H2SO4 + KMnO4 + H2S = H2O + K2SO4 + SO2 + MnSO4

Input interpretation

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H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + H_2S hydrogen sulfide ⟶ H_2O water + K_2SO_4 potassium sulfate + SO_2 sulfur dioxide + MnSO_4 manganese(II) sulfate

Balanced equation

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$Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + H_2S ⟶ H_2O + K_2SO_4 + SO_2 + MnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 H_2S ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 SO_2 + c_7 MnSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K and Mn: H: | 2 c_1 + 2 c_3 = 2 c_4 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 2 c_6 + 4 c_7 S: | c_1 + c_3 = c_5 + c_6 + c_7 K: | c_2 = 2 c_5 Mn: | c_2 = c_7 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_5 = 1 and solve the system of equations for the remaining coefficients: c_2 = 2 c_3 = c_1/3 + 2/3 c_4 = (4 c_1)/3 + 2/3 c_5 = 1 c_6 = (4 c_1)/3 - 7/3 c_7 = 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_2 = 4 c_3 = c_1/3 + 4/3 c_4 = (4 c_1)/3 + 4/3 c_5 = 2 c_6 = (4 c_1)/3 - 14/3 c_7 = 4 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 5 and solve for the remaining coefficients: c_1 = 5 c_2 = 4 c_3 = 3 c_4 = 8 c_5 = 2 c_6 = 2 c_7 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 H_2SO_4 + 4 KMnO_4 + 3 H_2S ⟶ 8 H_2O + 2 K_2SO_4 + 2 SO_2 + 4 MnSO_4$

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + H_2S ⟶ H_2O + K_2SO_4 + SO_2 + MnSO_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 K_2SO_4 + c_6 SO_2 + c_7 MnSO_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 + 2 c_6 + 4 c_7 S: | c_1 + c_3 = c_5 + c_6 + c_7 K: | c_2 = 2 c_5 Mn: | c_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_5 = 1 and solve the system of equations for the remaining coefficients: c_2 = 2 c_3 = c_1/3 + 2/3 c_4 = (4 c_1)/3 + 2/3 c_5 = 1 c_6 = (4 c_1)/3 - 7/3 c_7 = 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_2 = 4 c_3 = c_1/3 + 4/3 c_4 = (4 c_1)/3 + 4/3 c_5 = 2 c_6 = (4 c_1)/3 - 14/3 c_7 = 4 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 5 and solve for the remaining coefficients: c_1 = 5 c_2 = 4 c_3 = 3 c_4 = 8 c_5 = 2 c_6 = 2 c_7 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 H_2SO_4 + 4 KMnO_4 + 3 H_2S ⟶ 8 H_2O + 2 K_2SO_4 + 2 SO_2 + 4 MnSO_4

+ + ⟶ + + +

Names

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

Equilibrium constant

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K_c = ([H2O]^8 [K2SO4]^2 [SO2]^2 [MnSO4]^4)/([H2SO4]^5 [KMnO4]^4 [H2S]^3)

Rate of reaction

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rate = -1/5 (Δ[H2SO4])/(Δt) = -1/4 (Δ[KMnO4])/(Δt) = -1/3 (Δ[H2S])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/2 (Δ[K2SO4])/(Δt) = 1/2 (Δ[SO2])/(Δt) = 1/4 (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)