(III) sulfate hydrate + Mn(SO4)2

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + FeSO_4·7H_2O ⟶ H_2O + K_2SO_4 + Fe_2(SO_4)_3·xH_2O + Mn(SO4)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: 8 H_2SO_4 + 2 KMnO_4 + 6 FeSO_4·7H_2O ⟶ 50 H_2O + K_2SO_4 + 3 Fe_2(SO_4)_3·xH_2O + 2 Mn(SO4)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 | 8 | -8 KMnO_4 | 2 | -2 FeSO_4·7H_2O | 6 | -6 H_2O | 50 | 50 K_2SO_4 | 1 | 1 Fe_2(SO_4)_3·xH_2O | 3 | 3 Mn(SO4)2 | 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 | 8 | -8 | ([H2SO4])^(-8) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) FeSO_4·7H_2O | 6 | -6 | ([FeSO4·7H2O])^(-6) H_2O | 50 | 50 | ([H2O])^50 K_2SO_4 | 1 | 1 | [K2SO4] Fe_2(SO_4)_3·xH_2O | 3 | 3 | ([Fe2(SO4)3·xH2O])^3 Mn(SO4)2 | 2 | 2 | ([Mn(SO4)2])^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])^(-8) ([KMnO4])^(-2) ([FeSO4·7H2O])^(-6) ([H2O])^50 [K2SO4] ([Fe2(SO4)3·xH2O])^3 ([Mn(SO4)2])^2 = (([H2O])^50 [K2SO4] ([Fe2(SO4)3·xH2O])^3 ([Mn(SO4)2])^2)/(([H2SO4])^8 ([KMnO4])^2 ([FeSO4·7H2O])^6)
Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + FeSO_4·7H_2O ⟶ H_2O + K_2SO_4 + Fe_2(SO_4)_3·xH_2O + Mn(SO4)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: 8 H_2SO_4 + 2 KMnO_4 + 6 FeSO_4·7H_2O ⟶ 50 H_2O + K_2SO_4 + 3 Fe_2(SO_4)_3·xH_2O + 2 Mn(SO4)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 | 8 | -8 KMnO_4 | 2 | -2 FeSO_4·7H_2O | 6 | -6 H_2O | 50 | 50 K_2SO_4 | 1 | 1 Fe_2(SO_4)_3·xH_2O | 3 | 3 Mn(SO4)2 | 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 | 8 | -8 | ([H2SO4])^(-8) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) FeSO_4·7H_2O | 6 | -6 | ([FeSO4·7H2O])^(-6) H_2O | 50 | 50 | ([H2O])^50 K_2SO_4 | 1 | 1 | [K2SO4] Fe_2(SO_4)_3·xH_2O | 3 | 3 | ([Fe2(SO4)3·xH2O])^3 Mn(SO4)2 | 2 | 2 | ([Mn(SO4)2])^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])^(-8) ([KMnO4])^(-2) ([FeSO4·7H2O])^(-6) ([H2O])^50 [K2SO4] ([Fe2(SO4)3·xH2O])^3 ([Mn(SO4)2])^2 = (([H2O])^50 [K2SO4] ([Fe2(SO4)3·xH2O])^3 ([Mn(SO4)2])^2)/(([H2SO4])^8 ([KMnO4])^2 ([FeSO4·7H2O])^6)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + FeSO_4·7H_2O ⟶ H_2O + K_2SO_4 + Fe_2(SO_4)_3·xH_2O + Mn(SO4)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: 8 H_2SO_4 + 2 KMnO_4 + 6 FeSO_4·7H_2O ⟶ 50 H_2O + K_2SO_4 + 3 Fe_2(SO_4)_3·xH_2O + 2 Mn(SO4)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 | 8 | -8 KMnO_4 | 2 | -2 FeSO_4·7H_2O | 6 | -6 H_2O | 50 | 50 K_2SO_4 | 1 | 1 Fe_2(SO_4)_3·xH_2O | 3 | 3 Mn(SO4)2 | 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 | 8 | -8 | -1/8 (Δ[H2SO4])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) FeSO_4·7H_2O | 6 | -6 | -1/6 (Δ[FeSO4·7H2O])/(Δt) H_2O | 50 | 50 | 1/50 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) Fe_2(SO_4)_3·xH_2O | 3 | 3 | 1/3 (Δ[Fe2(SO4)3·xH2O])/(Δt) Mn(SO4)2 | 2 | 2 | 1/2 (Δ[Mn(SO4)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 = -1/8 (Δ[H2SO4])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/6 (Δ[FeSO4·7H2O])/(Δt) = 1/50 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/3 (Δ[Fe2(SO4)3·xH2O])/(Δt) = 1/2 (Δ[Mn(SO4)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 + FeSO_4·7H_2O ⟶ H_2O + K_2SO_4 + Fe_2(SO_4)_3·xH_2O + Mn(SO4)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: 8 H_2SO_4 + 2 KMnO_4 + 6 FeSO_4·7H_2O ⟶ 50 H_2O + K_2SO_4 + 3 Fe_2(SO_4)_3·xH_2O + 2 Mn(SO4)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 | 8 | -8 KMnO_4 | 2 | -2 FeSO_4·7H_2O | 6 | -6 H_2O | 50 | 50 K_2SO_4 | 1 | 1 Fe_2(SO_4)_3·xH_2O | 3 | 3 Mn(SO4)2 | 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 | 8 | -8 | -1/8 (Δ[H2SO4])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) FeSO_4·7H_2O | 6 | -6 | -1/6 (Δ[FeSO4·7H2O])/(Δt) H_2O | 50 | 50 | 1/50 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) Fe_2(SO_4)_3·xH_2O | 3 | 3 | 1/3 (Δ[Fe2(SO4)3·xH2O])/(Δt) Mn(SO4)2 | 2 | 2 | 1/2 (Δ[Mn(SO4)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 = -1/8 (Δ[H2SO4])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/6 (Δ[FeSO4·7H2O])/(Δt) = 1/50 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/3 (Δ[Fe2(SO4)3·xH2O])/(Δt) = 1/2 (Δ[Mn(SO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | potassium permanganate | ironate | water | potassium sulfate | iron(III) sulfate hydrate | Mn(SO4)2 formula | H_2SO_4 | KMnO_4 | FeSO_4·7H_2O | H_2O | K_2SO_4 | Fe_2(SO_4)_3·xH_2O | Mn(SO4)2 Hill formula | H_2O_4S | KMnO_4 | FeH_14O_11S | H_2O | K_2O_4S | Fe_2O_12S_3 | MnO8S2 name | sulfuric acid | potassium permanganate | ironate | water | potassium sulfate | iron(III) sulfate hydrate | IUPAC name | sulfuric acid | potassium permanganate | iron(+2) cation sulfate heptahydrate | water | dipotassium sulfate | diferric trisulfate |
| sulfuric acid | potassium permanganate | ironate | water | potassium sulfate | iron(III) sulfate hydrate | Mn(SO4)2 formula | H_2SO_4 | KMnO_4 | FeSO_4·7H_2O | H_2O | K_2SO_4 | Fe_2(SO_4)_3·xH_2O | Mn(SO4)2 Hill formula | H_2O_4S | KMnO_4 | FeH_14O_11S | H_2O | K_2O_4S | Fe_2O_12S_3 | MnO8S2 name | sulfuric acid | potassium permanganate | ironate | water | potassium sulfate | iron(III) sulfate hydrate | IUPAC name | sulfuric acid | potassium permanganate | iron(+2) cation sulfate heptahydrate | water | dipotassium sulfate | diferric trisulfate |

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