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MnO2 + H3PO4 + K3AsO3 = H2O + K3AsO4 + Mn3(PO4)2

Input interpretation

MnO_2 manganese dioxide + H_3PO_4 phosphoric acid + K3AsO3 ⟶ H_2O water + K3AsO4 + Mn3(PO4)2
MnO_2 manganese dioxide + H_3PO_4 phosphoric acid + K3AsO3 ⟶ H_2O water + K3AsO4 + Mn3(PO4)2

Balanced equation

Balance the chemical equation algebraically: MnO_2 + H_3PO_4 + K3AsO3 ⟶ H_2O + K3AsO4 + Mn3(PO4)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MnO_2 + c_2 H_3PO_4 + c_3 K3AsO3 ⟶ c_4 H_2O + c_5 K3AsO4 + c_6 Mn3(PO4)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Mn, O, H, P, K and As: Mn: | c_1 = 3 c_6 O: | 2 c_1 + 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 8 c_6 H: | 3 c_2 = 2 c_4 P: | c_2 = 2 c_6 K: | 3 c_3 = 3 c_5 As: | 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 3 c_5 = 3 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: |   | 3 MnO_2 + 2 H_3PO_4 + 3 K3AsO3 ⟶ 3 H_2O + 3 K3AsO4 + Mn3(PO4)2
Balance the chemical equation algebraically: MnO_2 + H_3PO_4 + K3AsO3 ⟶ H_2O + K3AsO4 + Mn3(PO4)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MnO_2 + c_2 H_3PO_4 + c_3 K3AsO3 ⟶ c_4 H_2O + c_5 K3AsO4 + c_6 Mn3(PO4)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Mn, O, H, P, K and As: Mn: | c_1 = 3 c_6 O: | 2 c_1 + 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 8 c_6 H: | 3 c_2 = 2 c_4 P: | c_2 = 2 c_6 K: | 3 c_3 = 3 c_5 As: | 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 3 c_5 = 3 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 MnO_2 + 2 H_3PO_4 + 3 K3AsO3 ⟶ 3 H_2O + 3 K3AsO4 + Mn3(PO4)2

Structures

 + + K3AsO3 ⟶ + K3AsO4 + Mn3(PO4)2
+ + K3AsO3 ⟶ + K3AsO4 + Mn3(PO4)2

Names

manganese dioxide + phosphoric acid + K3AsO3 ⟶ water + K3AsO4 + Mn3(PO4)2
manganese dioxide + phosphoric acid + K3AsO3 ⟶ water + K3AsO4 + Mn3(PO4)2

Equilibrium constant

Construct the equilibrium constant, K, expression for: MnO_2 + H_3PO_4 + K3AsO3 ⟶ H_2O + K3AsO4 + Mn3(PO4)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: 3 MnO_2 + 2 H_3PO_4 + 3 K3AsO3 ⟶ 3 H_2O + 3 K3AsO4 + Mn3(PO4)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 MnO_2 | 3 | -3 H_3PO_4 | 2 | -2 K3AsO3 | 3 | -3 H_2O | 3 | 3 K3AsO4 | 3 | 3 Mn3(PO4)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression MnO_2 | 3 | -3 | ([MnO2])^(-3) H_3PO_4 | 2 | -2 | ([H3PO4])^(-2) K3AsO3 | 3 | -3 | ([K3AsO3])^(-3) H_2O | 3 | 3 | ([H2O])^3 K3AsO4 | 3 | 3 | ([K3AsO4])^3 Mn3(PO4)2 | 1 | 1 | [Mn3(PO4)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 = ([MnO2])^(-3) ([H3PO4])^(-2) ([K3AsO3])^(-3) ([H2O])^3 ([K3AsO4])^3 [Mn3(PO4)2] = (([H2O])^3 ([K3AsO4])^3 [Mn3(PO4)2])/(([MnO2])^3 ([H3PO4])^2 ([K3AsO3])^3)
Construct the equilibrium constant, K, expression for: MnO_2 + H_3PO_4 + K3AsO3 ⟶ H_2O + K3AsO4 + Mn3(PO4)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: 3 MnO_2 + 2 H_3PO_4 + 3 K3AsO3 ⟶ 3 H_2O + 3 K3AsO4 + Mn3(PO4)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 MnO_2 | 3 | -3 H_3PO_4 | 2 | -2 K3AsO3 | 3 | -3 H_2O | 3 | 3 K3AsO4 | 3 | 3 Mn3(PO4)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression MnO_2 | 3 | -3 | ([MnO2])^(-3) H_3PO_4 | 2 | -2 | ([H3PO4])^(-2) K3AsO3 | 3 | -3 | ([K3AsO3])^(-3) H_2O | 3 | 3 | ([H2O])^3 K3AsO4 | 3 | 3 | ([K3AsO4])^3 Mn3(PO4)2 | 1 | 1 | [Mn3(PO4)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 = ([MnO2])^(-3) ([H3PO4])^(-2) ([K3AsO3])^(-3) ([H2O])^3 ([K3AsO4])^3 [Mn3(PO4)2] = (([H2O])^3 ([K3AsO4])^3 [Mn3(PO4)2])/(([MnO2])^3 ([H3PO4])^2 ([K3AsO3])^3)

Rate of reaction

Construct the rate of reaction expression for: MnO_2 + H_3PO_4 + K3AsO3 ⟶ H_2O + K3AsO4 + Mn3(PO4)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: 3 MnO_2 + 2 H_3PO_4 + 3 K3AsO3 ⟶ 3 H_2O + 3 K3AsO4 + Mn3(PO4)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 MnO_2 | 3 | -3 H_3PO_4 | 2 | -2 K3AsO3 | 3 | -3 H_2O | 3 | 3 K3AsO4 | 3 | 3 Mn3(PO4)2 | 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 MnO_2 | 3 | -3 | -1/3 (Δ[MnO2])/(Δt) H_3PO_4 | 2 | -2 | -1/2 (Δ[H3PO4])/(Δt) K3AsO3 | 3 | -3 | -1/3 (Δ[K3AsO3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) K3AsO4 | 3 | 3 | 1/3 (Δ[K3AsO4])/(Δt) Mn3(PO4)2 | 1 | 1 | (Δ[Mn3(PO4)2])/(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 = -1/3 (Δ[MnO2])/(Δt) = -1/2 (Δ[H3PO4])/(Δt) = -1/3 (Δ[K3AsO3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/3 (Δ[K3AsO4])/(Δt) = (Δ[Mn3(PO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: MnO_2 + H_3PO_4 + K3AsO3 ⟶ H_2O + K3AsO4 + Mn3(PO4)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: 3 MnO_2 + 2 H_3PO_4 + 3 K3AsO3 ⟶ 3 H_2O + 3 K3AsO4 + Mn3(PO4)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 MnO_2 | 3 | -3 H_3PO_4 | 2 | -2 K3AsO3 | 3 | -3 H_2O | 3 | 3 K3AsO4 | 3 | 3 Mn3(PO4)2 | 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 MnO_2 | 3 | -3 | -1/3 (Δ[MnO2])/(Δt) H_3PO_4 | 2 | -2 | -1/2 (Δ[H3PO4])/(Δt) K3AsO3 | 3 | -3 | -1/3 (Δ[K3AsO3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) K3AsO4 | 3 | 3 | 1/3 (Δ[K3AsO4])/(Δt) Mn3(PO4)2 | 1 | 1 | (Δ[Mn3(PO4)2])/(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 = -1/3 (Δ[MnO2])/(Δt) = -1/2 (Δ[H3PO4])/(Δt) = -1/3 (Δ[K3AsO3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/3 (Δ[K3AsO4])/(Δt) = (Δ[Mn3(PO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

 | manganese dioxide | phosphoric acid | K3AsO3 | water | K3AsO4 | Mn3(PO4)2 formula | MnO_2 | H_3PO_4 | K3AsO3 | H_2O | K3AsO4 | Mn3(PO4)2 Hill formula | MnO_2 | H_3O_4P | AsK3O3 | H_2O | AsK3O4 | Mn3O8P2 name | manganese dioxide | phosphoric acid | | water | |  IUPAC name | dioxomanganese | phosphoric acid | | water | |
| manganese dioxide | phosphoric acid | K3AsO3 | water | K3AsO4 | Mn3(PO4)2 formula | MnO_2 | H_3PO_4 | K3AsO3 | H_2O | K3AsO4 | Mn3(PO4)2 Hill formula | MnO_2 | H_3O_4P | AsK3O3 | H_2O | AsK3O4 | Mn3O8P2 name | manganese dioxide | phosphoric acid | | water | | IUPAC name | dioxomanganese | phosphoric acid | | water | |

Substance properties

 | manganese dioxide | phosphoric acid | K3AsO3 | water | K3AsO4 | Mn3(PO4)2 molar mass | 86.936 g/mol | 97.994 g/mol | 240.213 g/mol | 18.015 g/mol | 256.212 g/mol | 354.75 g/mol phase | solid (at STP) | liquid (at STP) | | liquid (at STP) | |  melting point | 535 °C | 42.4 °C | | 0 °C | |  boiling point | | 158 °C | | 99.9839 °C | |  density | 5.03 g/cm^3 | 1.685 g/cm^3 | | 1 g/cm^3 | |  solubility in water | insoluble | very soluble | | | |  surface tension | | | | 0.0728 N/m | |  dynamic viscosity | | | | 8.9×10^-4 Pa s (at 25 °C) | |  odor | | odorless | | odorless | |
| manganese dioxide | phosphoric acid | K3AsO3 | water | K3AsO4 | Mn3(PO4)2 molar mass | 86.936 g/mol | 97.994 g/mol | 240.213 g/mol | 18.015 g/mol | 256.212 g/mol | 354.75 g/mol phase | solid (at STP) | liquid (at STP) | | liquid (at STP) | | melting point | 535 °C | 42.4 °C | | 0 °C | | boiling point | | 158 °C | | 99.9839 °C | | density | 5.03 g/cm^3 | 1.685 g/cm^3 | | 1 g/cm^3 | | solubility in water | insoluble | very soluble | | | | surface tension | | | | 0.0728 N/m | | dynamic viscosity | | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | odorless | | odorless | |

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