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NaOH + KMnO4 + H2O2 = H2O + O2 + KOH + MnO2 + Na2O

Input interpretation

NaOH (sodium hydroxide) + KMnO_4 (potassium permanganate) + H_2O_2 (hydrogen peroxide) ⟶ H_2O (water) + O_2 (oxygen) + KOH (potassium hydroxide) + MnO_2 (manganese dioxide) + Na_2O (sodium oxide)
NaOH (sodium hydroxide) + KMnO_4 (potassium permanganate) + H_2O_2 (hydrogen peroxide) ⟶ H_2O (water) + O_2 (oxygen) + KOH (potassium hydroxide) + MnO_2 (manganese dioxide) + Na_2O (sodium oxide)

Balanced equation

Balance the chemical equation algebraically: NaOH + KMnO_4 + H_2O_2 ⟶ H_2O + O_2 + KOH + MnO_2 + Na_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 KMnO_4 + c_3 H_2O_2 ⟶ c_4 H_2O + c_5 O_2 + c_6 KOH + c_7 MnO_2 + c_8 Na_2O Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, K and Mn: H: | c_1 + 2 c_3 = 2 c_4 + c_6 Na: | c_1 = 2 c_8 O: | c_1 + 4 c_2 + 2 c_3 = c_4 + 2 c_5 + c_6 + 2 c_7 + c_8 K: | c_2 = c_6 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_3 = 1 and solve the system of equations for the remaining coefficients: c_3 = 1 c_4 = 1 + c_1/2 - c_2/2 c_5 = (3 c_2)/4 + 1/2 c_6 = c_2 c_7 = c_2 c_8 = c_1/2 The resulting system of equations is still underdetermined, so additional coefficients must be set arbitrarily. Set c_1 = 2 and c_2 = 2 and solve for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 c_4 = 1 c_5 = 2 c_6 = 2 c_7 = 2 c_8 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + 2 KMnO_4 + H_2O_2 ⟶ H_2O + 2 O_2 + 2 KOH + 2 MnO_2 + Na_2O
Balance the chemical equation algebraically: NaOH + KMnO_4 + H_2O_2 ⟶ H_2O + O_2 + KOH + MnO_2 + Na_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 KMnO_4 + c_3 H_2O_2 ⟶ c_4 H_2O + c_5 O_2 + c_6 KOH + c_7 MnO_2 + c_8 Na_2O Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, K and Mn: H: | c_1 + 2 c_3 = 2 c_4 + c_6 Na: | c_1 = 2 c_8 O: | c_1 + 4 c_2 + 2 c_3 = c_4 + 2 c_5 + c_6 + 2 c_7 + c_8 K: | c_2 = c_6 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_3 = 1 and solve the system of equations for the remaining coefficients: c_3 = 1 c_4 = 1 + c_1/2 - c_2/2 c_5 = (3 c_2)/4 + 1/2 c_6 = c_2 c_7 = c_2 c_8 = c_1/2 The resulting system of equations is still underdetermined, so additional coefficients must be set arbitrarily. Set c_1 = 2 and c_2 = 2 and solve for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 c_4 = 1 c_5 = 2 c_6 = 2 c_7 = 2 c_8 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + 2 KMnO_4 + H_2O_2 ⟶ H_2O + 2 O_2 + 2 KOH + 2 MnO_2 + Na_2O

Structures

+ + ⟶ + + + +
+ + ⟶ + + + +

Names

sodium hydroxide + potassium permanganate + hydrogen peroxide ⟶ water + oxygen + potassium hydroxide + manganese dioxide + sodium oxide
sodium hydroxide + potassium permanganate + hydrogen peroxide ⟶ water + oxygen + potassium hydroxide + manganese dioxide + sodium oxide

Equilibrium constant

Construct the equilibrium constant, K, expression for: NaOH + KMnO_4 + H_2O_2 ⟶ H_2O + O_2 + KOH + MnO_2 + Na_2O 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 + H_2O_2 ⟶ H_2O + 2 O_2 + 2 KOH + 2 MnO_2 + Na_2O 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 H_2O_2 | 1 | -1 H_2O | 1 | 1 O_2 | 2 | 2 KOH | 2 | 2 MnO_2 | 2 | 2 Na_2O | 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) H_2O_2 | 1 | -1 | ([H2O2])^(-1) H_2O | 1 | 1 | [H2O] O_2 | 2 | 2 | ([O2])^2 KOH | 2 | 2 | ([KOH])^2 MnO_2 | 2 | 2 | ([MnO2])^2 Na_2O | 1 | 1 | [Na2O] 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) ([H2O2])^(-1) [H2O] ([O2])^2 ([KOH])^2 ([MnO2])^2 [Na2O] = ([H2O] ([O2])^2 ([KOH])^2 ([MnO2])^2 [Na2O])/(([NaOH])^2 ([KMnO4])^2 [H2O2])
Construct the equilibrium constant, K, expression for: NaOH + KMnO_4 + H_2O_2 ⟶ H_2O + O_2 + KOH + MnO_2 + Na_2O 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 + H_2O_2 ⟶ H_2O + 2 O_2 + 2 KOH + 2 MnO_2 + Na_2O 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 H_2O_2 | 1 | -1 H_2O | 1 | 1 O_2 | 2 | 2 KOH | 2 | 2 MnO_2 | 2 | 2 Na_2O | 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) H_2O_2 | 1 | -1 | ([H2O2])^(-1) H_2O | 1 | 1 | [H2O] O_2 | 2 | 2 | ([O2])^2 KOH | 2 | 2 | ([KOH])^2 MnO_2 | 2 | 2 | ([MnO2])^2 Na_2O | 1 | 1 | [Na2O] 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) ([H2O2])^(-1) [H2O] ([O2])^2 ([KOH])^2 ([MnO2])^2 [Na2O] = ([H2O] ([O2])^2 ([KOH])^2 ([MnO2])^2 [Na2O])/(([NaOH])^2 ([KMnO4])^2 [H2O2])

Rate of reaction

Construct the rate of reaction expression for: NaOH + KMnO_4 + H_2O_2 ⟶ H_2O + O_2 + KOH + MnO_2 + Na_2O 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 + H_2O_2 ⟶ H_2O + 2 O_2 + 2 KOH + 2 MnO_2 + Na_2O 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 H_2O_2 | 1 | -1 H_2O | 1 | 1 O_2 | 2 | 2 KOH | 2 | 2 MnO_2 | 2 | 2 Na_2O | 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) H_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) O_2 | 2 | 2 | 1/2 (Δ[O2])/(Δt) KOH | 2 | 2 | 1/2 (Δ[KOH])/(Δt) MnO_2 | 2 | 2 | 1/2 (Δ[MnO2])/(Δt) Na_2O | 1 | 1 | (Δ[Na2O])/(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[H2O2])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[O2])/(Δt) = 1/2 (Δ[KOH])/(Δt) = 1/2 (Δ[MnO2])/(Δt) = (Δ[Na2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: NaOH + KMnO_4 + H_2O_2 ⟶ H_2O + O_2 + KOH + MnO_2 + Na_2O 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 + H_2O_2 ⟶ H_2O + 2 O_2 + 2 KOH + 2 MnO_2 + Na_2O 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 H_2O_2 | 1 | -1 H_2O | 1 | 1 O_2 | 2 | 2 KOH | 2 | 2 MnO_2 | 2 | 2 Na_2O | 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) H_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) O_2 | 2 | 2 | 1/2 (Δ[O2])/(Δt) KOH | 2 | 2 | 1/2 (Δ[KOH])/(Δt) MnO_2 | 2 | 2 | 1/2 (Δ[MnO2])/(Δt) Na_2O | 1 | 1 | (Δ[Na2O])/(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[H2O2])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[O2])/(Δt) = 1/2 (Δ[KOH])/(Δt) = 1/2 (Δ[MnO2])/(Δt) = (Δ[Na2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sodium hydroxide | potassium permanganate | hydrogen peroxide | water | oxygen | potassium hydroxide | manganese dioxide | sodium oxide formula | NaOH | KMnO_4 | H_2O_2 | H_2O | O_2 | KOH | MnO_2 | Na_2O Hill formula | HNaO | KMnO_4 | H_2O_2 | H_2O | O_2 | HKO | MnO_2 | Na_2O name | sodium hydroxide | potassium permanganate | hydrogen peroxide | water | oxygen | potassium hydroxide | manganese dioxide | sodium oxide IUPAC name | sodium hydroxide | potassium permanganate | hydrogen peroxide | water | molecular oxygen | potassium hydroxide | dioxomanganese | disodium oxygen(-2) anion
| sodium hydroxide | potassium permanganate | hydrogen peroxide | water | oxygen | potassium hydroxide | manganese dioxide | sodium oxide formula | NaOH | KMnO_4 | H_2O_2 | H_2O | O_2 | KOH | MnO_2 | Na_2O Hill formula | HNaO | KMnO_4 | H_2O_2 | H_2O | O_2 | HKO | MnO_2 | Na_2O name | sodium hydroxide | potassium permanganate | hydrogen peroxide | water | oxygen | potassium hydroxide | manganese dioxide | sodium oxide IUPAC name | sodium hydroxide | potassium permanganate | hydrogen peroxide | water | molecular oxygen | potassium hydroxide | dioxomanganese | disodium oxygen(-2) anion

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