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H2SO4 + KMnO4 + H2S = H2O + MnSO4 + SK2SO4

Input interpretation

H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + H_2S hydrogen sulfide ⟶ H_2O water + MnSO_4 manganese(II) sulfate + K_2S_2O_4 potassium dithionite
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + H_2S hydrogen sulfide ⟶ H_2O water + MnSO_4 manganese(II) sulfate + K_2S_2O_4 potassium dithionite

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + H_2S ⟶ H_2O + MnSO_4 + K_2S_2O_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 H_2S ⟶ c_4 H_2O + c_5 MnSO_4 + c_6 K_2S_2O_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 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 4 c_6 S: | c_1 + c_3 = c_5 + 2 c_6 K: | c_2 = 2 c_6 Mn: | c_2 = 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 2 c_4 = 4 c_5 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + 2 KMnO_4 + 2 H_2S ⟶ 4 H_2O + 2 MnSO_4 + K_2S_2O_4
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + H_2S ⟶ H_2O + MnSO_4 + K_2S_2O_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 H_2S ⟶ c_4 H_2O + c_5 MnSO_4 + c_6 K_2S_2O_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 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 4 c_6 S: | c_1 + c_3 = c_5 + 2 c_6 K: | c_2 = 2 c_6 Mn: | c_2 = 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 2 c_4 = 4 c_5 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + 2 KMnO_4 + 2 H_2S ⟶ 4 H_2O + 2 MnSO_4 + K_2S_2O_4

Structures

+ + ⟶ + +
+ + ⟶ + +

Names

sulfuric acid + potassium permanganate + hydrogen sulfide ⟶ water + manganese(II) sulfate + potassium dithionite
sulfuric acid + potassium permanganate + hydrogen sulfide ⟶ water + manganese(II) sulfate + potassium dithionite

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + H_2S ⟶ H_2O + MnSO_4 + K_2S_2O_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: 2 H_2SO_4 + 2 KMnO_4 + 2 H_2S ⟶ 4 H_2O + 2 MnSO_4 + K_2S_2O_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 | 2 | -2 KMnO_4 | 2 | -2 H_2S | 2 | -2 H_2O | 4 | 4 MnSO_4 | 2 | 2 K_2S_2O_4 | 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 | 2 | -2 | ([KMnO4])^(-2) H_2S | 2 | -2 | ([H2S])^(-2) H_2O | 4 | 4 | ([H2O])^4 MnSO_4 | 2 | 2 | ([MnSO4])^2 K_2S_2O_4 | 1 | 1 | [K2S2O4] 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])^(-2) ([H2S])^(-2) ([H2O])^4 ([MnSO4])^2 [K2S2O4] = (([H2O])^4 ([MnSO4])^2 [K2S2O4])/(([H2SO4])^2 ([KMnO4])^2 ([H2S])^2)
Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + H_2S ⟶ H_2O + MnSO_4 + K_2S_2O_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: 2 H_2SO_4 + 2 KMnO_4 + 2 H_2S ⟶ 4 H_2O + 2 MnSO_4 + K_2S_2O_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 | 2 | -2 KMnO_4 | 2 | -2 H_2S | 2 | -2 H_2O | 4 | 4 MnSO_4 | 2 | 2 K_2S_2O_4 | 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 | 2 | -2 | ([KMnO4])^(-2) H_2S | 2 | -2 | ([H2S])^(-2) H_2O | 4 | 4 | ([H2O])^4 MnSO_4 | 2 | 2 | ([MnSO4])^2 K_2S_2O_4 | 1 | 1 | [K2S2O4] 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])^(-2) ([H2S])^(-2) ([H2O])^4 ([MnSO4])^2 [K2S2O4] = (([H2O])^4 ([MnSO4])^2 [K2S2O4])/(([H2SO4])^2 ([KMnO4])^2 ([H2S])^2)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + H_2S ⟶ H_2O + MnSO_4 + K_2S_2O_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: 2 H_2SO_4 + 2 KMnO_4 + 2 H_2S ⟶ 4 H_2O + 2 MnSO_4 + K_2S_2O_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 | 2 | -2 KMnO_4 | 2 | -2 H_2S | 2 | -2 H_2O | 4 | 4 MnSO_4 | 2 | 2 K_2S_2O_4 | 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 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) H_2S | 2 | -2 | -1/2 (Δ[H2S])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) K_2S_2O_4 | 1 | 1 | (Δ[K2S2O4])/(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) = -1/2 (Δ[KMnO4])/(Δt) = -1/2 (Δ[H2S])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = (Δ[K2S2O4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + H_2S ⟶ H_2O + MnSO_4 + K_2S_2O_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: 2 H_2SO_4 + 2 KMnO_4 + 2 H_2S ⟶ 4 H_2O + 2 MnSO_4 + K_2S_2O_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 | 2 | -2 KMnO_4 | 2 | -2 H_2S | 2 | -2 H_2O | 4 | 4 MnSO_4 | 2 | 2 K_2S_2O_4 | 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 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) H_2S | 2 | -2 | -1/2 (Δ[H2S])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) K_2S_2O_4 | 1 | 1 | (Δ[K2S2O4])/(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) = -1/2 (Δ[KMnO4])/(Δt) = -1/2 (Δ[H2S])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = (Δ[K2S2O4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | potassium permanganate | hydrogen sulfide | water | manganese(II) sulfate | potassium dithionite formula | H_2SO_4 | KMnO_4 | H_2S | H_2O | MnSO_4 | K_2S_2O_4 Hill formula | H_2O_4S | KMnO_4 | H_2S | H_2O | MnSO_4 | K_2O_4S_2 name | sulfuric acid | potassium permanganate | hydrogen sulfide | water | manganese(II) sulfate | potassium dithionite IUPAC name | sulfuric acid | potassium permanganate | hydrogen sulfide | water | manganese(+2) cation sulfate |
| sulfuric acid | potassium permanganate | hydrogen sulfide | water | manganese(II) sulfate | potassium dithionite formula | H_2SO_4 | KMnO_4 | H_2S | H_2O | MnSO_4 | K_2S_2O_4 Hill formula | H_2O_4S | KMnO_4 | H_2S | H_2O | MnSO_4 | K_2O_4S_2 name | sulfuric acid | potassium permanganate | hydrogen sulfide | water | manganese(II) sulfate | potassium dithionite IUPAC name | sulfuric acid | potassium permanganate | hydrogen sulfide | water | manganese(+2) cation sulfate |

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