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KOH + KMnO4 + Na2SO3 = H2O + Na2SO4 + K2MnO4

Input interpretation

KOH (potassium hydroxide) + KMnO_4 (potassium permanganate) + Na_2SO_3 (sodium sulfite) ⟶ H_2O (water) + Na_2SO_4 (sodium sulfate) + K_2MnO_4 (potassium manganate)
KOH (potassium hydroxide) + KMnO_4 (potassium permanganate) + Na_2SO_3 (sodium sulfite) ⟶ H_2O (water) + Na_2SO_4 (sodium sulfate) + K_2MnO_4 (potassium manganate)

Balanced equation

Balance the chemical equation algebraically: KOH + KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + K_2MnO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 KMnO_4 + c_3 Na_2SO_3 ⟶ c_4 H_2O + c_5 Na_2SO_4 + c_6 K_2MnO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Mn, Na and S: H: | c_1 = 2 c_4 K: | c_1 + c_2 = 2 c_6 O: | c_1 + 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 4 c_6 Mn: | c_2 = c_6 Na: | 2 c_3 = 2 c_5 S: | c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 c_4 = 1 c_5 = 1 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KOH + 2 KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + 2 K_2MnO_4
Balance the chemical equation algebraically: KOH + KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + K_2MnO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 KMnO_4 + c_3 Na_2SO_3 ⟶ c_4 H_2O + c_5 Na_2SO_4 + c_6 K_2MnO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Mn, Na and S: H: | c_1 = 2 c_4 K: | c_1 + c_2 = 2 c_6 O: | c_1 + 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 4 c_6 Mn: | c_2 = c_6 Na: | 2 c_3 = 2 c_5 S: | c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 c_4 = 1 c_5 = 1 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KOH + 2 KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + 2 K_2MnO_4

Structures

+ + ⟶ + +
+ + ⟶ + +

Names

potassium hydroxide + potassium permanganate + sodium sulfite ⟶ water + sodium sulfate + potassium manganate
potassium hydroxide + potassium permanganate + sodium sulfite ⟶ water + sodium sulfate + potassium manganate

Equilibrium constant

Construct the equilibrium constant, K, expression for: KOH + KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + K_2MnO_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 KOH + 2 KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + 2 K_2MnO_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 KOH | 2 | -2 KMnO_4 | 2 | -2 Na_2SO_3 | 1 | -1 H_2O | 1 | 1 Na_2SO_4 | 1 | 1 K_2MnO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 2 | -2 | ([KOH])^(-2) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) Na_2SO_3 | 1 | -1 | ([Na2SO3])^(-1) H_2O | 1 | 1 | [H2O] Na_2SO_4 | 1 | 1 | [Na2SO4] K_2MnO_4 | 2 | 2 | ([K2MnO4])^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 = ([KOH])^(-2) ([KMnO4])^(-2) ([Na2SO3])^(-1) [H2O] [Na2SO4] ([K2MnO4])^2 = ([H2O] [Na2SO4] ([K2MnO4])^2)/(([KOH])^2 ([KMnO4])^2 [Na2SO3])
Construct the equilibrium constant, K, expression for: KOH + KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + K_2MnO_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 KOH + 2 KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + 2 K_2MnO_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 KOH | 2 | -2 KMnO_4 | 2 | -2 Na_2SO_3 | 1 | -1 H_2O | 1 | 1 Na_2SO_4 | 1 | 1 K_2MnO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 2 | -2 | ([KOH])^(-2) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) Na_2SO_3 | 1 | -1 | ([Na2SO3])^(-1) H_2O | 1 | 1 | [H2O] Na_2SO_4 | 1 | 1 | [Na2SO4] K_2MnO_4 | 2 | 2 | ([K2MnO4])^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 = ([KOH])^(-2) ([KMnO4])^(-2) ([Na2SO3])^(-1) [H2O] [Na2SO4] ([K2MnO4])^2 = ([H2O] [Na2SO4] ([K2MnO4])^2)/(([KOH])^2 ([KMnO4])^2 [Na2SO3])

Rate of reaction

Construct the rate of reaction expression for: KOH + KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + K_2MnO_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 KOH + 2 KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + 2 K_2MnO_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 KOH | 2 | -2 KMnO_4 | 2 | -2 Na_2SO_3 | 1 | -1 H_2O | 1 | 1 Na_2SO_4 | 1 | 1 K_2MnO_4 | 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 KOH | 2 | -2 | -1/2 (Δ[KOH])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) Na_2SO_3 | 1 | -1 | -(Δ[Na2SO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) Na_2SO_4 | 1 | 1 | (Δ[Na2SO4])/(Δt) K_2MnO_4 | 2 | 2 | 1/2 (Δ[K2MnO4])/(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[KOH])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -(Δ[Na2SO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[Na2SO4])/(Δt) = 1/2 (Δ[K2MnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: KOH + KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + K_2MnO_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 KOH + 2 KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + 2 K_2MnO_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 KOH | 2 | -2 KMnO_4 | 2 | -2 Na_2SO_3 | 1 | -1 H_2O | 1 | 1 Na_2SO_4 | 1 | 1 K_2MnO_4 | 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 KOH | 2 | -2 | -1/2 (Δ[KOH])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) Na_2SO_3 | 1 | -1 | -(Δ[Na2SO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) Na_2SO_4 | 1 | 1 | (Δ[Na2SO4])/(Δt) K_2MnO_4 | 2 | 2 | 1/2 (Δ[K2MnO4])/(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[KOH])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -(Δ[Na2SO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[Na2SO4])/(Δt) = 1/2 (Δ[K2MnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| potassium hydroxide | potassium permanganate | sodium sulfite | water | sodium sulfate | potassium manganate formula | KOH | KMnO_4 | Na_2SO_3 | H_2O | Na_2SO_4 | K_2MnO_4 Hill formula | HKO | KMnO_4 | Na_2O_3S | H_2O | Na_2O_4S | K_2MnO_4 name | potassium hydroxide | potassium permanganate | sodium sulfite | water | sodium sulfate | potassium manganate IUPAC name | potassium hydroxide | potassium permanganate | disodium sulfite | water | disodium sulfate | dipotassium dioxido-dioxomanganese
| potassium hydroxide | potassium permanganate | sodium sulfite | water | sodium sulfate | potassium manganate formula | KOH | KMnO_4 | Na_2SO_3 | H_2O | Na_2SO_4 | K_2MnO_4 Hill formula | HKO | KMnO_4 | Na_2O_3S | H_2O | Na_2O_4S | K_2MnO_4 name | potassium hydroxide | potassium permanganate | sodium sulfite | water | sodium sulfate | potassium manganate IUPAC name | potassium hydroxide | potassium permanganate | disodium sulfite | water | disodium sulfate | dipotassium dioxido-dioxomanganese

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