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KOH + KMnO4 + Na3AsO3 = H2O + K2MnO4 + Na3AsO4

Input interpretation

KOH potassium hydroxide + KMnO_4 potassium permanganate + Na3AsO3 ⟶ H_2O water + K_2MnO_4 potassium manganate + AsNa_3O_4 arsenic acid, trisodium salt
KOH potassium hydroxide + KMnO_4 potassium permanganate + Na3AsO3 ⟶ H_2O water + K_2MnO_4 potassium manganate + AsNa_3O_4 arsenic acid, trisodium salt

Balanced equation

Balance the chemical equation algebraically: KOH + KMnO_4 + Na3AsO3 ⟶ H_2O + K_2MnO_4 + AsNa_3O_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 KMnO_4 + c_3 Na3AsO3 ⟶ c_4 H_2O + c_5 K_2MnO_4 + c_6 AsNa_3O_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 As: H: | c_1 = 2 c_4 K: | c_1 + c_2 = 2 c_5 O: | c_1 + 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 4 c_6 Mn: | c_2 = c_5 Na: | 3 c_3 = 3 c_6 As: | c_3 = 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_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 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KOH + 2 KMnO_4 + Na3AsO3 ⟶ H_2O + 2 K_2MnO_4 + AsNa_3O_4
Balance the chemical equation algebraically: KOH + KMnO_4 + Na3AsO3 ⟶ H_2O + K_2MnO_4 + AsNa_3O_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 KMnO_4 + c_3 Na3AsO3 ⟶ c_4 H_2O + c_5 K_2MnO_4 + c_6 AsNa_3O_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 As: H: | c_1 = 2 c_4 K: | c_1 + c_2 = 2 c_5 O: | c_1 + 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 4 c_6 Mn: | c_2 = c_5 Na: | 3 c_3 = 3 c_6 As: | c_3 = 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_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 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KOH + 2 KMnO_4 + Na3AsO3 ⟶ H_2O + 2 K_2MnO_4 + AsNa_3O_4

Structures

+ + Na3AsO3 ⟶ + +
+ + Na3AsO3 ⟶ + +

Names

potassium hydroxide + potassium permanganate + Na3AsO3 ⟶ water + potassium manganate + arsenic acid, trisodium salt
potassium hydroxide + potassium permanganate + Na3AsO3 ⟶ water + potassium manganate + arsenic acid, trisodium salt

Equilibrium constant

Construct the equilibrium constant, K, expression for: KOH + KMnO_4 + Na3AsO3 ⟶ H_2O + K_2MnO_4 + AsNa_3O_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 + Na3AsO3 ⟶ H_2O + 2 K_2MnO_4 + AsNa_3O_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 Na3AsO3 | 1 | -1 H_2O | 1 | 1 K_2MnO_4 | 2 | 2 AsNa_3O_4 | 1 | 1 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) Na3AsO3 | 1 | -1 | ([Na3AsO3])^(-1) H_2O | 1 | 1 | [H2O] K_2MnO_4 | 2 | 2 | ([K2MnO4])^2 AsNa_3O_4 | 1 | 1 | [AsNa3O4] 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) ([Na3AsO3])^(-1) [H2O] ([K2MnO4])^2 [AsNa3O4] = ([H2O] ([K2MnO4])^2 [AsNa3O4])/(([KOH])^2 ([KMnO4])^2 [Na3AsO3])
Construct the equilibrium constant, K, expression for: KOH + KMnO_4 + Na3AsO3 ⟶ H_2O + K_2MnO_4 + AsNa_3O_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 + Na3AsO3 ⟶ H_2O + 2 K_2MnO_4 + AsNa_3O_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 Na3AsO3 | 1 | -1 H_2O | 1 | 1 K_2MnO_4 | 2 | 2 AsNa_3O_4 | 1 | 1 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) Na3AsO3 | 1 | -1 | ([Na3AsO3])^(-1) H_2O | 1 | 1 | [H2O] K_2MnO_4 | 2 | 2 | ([K2MnO4])^2 AsNa_3O_4 | 1 | 1 | [AsNa3O4] 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) ([Na3AsO3])^(-1) [H2O] ([K2MnO4])^2 [AsNa3O4] = ([H2O] ([K2MnO4])^2 [AsNa3O4])/(([KOH])^2 ([KMnO4])^2 [Na3AsO3])

Rate of reaction

Construct the rate of reaction expression for: KOH + KMnO_4 + Na3AsO3 ⟶ H_2O + K_2MnO_4 + AsNa_3O_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 + Na3AsO3 ⟶ H_2O + 2 K_2MnO_4 + AsNa_3O_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 Na3AsO3 | 1 | -1 H_2O | 1 | 1 K_2MnO_4 | 2 | 2 AsNa_3O_4 | 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 KOH | 2 | -2 | -1/2 (Δ[KOH])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) Na3AsO3 | 1 | -1 | -(Δ[Na3AsO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) K_2MnO_4 | 2 | 2 | 1/2 (Δ[K2MnO4])/(Δt) AsNa_3O_4 | 1 | 1 | (Δ[AsNa3O4])/(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[Na3AsO3])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[K2MnO4])/(Δt) = (Δ[AsNa3O4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: KOH + KMnO_4 + Na3AsO3 ⟶ H_2O + K_2MnO_4 + AsNa_3O_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 + Na3AsO3 ⟶ H_2O + 2 K_2MnO_4 + AsNa_3O_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 Na3AsO3 | 1 | -1 H_2O | 1 | 1 K_2MnO_4 | 2 | 2 AsNa_3O_4 | 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 KOH | 2 | -2 | -1/2 (Δ[KOH])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) Na3AsO3 | 1 | -1 | -(Δ[Na3AsO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) K_2MnO_4 | 2 | 2 | 1/2 (Δ[K2MnO4])/(Δt) AsNa_3O_4 | 1 | 1 | (Δ[AsNa3O4])/(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[Na3AsO3])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[K2MnO4])/(Δt) = (Δ[AsNa3O4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| potassium hydroxide | potassium permanganate | Na3AsO3 | water | potassium manganate | arsenic acid, trisodium salt formula | KOH | KMnO_4 | Na3AsO3 | H_2O | K_2MnO_4 | AsNa_3O_4 Hill formula | HKO | KMnO_4 | AsNa3O3 | H_2O | K_2MnO_4 | AsNa_3O_4 name | potassium hydroxide | potassium permanganate | | water | potassium manganate | arsenic acid, trisodium salt IUPAC name | potassium hydroxide | potassium permanganate | | water | dipotassium dioxido-dioxomanganese |
| potassium hydroxide | potassium permanganate | Na3AsO3 | water | potassium manganate | arsenic acid, trisodium salt formula | KOH | KMnO_4 | Na3AsO3 | H_2O | K_2MnO_4 | AsNa_3O_4 Hill formula | HKO | KMnO_4 | AsNa3O3 | H_2O | K_2MnO_4 | AsNa_3O_4 name | potassium hydroxide | potassium permanganate | | water | potassium manganate | arsenic acid, trisodium salt IUPAC name | potassium hydroxide | potassium permanganate | | water | dipotassium dioxido-dioxomanganese |

Substance properties

| potassium hydroxide | potassium permanganate | Na3AsO3 | water | potassium manganate | arsenic acid, trisodium salt molar mass | 56.105 g/mol | 158.03 g/mol | 191.888 g/mol | 18.015 g/mol | 197.13 g/mol | 207.887 g/mol phase | solid (at STP) | solid (at STP) | | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 406 °C | 240 °C | | 0 °C | 190 °C | 1260 °C boiling point | 1327 °C | | | 99.9839 °C | | density | 2.044 g/cm^3 | 1 g/cm^3 | | 1 g/cm^3 | | 2.81 g/cm^3 solubility in water | soluble | | | | decomposes | surface tension | | | | 0.0728 N/m | | dynamic viscosity | 0.001 Pa s (at 550 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | odorless | | odorless | |
| potassium hydroxide | potassium permanganate | Na3AsO3 | water | potassium manganate | arsenic acid, trisodium salt molar mass | 56.105 g/mol | 158.03 g/mol | 191.888 g/mol | 18.015 g/mol | 197.13 g/mol | 207.887 g/mol phase | solid (at STP) | solid (at STP) | | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 406 °C | 240 °C | | 0 °C | 190 °C | 1260 °C boiling point | 1327 °C | | | 99.9839 °C | | density | 2.044 g/cm^3 | 1 g/cm^3 | | 1 g/cm^3 | | 2.81 g/cm^3 solubility in water | soluble | | | | decomposes | surface tension | | | | 0.0728 N/m | | dynamic viscosity | 0.001 Pa s (at 550 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | odorless | | odorless | |

Units

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