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NaOH + KMnO4 + Na2SO3 = H2O + Na2SO4 + K2MnO4 + Na2MnO4

Input interpretation

NaOH (sodium hydroxide) + KMnO_4 (potassium permanganate) + Na_2SO_3 (sodium sulfite) ⟶ H_2O (water) + Na_2SO_4 (sodium sulfate) + K_2MnO_4 (potassium manganate) + Na2MnO4
NaOH (sodium hydroxide) + KMnO_4 (potassium permanganate) + Na_2SO_3 (sodium sulfite) ⟶ H_2O (water) + Na_2SO_4 (sodium sulfate) + K_2MnO_4 (potassium manganate) + Na2MnO4

Balanced equation

Balance the chemical equation algebraically: NaOH + KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + K_2MnO_4 + Na2MnO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 KMnO_4 + c_3 Na_2SO_3 ⟶ c_4 H_2O + c_5 Na_2SO_4 + c_6 K_2MnO_4 + c_7 Na2MnO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, K, Mn and S: H: | c_1 = 2 c_4 Na: | c_1 + 2 c_3 = 2 c_5 + 2 c_7 O: | c_1 + 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 4 c_6 + 4 c_7 K: | c_2 = 2 c_6 Mn: | c_2 = c_6 + c_7 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 = 1 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + 2 KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + K_2MnO_4 + Na2MnO4
Balance the chemical equation algebraically: NaOH + KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + K_2MnO_4 + Na2MnO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 KMnO_4 + c_3 Na_2SO_3 ⟶ c_4 H_2O + c_5 Na_2SO_4 + c_6 K_2MnO_4 + c_7 Na2MnO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, K, Mn and S: H: | c_1 = 2 c_4 Na: | c_1 + 2 c_3 = 2 c_5 + 2 c_7 O: | c_1 + 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 4 c_6 + 4 c_7 K: | c_2 = 2 c_6 Mn: | c_2 = c_6 + c_7 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 = 1 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + 2 KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + K_2MnO_4 + Na2MnO4

Structures

+ + ⟶ + + + Na2MnO4
+ + ⟶ + + + Na2MnO4

Names

sodium hydroxide + potassium permanganate + sodium sulfite ⟶ water + sodium sulfate + potassium manganate + Na2MnO4
sodium hydroxide + potassium permanganate + sodium sulfite ⟶ water + sodium sulfate + potassium manganate + Na2MnO4

Equilibrium constant

Construct the equilibrium constant, K, expression for: NaOH + KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + K_2MnO_4 + Na2MnO4 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 NaOH + 2 KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + K_2MnO_4 + Na2MnO4 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 NaOH | 2 | -2 KMnO_4 | 2 | -2 Na_2SO_3 | 1 | -1 H_2O | 1 | 1 Na_2SO_4 | 1 | 1 K_2MnO_4 | 1 | 1 Na2MnO4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 2 | -2 | ([NaOH])^(-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 | 1 | 1 | [K2MnO4] Na2MnO4 | 1 | 1 | [Na2MnO4] 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 = ([NaOH])^(-2) ([KMnO4])^(-2) ([Na2SO3])^(-1) [H2O] [Na2SO4] [K2MnO4] [Na2MnO4] = ([H2O] [Na2SO4] [K2MnO4] [Na2MnO4])/(([NaOH])^2 ([KMnO4])^2 [Na2SO3])
Construct the equilibrium constant, K, expression for: NaOH + KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + K_2MnO_4 + Na2MnO4 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 NaOH + 2 KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + K_2MnO_4 + Na2MnO4 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 NaOH | 2 | -2 KMnO_4 | 2 | -2 Na_2SO_3 | 1 | -1 H_2O | 1 | 1 Na_2SO_4 | 1 | 1 K_2MnO_4 | 1 | 1 Na2MnO4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 2 | -2 | ([NaOH])^(-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 | 1 | 1 | [K2MnO4] Na2MnO4 | 1 | 1 | [Na2MnO4] 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 = ([NaOH])^(-2) ([KMnO4])^(-2) ([Na2SO3])^(-1) [H2O] [Na2SO4] [K2MnO4] [Na2MnO4] = ([H2O] [Na2SO4] [K2MnO4] [Na2MnO4])/(([NaOH])^2 ([KMnO4])^2 [Na2SO3])

Rate of reaction

Construct the rate of reaction expression for: NaOH + KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + K_2MnO_4 + Na2MnO4 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 NaOH + 2 KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + K_2MnO_4 + Na2MnO4 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 NaOH | 2 | -2 KMnO_4 | 2 | -2 Na_2SO_3 | 1 | -1 H_2O | 1 | 1 Na_2SO_4 | 1 | 1 K_2MnO_4 | 1 | 1 Na2MnO4 | 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 NaOH | 2 | -2 | -1/2 (Δ[NaOH])/(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 | 1 | 1 | (Δ[K2MnO4])/(Δt) Na2MnO4 | 1 | 1 | (Δ[Na2MnO4])/(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[NaOH])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -(Δ[Na2SO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[Na2SO4])/(Δt) = (Δ[K2MnO4])/(Δt) = (Δ[Na2MnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: NaOH + KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + K_2MnO_4 + Na2MnO4 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 NaOH + 2 KMnO_4 + Na_2SO_3 ⟶ H_2O + Na_2SO_4 + K_2MnO_4 + Na2MnO4 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 NaOH | 2 | -2 KMnO_4 | 2 | -2 Na_2SO_3 | 1 | -1 H_2O | 1 | 1 Na_2SO_4 | 1 | 1 K_2MnO_4 | 1 | 1 Na2MnO4 | 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 NaOH | 2 | -2 | -1/2 (Δ[NaOH])/(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 | 1 | 1 | (Δ[K2MnO4])/(Δt) Na2MnO4 | 1 | 1 | (Δ[Na2MnO4])/(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[NaOH])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -(Δ[Na2SO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[Na2SO4])/(Δt) = (Δ[K2MnO4])/(Δt) = (Δ[Na2MnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sodium hydroxide | potassium permanganate | sodium sulfite | water | sodium sulfate | potassium manganate | Na2MnO4 formula | NaOH | KMnO_4 | Na_2SO_3 | H_2O | Na_2SO_4 | K_2MnO_4 | Na2MnO4 Hill formula | HNaO | KMnO_4 | Na_2O_3S | H_2O | Na_2O_4S | K_2MnO_4 | MnNa2O4 name | sodium hydroxide | potassium permanganate | sodium sulfite | water | sodium sulfate | potassium manganate | IUPAC name | sodium hydroxide | potassium permanganate | disodium sulfite | water | disodium sulfate | dipotassium dioxido-dioxomanganese |
| sodium hydroxide | potassium permanganate | sodium sulfite | water | sodium sulfate | potassium manganate | Na2MnO4 formula | NaOH | KMnO_4 | Na_2SO_3 | H_2O | Na_2SO_4 | K_2MnO_4 | Na2MnO4 Hill formula | HNaO | KMnO_4 | Na_2O_3S | H_2O | Na_2O_4S | K_2MnO_4 | MnNa2O4 name | sodium hydroxide | potassium permanganate | sodium sulfite | water | sodium sulfate | potassium manganate | IUPAC name | sodium hydroxide | potassium permanganate | disodium sulfite | water | disodium sulfate | dipotassium dioxido-dioxomanganese |

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