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H2SO4 + KMnO4 + Na3AsO3 = H2O + K2SO4 + MnSO4 + Na3AsO4

Input interpretation

H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + Na3AsO3 ⟶ H_2O water + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + AsNa_3O_4 arsenic acid, trisodium salt
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + Na3AsO3 ⟶ H_2O water + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + AsNa_3O_4 arsenic acid, trisodium salt

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + Na3AsO3 ⟶ H_2O + K_2SO_4 + MnSO_4 + AsNa_3O_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 Na3AsO3 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 MnSO_4 + c_7 AsNa_3O_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn, Na and As: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 4 c_6 + 4 c_7 S: | c_1 = c_5 + c_6 K: | c_2 = 2 c_5 Mn: | c_2 = c_6 Na: | 3 c_3 = 3 c_7 As: | c_3 = 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 5 c_4 = 3 c_5 = 1 c_6 = 2 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + 2 KMnO_4 + 5 Na3AsO3 ⟶ 3 H_2O + K_2SO_4 + 2 MnSO_4 + 5 AsNa_3O_4
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + Na3AsO3 ⟶ H_2O + K_2SO_4 + MnSO_4 + AsNa_3O_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 Na3AsO3 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 MnSO_4 + c_7 AsNa_3O_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn, Na and As: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 4 c_6 + 4 c_7 S: | c_1 = c_5 + c_6 K: | c_2 = 2 c_5 Mn: | c_2 = c_6 Na: | 3 c_3 = 3 c_7 As: | c_3 = 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 5 c_4 = 3 c_5 = 1 c_6 = 2 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + 2 KMnO_4 + 5 Na3AsO3 ⟶ 3 H_2O + K_2SO_4 + 2 MnSO_4 + 5 AsNa_3O_4

Structures

+ + Na3AsO3 ⟶ + + +
+ + Na3AsO3 ⟶ + + +

Names

sulfuric acid + potassium permanganate + Na3AsO3 ⟶ water + potassium sulfate + manganese(II) sulfate + arsenic acid, trisodium salt
sulfuric acid + potassium permanganate + Na3AsO3 ⟶ water + potassium sulfate + manganese(II) sulfate + arsenic acid, trisodium salt

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + Na3AsO3 ⟶ H_2O + K_2SO_4 + MnSO_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: 3 H_2SO_4 + 2 KMnO_4 + 5 Na3AsO3 ⟶ 3 H_2O + K_2SO_4 + 2 MnSO_4 + 5 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 H_2SO_4 | 3 | -3 KMnO_4 | 2 | -2 Na3AsO3 | 5 | -5 H_2O | 3 | 3 K_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 AsNa_3O_4 | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 3 | -3 | ([H2SO4])^(-3) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) Na3AsO3 | 5 | -5 | ([Na3AsO3])^(-5) H_2O | 3 | 3 | ([H2O])^3 K_2SO_4 | 1 | 1 | [K2SO4] MnSO_4 | 2 | 2 | ([MnSO4])^2 AsNa_3O_4 | 5 | 5 | ([AsNa3O4])^5 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 = ([H2SO4])^(-3) ([KMnO4])^(-2) ([Na3AsO3])^(-5) ([H2O])^3 [K2SO4] ([MnSO4])^2 ([AsNa3O4])^5 = (([H2O])^3 [K2SO4] ([MnSO4])^2 ([AsNa3O4])^5)/(([H2SO4])^3 ([KMnO4])^2 ([Na3AsO3])^5)
Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + Na3AsO3 ⟶ H_2O + K_2SO_4 + MnSO_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: 3 H_2SO_4 + 2 KMnO_4 + 5 Na3AsO3 ⟶ 3 H_2O + K_2SO_4 + 2 MnSO_4 + 5 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 H_2SO_4 | 3 | -3 KMnO_4 | 2 | -2 Na3AsO3 | 5 | -5 H_2O | 3 | 3 K_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 AsNa_3O_4 | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 3 | -3 | ([H2SO4])^(-3) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) Na3AsO3 | 5 | -5 | ([Na3AsO3])^(-5) H_2O | 3 | 3 | ([H2O])^3 K_2SO_4 | 1 | 1 | [K2SO4] MnSO_4 | 2 | 2 | ([MnSO4])^2 AsNa_3O_4 | 5 | 5 | ([AsNa3O4])^5 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 = ([H2SO4])^(-3) ([KMnO4])^(-2) ([Na3AsO3])^(-5) ([H2O])^3 [K2SO4] ([MnSO4])^2 ([AsNa3O4])^5 = (([H2O])^3 [K2SO4] ([MnSO4])^2 ([AsNa3O4])^5)/(([H2SO4])^3 ([KMnO4])^2 ([Na3AsO3])^5)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + Na3AsO3 ⟶ H_2O + K_2SO_4 + MnSO_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: 3 H_2SO_4 + 2 KMnO_4 + 5 Na3AsO3 ⟶ 3 H_2O + K_2SO_4 + 2 MnSO_4 + 5 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 H_2SO_4 | 3 | -3 KMnO_4 | 2 | -2 Na3AsO3 | 5 | -5 H_2O | 3 | 3 K_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 AsNa_3O_4 | 5 | 5 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 H_2SO_4 | 3 | -3 | -1/3 (Δ[H2SO4])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) Na3AsO3 | 5 | -5 | -1/5 (Δ[Na3AsO3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) AsNa_3O_4 | 5 | 5 | 1/5 (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 = -1/3 (Δ[H2SO4])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/5 (Δ[Na3AsO3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = 1/5 (Δ[AsNa3O4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + Na3AsO3 ⟶ H_2O + K_2SO_4 + MnSO_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: 3 H_2SO_4 + 2 KMnO_4 + 5 Na3AsO3 ⟶ 3 H_2O + K_2SO_4 + 2 MnSO_4 + 5 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 H_2SO_4 | 3 | -3 KMnO_4 | 2 | -2 Na3AsO3 | 5 | -5 H_2O | 3 | 3 K_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 AsNa_3O_4 | 5 | 5 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 H_2SO_4 | 3 | -3 | -1/3 (Δ[H2SO4])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) Na3AsO3 | 5 | -5 | -1/5 (Δ[Na3AsO3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) AsNa_3O_4 | 5 | 5 | 1/5 (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 = -1/3 (Δ[H2SO4])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/5 (Δ[Na3AsO3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = 1/5 (Δ[AsNa3O4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | potassium permanganate | Na3AsO3 | water | potassium sulfate | manganese(II) sulfate | arsenic acid, trisodium salt formula | H_2SO_4 | KMnO_4 | Na3AsO3 | H_2O | K_2SO_4 | MnSO_4 | AsNa_3O_4 Hill formula | H_2O_4S | KMnO_4 | AsNa3O3 | H_2O | K_2O_4S | MnSO_4 | AsNa_3O_4 name | sulfuric acid | potassium permanganate | | water | potassium sulfate | manganese(II) sulfate | arsenic acid, trisodium salt IUPAC name | sulfuric acid | potassium permanganate | | water | dipotassium sulfate | manganese(+2) cation sulfate |
| sulfuric acid | potassium permanganate | Na3AsO3 | water | potassium sulfate | manganese(II) sulfate | arsenic acid, trisodium salt formula | H_2SO_4 | KMnO_4 | Na3AsO3 | H_2O | K_2SO_4 | MnSO_4 | AsNa_3O_4 Hill formula | H_2O_4S | KMnO_4 | AsNa3O3 | H_2O | K_2O_4S | MnSO_4 | AsNa_3O_4 name | sulfuric acid | potassium permanganate | | water | potassium sulfate | manganese(II) sulfate | arsenic acid, trisodium salt IUPAC name | sulfuric acid | potassium permanganate | | water | dipotassium sulfate | manganese(+2) cation sulfate |

Substance properties

| sulfuric acid | potassium permanganate | Na3AsO3 | water | potassium sulfate | manganese(II) sulfate | arsenic acid, trisodium salt molar mass | 98.07 g/mol | 158.03 g/mol | 191.888 g/mol | 18.015 g/mol | 174.25 g/mol | 150.99 g/mol | 207.887 g/mol phase | liquid (at STP) | solid (at STP) | | liquid (at STP) | | solid (at STP) | solid (at STP) melting point | 10.371 °C | 240 °C | | 0 °C | | 710 °C | 1260 °C boiling point | 279.6 °C | | | 99.9839 °C | | | density | 1.8305 g/cm^3 | 1 g/cm^3 | | 1 g/cm^3 | | 3.25 g/cm^3 | 2.81 g/cm^3 solubility in water | very soluble | | | | soluble | soluble | surface tension | 0.0735 N/m | | | 0.0728 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | | odor | odorless | odorless | | odorless | | |
| sulfuric acid | potassium permanganate | Na3AsO3 | water | potassium sulfate | manganese(II) sulfate | arsenic acid, trisodium salt molar mass | 98.07 g/mol | 158.03 g/mol | 191.888 g/mol | 18.015 g/mol | 174.25 g/mol | 150.99 g/mol | 207.887 g/mol phase | liquid (at STP) | solid (at STP) | | liquid (at STP) | | solid (at STP) | solid (at STP) melting point | 10.371 °C | 240 °C | | 0 °C | | 710 °C | 1260 °C boiling point | 279.6 °C | | | 99.9839 °C | | | density | 1.8305 g/cm^3 | 1 g/cm^3 | | 1 g/cm^3 | | 3.25 g/cm^3 | 2.81 g/cm^3 solubility in water | very soluble | | | | soluble | soluble | surface tension | 0.0735 N/m | | | 0.0728 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | | odor | odorless | odorless | | odorless | | |

Units

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