H2O + KMnO4 + Na2S2O3 = KOH + Na2SO4 + MnO2 + K2S2O4

Input interpretation

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H_2O (water) + KMnO_4 (potassium permanganate) + Na_2S_2O_3 (sodium hyposulfite) ⟶ KOH (potassium hydroxide) + Na_2SO_4 (sodium sulfate) + MnO_2 (manganese dioxide) + K_2S_2O_4 (potassium dithionite)

Balanced equation

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$Balance the chemical equation algebraically: H_2O + KMnO_4 + Na_2S_2O_3 ⟶ KOH + Na_2SO_4 + MnO_2 + K_2S_2O_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KMnO_4 + c_3 Na_2S_2O_3 ⟶ c_4 KOH + c_5 Na_2SO_4 + c_6 MnO_2 + c_7 K_2S_2O_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K, Mn, Na and S: H: | 2 c_1 = c_4 O: | c_1 + 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 2 c_6 + 4 c_7 K: | c_2 = c_4 + 2 c_7 Mn: | c_2 = c_6 Na: | 2 c_3 = 2 c_5 S: | 2 c_3 = c_5 + 2 c_7 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 5 c_3 = 3 c_4 = 2 c_5 = 3 c_6 = 5 c_7 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 10 c_3 = 6 c_4 = 4 c_5 = 6 c_6 = 10 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 10 KMnO_4 + 6 Na_2S_2O_3 ⟶ 4 KOH + 6 Na_2SO_4 + 10 MnO_2 + 3 K_2S_2O_4$

Balance the chemical equation algebraically: H_2O + KMnO_4 + Na_2S_2O_3 ⟶ KOH + Na_2SO_4 + MnO_2 + K_2S_2O_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KMnO_4 + c_3 Na_2S_2O_3 ⟶ c_4 KOH + c_5 Na_2SO_4 + c_6 MnO_2 + c_7 K_2S_2O_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K, Mn, Na and S: H: | 2 c_1 = c_4 O: | c_1 + 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 2 c_6 + 4 c_7 K: | c_2 = c_4 + 2 c_7 Mn: | c_2 = c_6 Na: | 2 c_3 = 2 c_5 S: | 2 c_3 = c_5 + 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 5 c_3 = 3 c_4 = 2 c_5 = 3 c_6 = 5 c_7 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 10 c_3 = 6 c_4 = 4 c_5 = 6 c_6 = 10 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 10 KMnO_4 + 6 Na_2S_2O_3 ⟶ 4 KOH + 6 Na_2SO_4 + 10 MnO_2 + 3 K_2S_2O_4

+ + ⟶ + + +

Names

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water + potassium permanganate + sodium hyposulfite ⟶ potassium hydroxide + sodium sulfate + manganese dioxide + potassium dithionite

Equilibrium constant

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K_c = ([KOH]^4 [Na2SO4]^6 [MnO2]^10 [K2S2O4]^3)/([H2O]^2 [KMnO4]^10 [Na2S2O3]^6)

Rate of reaction

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rate = -1/2 (Δ[H2O])/(Δt) = -1/10 (Δ[KMnO4])/(Δt) = -1/6 (Δ[Na2S2O3])/(Δt) = 1/4 (Δ[KOH])/(Δt) = 1/6 (Δ[Na2SO4])/(Δt) = 1/10 (Δ[MnO2])/(Δt) = 1/3 (Δ[K2S2O4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)