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H2SO4 + Na2SO3 + KMnO2 = H2O + K2SO4 + Na2SO4 + MnSO4

Input interpretation

H_2SO_4 sulfuric acid + Na_2SO_3 sodium sulfite + KMnO2 ⟶ H_2O water + K_2SO_4 potassium sulfate + Na_2SO_4 sodium sulfate + MnSO_4 manganese(II) sulfate
H_2SO_4 sulfuric acid + Na_2SO_3 sodium sulfite + KMnO2 ⟶ H_2O water + K_2SO_4 potassium sulfate + Na_2SO_4 sodium sulfate + MnSO_4 manganese(II) sulfate

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + Na_2SO_3 + KMnO2 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + MnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Na_2SO_3 + c_3 KMnO2 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Na_2SO_4 + c_7 MnSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Na, K and Mn: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 3 c_2 + 2 c_3 = c_4 + 4 c_5 + 4 c_6 + 4 c_7 S: | c_1 + c_2 = c_5 + c_6 + c_7 Na: | 2 c_2 = 2 c_6 K: | c_3 = 2 c_5 Mn: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 2 c_4 = 3 c_5 = 1 c_6 = 1 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + Na_2SO_3 + 2 KMnO2 ⟶ 3 H_2O + K_2SO_4 + Na_2SO_4 + 2 MnSO_4
Balance the chemical equation algebraically: H_2SO_4 + Na_2SO_3 + KMnO2 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + MnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Na_2SO_3 + c_3 KMnO2 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Na_2SO_4 + c_7 MnSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Na, K and Mn: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 3 c_2 + 2 c_3 = c_4 + 4 c_5 + 4 c_6 + 4 c_7 S: | c_1 + c_2 = c_5 + c_6 + c_7 Na: | 2 c_2 = 2 c_6 K: | c_3 = 2 c_5 Mn: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 2 c_4 = 3 c_5 = 1 c_6 = 1 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + Na_2SO_3 + 2 KMnO2 ⟶ 3 H_2O + K_2SO_4 + Na_2SO_4 + 2 MnSO_4

Structures

+ + KMnO2 ⟶ + + +
+ + KMnO2 ⟶ + + +

Names

sulfuric acid + sodium sulfite + KMnO2 ⟶ water + potassium sulfate + sodium sulfate + manganese(II) sulfate
sulfuric acid + sodium sulfite + KMnO2 ⟶ water + potassium sulfate + sodium sulfate + manganese(II) sulfate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + Na_2SO_3 + KMnO2 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + MnSO_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 + Na_2SO_3 + 2 KMnO2 ⟶ 3 H_2O + K_2SO_4 + Na_2SO_4 + 2 MnSO_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 Na_2SO_3 | 1 | -1 KMnO2 | 2 | -2 H_2O | 3 | 3 K_2SO_4 | 1 | 1 Na_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 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) Na_2SO_3 | 1 | -1 | ([Na2SO3])^(-1) KMnO2 | 2 | -2 | ([KMnO2])^(-2) H_2O | 3 | 3 | ([H2O])^3 K_2SO_4 | 1 | 1 | [K2SO4] Na_2SO_4 | 1 | 1 | [Na2SO4] MnSO_4 | 2 | 2 | ([MnSO4])^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 = ([H2SO4])^(-3) ([Na2SO3])^(-1) ([KMnO2])^(-2) ([H2O])^3 [K2SO4] [Na2SO4] ([MnSO4])^2 = (([H2O])^3 [K2SO4] [Na2SO4] ([MnSO4])^2)/(([H2SO4])^3 [Na2SO3] ([KMnO2])^2)
Construct the equilibrium constant, K, expression for: H_2SO_4 + Na_2SO_3 + KMnO2 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + MnSO_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 + Na_2SO_3 + 2 KMnO2 ⟶ 3 H_2O + K_2SO_4 + Na_2SO_4 + 2 MnSO_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 Na_2SO_3 | 1 | -1 KMnO2 | 2 | -2 H_2O | 3 | 3 K_2SO_4 | 1 | 1 Na_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 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) Na_2SO_3 | 1 | -1 | ([Na2SO3])^(-1) KMnO2 | 2 | -2 | ([KMnO2])^(-2) H_2O | 3 | 3 | ([H2O])^3 K_2SO_4 | 1 | 1 | [K2SO4] Na_2SO_4 | 1 | 1 | [Na2SO4] MnSO_4 | 2 | 2 | ([MnSO4])^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 = ([H2SO4])^(-3) ([Na2SO3])^(-1) ([KMnO2])^(-2) ([H2O])^3 [K2SO4] [Na2SO4] ([MnSO4])^2 = (([H2O])^3 [K2SO4] [Na2SO4] ([MnSO4])^2)/(([H2SO4])^3 [Na2SO3] ([KMnO2])^2)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + Na_2SO_3 + KMnO2 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + MnSO_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 + Na_2SO_3 + 2 KMnO2 ⟶ 3 H_2O + K_2SO_4 + Na_2SO_4 + 2 MnSO_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 Na_2SO_3 | 1 | -1 KMnO2 | 2 | -2 H_2O | 3 | 3 K_2SO_4 | 1 | 1 Na_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 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) Na_2SO_3 | 1 | -1 | -(Δ[Na2SO3])/(Δt) KMnO2 | 2 | -2 | -1/2 (Δ[KMnO2])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) Na_2SO_4 | 1 | 1 | (Δ[Na2SO4])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(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) = -(Δ[Na2SO3])/(Δt) = -1/2 (Δ[KMnO2])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[Na2SO4])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + Na_2SO_3 + KMnO2 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + MnSO_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 + Na_2SO_3 + 2 KMnO2 ⟶ 3 H_2O + K_2SO_4 + Na_2SO_4 + 2 MnSO_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 Na_2SO_3 | 1 | -1 KMnO2 | 2 | -2 H_2O | 3 | 3 K_2SO_4 | 1 | 1 Na_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 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) Na_2SO_3 | 1 | -1 | -(Δ[Na2SO3])/(Δt) KMnO2 | 2 | -2 | -1/2 (Δ[KMnO2])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) Na_2SO_4 | 1 | 1 | (Δ[Na2SO4])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(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) = -(Δ[Na2SO3])/(Δt) = -1/2 (Δ[KMnO2])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[Na2SO4])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | sodium sulfite | KMnO2 | water | potassium sulfate | sodium sulfate | manganese(II) sulfate formula | H_2SO_4 | Na_2SO_3 | KMnO2 | H_2O | K_2SO_4 | Na_2SO_4 | MnSO_4 Hill formula | H_2O_4S | Na_2O_3S | KMnO2 | H_2O | K_2O_4S | Na_2O_4S | MnSO_4 name | sulfuric acid | sodium sulfite | | water | potassium sulfate | sodium sulfate | manganese(II) sulfate IUPAC name | sulfuric acid | disodium sulfite | | water | dipotassium sulfate | disodium sulfate | manganese(+2) cation sulfate
| sulfuric acid | sodium sulfite | KMnO2 | water | potassium sulfate | sodium sulfate | manganese(II) sulfate formula | H_2SO_4 | Na_2SO_3 | KMnO2 | H_2O | K_2SO_4 | Na_2SO_4 | MnSO_4 Hill formula | H_2O_4S | Na_2O_3S | KMnO2 | H_2O | K_2O_4S | Na_2O_4S | MnSO_4 name | sulfuric acid | sodium sulfite | | water | potassium sulfate | sodium sulfate | manganese(II) sulfate IUPAC name | sulfuric acid | disodium sulfite | | water | dipotassium sulfate | disodium sulfate | manganese(+2) cation sulfate

Substance properties

| sulfuric acid | sodium sulfite | KMnO2 | water | potassium sulfate | sodium sulfate | manganese(II) sulfate molar mass | 98.07 g/mol | 126.04 g/mol | 126.034 g/mol | 18.015 g/mol | 174.25 g/mol | 142.04 g/mol | 150.99 g/mol phase | liquid (at STP) | solid (at STP) | | liquid (at STP) | | solid (at STP) | solid (at STP) melting point | 10.371 °C | 500 °C | | 0 °C | | 884 °C | 710 °C boiling point | 279.6 °C | | | 99.9839 °C | | 1429 °C | density | 1.8305 g/cm^3 | 2.63 g/cm^3 | | 1 g/cm^3 | | 2.68 g/cm^3 | 3.25 g/cm^3 solubility in water | very soluble | | | | 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 | | |
| sulfuric acid | sodium sulfite | KMnO2 | water | potassium sulfate | sodium sulfate | manganese(II) sulfate molar mass | 98.07 g/mol | 126.04 g/mol | 126.034 g/mol | 18.015 g/mol | 174.25 g/mol | 142.04 g/mol | 150.99 g/mol phase | liquid (at STP) | solid (at STP) | | liquid (at STP) | | solid (at STP) | solid (at STP) melting point | 10.371 °C | 500 °C | | 0 °C | | 884 °C | 710 °C boiling point | 279.6 °C | | | 99.9839 °C | | 1429 °C | density | 1.8305 g/cm^3 | 2.63 g/cm^3 | | 1 g/cm^3 | | 2.68 g/cm^3 | 3.25 g/cm^3 solubility in water | very soluble | | | | 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 | | |

Units

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