Input interpretation
H_2O water + KMnO_4 potassium permanganate + Na_2S_2O_3 sodium hyposulfite ⟶ K_2SO_4 potassium sulfate + KOH potassium hydroxide + Na_2SO_4 sodium sulfate + MnO_2 manganese dioxide
Balanced equation
Balance the chemical equation algebraically: H_2O + KMnO_4 + Na_2S_2O_3 ⟶ K_2SO_4 + KOH + Na_2SO_4 + MnO_2 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 K_2SO_4 + c_5 KOH + c_6 Na_2SO_4 + c_7 MnO_2 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_5 O: | c_1 + 4 c_2 + 3 c_3 = 4 c_4 + c_5 + 4 c_6 + 2 c_7 K: | c_2 = 2 c_4 + c_5 Mn: | c_2 = c_7 Na: | 2 c_3 = 2 c_6 S: | 2 c_3 = c_4 + 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 8 c_3 = 3 c_4 = 3 c_5 = 2 c_6 = 3 c_7 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + 8 KMnO_4 + 3 Na_2S_2O_3 ⟶ 3 K_2SO_4 + 2 KOH + 3 Na_2SO_4 + 8 MnO_2
Structures
+ + ⟶ + + +
Names
water + potassium permanganate + sodium hyposulfite ⟶ potassium sulfate + potassium hydroxide + sodium sulfate + manganese dioxide
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2O + KMnO_4 + Na_2S_2O_3 ⟶ K_2SO_4 + KOH + Na_2SO_4 + MnO_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: H_2O + 8 KMnO_4 + 3 Na_2S_2O_3 ⟶ 3 K_2SO_4 + 2 KOH + 3 Na_2SO_4 + 8 MnO_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_2O | 1 | -1 KMnO_4 | 8 | -8 Na_2S_2O_3 | 3 | -3 K_2SO_4 | 3 | 3 KOH | 2 | 2 Na_2SO_4 | 3 | 3 MnO_2 | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 1 | -1 | ([H2O])^(-1) KMnO_4 | 8 | -8 | ([KMnO4])^(-8) Na_2S_2O_3 | 3 | -3 | ([Na2S2O3])^(-3) K_2SO_4 | 3 | 3 | ([K2SO4])^3 KOH | 2 | 2 | ([KOH])^2 Na_2SO_4 | 3 | 3 | ([Na2SO4])^3 MnO_2 | 8 | 8 | ([MnO2])^8 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 = ([H2O])^(-1) ([KMnO4])^(-8) ([Na2S2O3])^(-3) ([K2SO4])^3 ([KOH])^2 ([Na2SO4])^3 ([MnO2])^8 = (([K2SO4])^3 ([KOH])^2 ([Na2SO4])^3 ([MnO2])^8)/([H2O] ([KMnO4])^8 ([Na2S2O3])^3)](../image_source/14a735e2f0938f22feb4b3dca5427c6d.png)
Construct the equilibrium constant, K, expression for: H_2O + KMnO_4 + Na_2S_2O_3 ⟶ K_2SO_4 + KOH + Na_2SO_4 + MnO_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: H_2O + 8 KMnO_4 + 3 Na_2S_2O_3 ⟶ 3 K_2SO_4 + 2 KOH + 3 Na_2SO_4 + 8 MnO_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_2O | 1 | -1 KMnO_4 | 8 | -8 Na_2S_2O_3 | 3 | -3 K_2SO_4 | 3 | 3 KOH | 2 | 2 Na_2SO_4 | 3 | 3 MnO_2 | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 1 | -1 | ([H2O])^(-1) KMnO_4 | 8 | -8 | ([KMnO4])^(-8) Na_2S_2O_3 | 3 | -3 | ([Na2S2O3])^(-3) K_2SO_4 | 3 | 3 | ([K2SO4])^3 KOH | 2 | 2 | ([KOH])^2 Na_2SO_4 | 3 | 3 | ([Na2SO4])^3 MnO_2 | 8 | 8 | ([MnO2])^8 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 = ([H2O])^(-1) ([KMnO4])^(-8) ([Na2S2O3])^(-3) ([K2SO4])^3 ([KOH])^2 ([Na2SO4])^3 ([MnO2])^8 = (([K2SO4])^3 ([KOH])^2 ([Na2SO4])^3 ([MnO2])^8)/([H2O] ([KMnO4])^8 ([Na2S2O3])^3)
Rate of reaction
![Construct the rate of reaction expression for: H_2O + KMnO_4 + Na_2S_2O_3 ⟶ K_2SO_4 + KOH + Na_2SO_4 + MnO_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: H_2O + 8 KMnO_4 + 3 Na_2S_2O_3 ⟶ 3 K_2SO_4 + 2 KOH + 3 Na_2SO_4 + 8 MnO_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_2O | 1 | -1 KMnO_4 | 8 | -8 Na_2S_2O_3 | 3 | -3 K_2SO_4 | 3 | 3 KOH | 2 | 2 Na_2SO_4 | 3 | 3 MnO_2 | 8 | 8 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_2O | 1 | -1 | -(Δ[H2O])/(Δt) KMnO_4 | 8 | -8 | -1/8 (Δ[KMnO4])/(Δt) Na_2S_2O_3 | 3 | -3 | -1/3 (Δ[Na2S2O3])/(Δt) K_2SO_4 | 3 | 3 | 1/3 (Δ[K2SO4])/(Δt) KOH | 2 | 2 | 1/2 (Δ[KOH])/(Δt) Na_2SO_4 | 3 | 3 | 1/3 (Δ[Na2SO4])/(Δt) MnO_2 | 8 | 8 | 1/8 (Δ[MnO2])/(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 = -(Δ[H2O])/(Δt) = -1/8 (Δ[KMnO4])/(Δt) = -1/3 (Δ[Na2S2O3])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = 1/2 (Δ[KOH])/(Δt) = 1/3 (Δ[Na2SO4])/(Δt) = 1/8 (Δ[MnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/ca1c92b5ecca36c6cb490895d2ee8895.png)
Construct the rate of reaction expression for: H_2O + KMnO_4 + Na_2S_2O_3 ⟶ K_2SO_4 + KOH + Na_2SO_4 + MnO_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: H_2O + 8 KMnO_4 + 3 Na_2S_2O_3 ⟶ 3 K_2SO_4 + 2 KOH + 3 Na_2SO_4 + 8 MnO_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_2O | 1 | -1 KMnO_4 | 8 | -8 Na_2S_2O_3 | 3 | -3 K_2SO_4 | 3 | 3 KOH | 2 | 2 Na_2SO_4 | 3 | 3 MnO_2 | 8 | 8 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_2O | 1 | -1 | -(Δ[H2O])/(Δt) KMnO_4 | 8 | -8 | -1/8 (Δ[KMnO4])/(Δt) Na_2S_2O_3 | 3 | -3 | -1/3 (Δ[Na2S2O3])/(Δt) K_2SO_4 | 3 | 3 | 1/3 (Δ[K2SO4])/(Δt) KOH | 2 | 2 | 1/2 (Δ[KOH])/(Δt) Na_2SO_4 | 3 | 3 | 1/3 (Δ[Na2SO4])/(Δt) MnO_2 | 8 | 8 | 1/8 (Δ[MnO2])/(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 = -(Δ[H2O])/(Δt) = -1/8 (Δ[KMnO4])/(Δt) = -1/3 (Δ[Na2S2O3])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = 1/2 (Δ[KOH])/(Δt) = 1/3 (Δ[Na2SO4])/(Δt) = 1/8 (Δ[MnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| water | potassium permanganate | sodium hyposulfite | potassium sulfate | potassium hydroxide | sodium sulfate | manganese dioxide formula | H_2O | KMnO_4 | Na_2S_2O_3 | K_2SO_4 | KOH | Na_2SO_4 | MnO_2 Hill formula | H_2O | KMnO_4 | Na_2O_3S_2 | K_2O_4S | HKO | Na_2O_4S | MnO_2 name | water | potassium permanganate | sodium hyposulfite | potassium sulfate | potassium hydroxide | sodium sulfate | manganese dioxide IUPAC name | water | potassium permanganate | | dipotassium sulfate | potassium hydroxide | disodium sulfate | dioxomanganese