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NaOH + KMnO4 + NaHSO3 = H2O + K2SO4 + Na2SO4 + MnO2

Input interpretation

NaOH sodium hydroxide + KMnO_4 potassium permanganate + NaHSO_3 sodium bisulfite ⟶ H_2O water + K_2SO_4 potassium sulfate + Na_2SO_4 sodium sulfate + MnO_2 manganese dioxide
NaOH sodium hydroxide + KMnO_4 potassium permanganate + NaHSO_3 sodium bisulfite ⟶ H_2O water + K_2SO_4 potassium sulfate + Na_2SO_4 sodium sulfate + MnO_2 manganese dioxide

Balanced equation

Balance the chemical equation algebraically: NaOH + KMnO_4 + NaHSO_3 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + MnO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 KMnO_4 + c_3 NaHSO_3 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Na_2SO_4 + c_7 MnO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, K, Mn and S: H: | c_1 + c_3 = 2 c_4 Na: | c_1 + c_3 = 2 c_6 O: | c_1 + 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 4 c_6 + 2 c_7 K: | c_2 = 2 c_5 Mn: | c_2 = c_7 S: | c_3 = c_5 + 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 3 c_4 = 2 c_5 = 1 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | NaOH + 2 KMnO_4 + 3 NaHSO_3 ⟶ 2 H_2O + K_2SO_4 + 2 Na_2SO_4 + 2 MnO_2
Balance the chemical equation algebraically: NaOH + KMnO_4 + NaHSO_3 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + MnO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 KMnO_4 + c_3 NaHSO_3 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Na_2SO_4 + c_7 MnO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, K, Mn and S: H: | c_1 + c_3 = 2 c_4 Na: | c_1 + c_3 = 2 c_6 O: | c_1 + 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 4 c_6 + 2 c_7 K: | c_2 = 2 c_5 Mn: | c_2 = c_7 S: | c_3 = c_5 + 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 3 c_4 = 2 c_5 = 1 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | NaOH + 2 KMnO_4 + 3 NaHSO_3 ⟶ 2 H_2O + K_2SO_4 + 2 Na_2SO_4 + 2 MnO_2

Structures

+ + ⟶ + + +
+ + ⟶ + + +

Names

sodium hydroxide + potassium permanganate + sodium bisulfite ⟶ water + potassium sulfate + sodium sulfate + manganese dioxide
sodium hydroxide + potassium permanganate + sodium bisulfite ⟶ water + potassium sulfate + sodium sulfate + manganese dioxide

Equilibrium constant

Construct the equilibrium constant, K, expression for: NaOH + KMnO_4 + NaHSO_3 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + MnO_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: NaOH + 2 KMnO_4 + 3 NaHSO_3 ⟶ 2 H_2O + K_2SO_4 + 2 Na_2SO_4 + 2 MnO_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 NaOH | 1 | -1 KMnO_4 | 2 | -2 NaHSO_3 | 3 | -3 H_2O | 2 | 2 K_2SO_4 | 1 | 1 Na_2SO_4 | 2 | 2 MnO_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 1 | -1 | ([NaOH])^(-1) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) NaHSO_3 | 3 | -3 | ([NaHSO3])^(-3) H_2O | 2 | 2 | ([H2O])^2 K_2SO_4 | 1 | 1 | [K2SO4] Na_2SO_4 | 2 | 2 | ([Na2SO4])^2 MnO_2 | 2 | 2 | ([MnO2])^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 = ([NaOH])^(-1) ([KMnO4])^(-2) ([NaHSO3])^(-3) ([H2O])^2 [K2SO4] ([Na2SO4])^2 ([MnO2])^2 = (([H2O])^2 [K2SO4] ([Na2SO4])^2 ([MnO2])^2)/([NaOH] ([KMnO4])^2 ([NaHSO3])^3)
Construct the equilibrium constant, K, expression for: NaOH + KMnO_4 + NaHSO_3 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + MnO_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: NaOH + 2 KMnO_4 + 3 NaHSO_3 ⟶ 2 H_2O + K_2SO_4 + 2 Na_2SO_4 + 2 MnO_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 NaOH | 1 | -1 KMnO_4 | 2 | -2 NaHSO_3 | 3 | -3 H_2O | 2 | 2 K_2SO_4 | 1 | 1 Na_2SO_4 | 2 | 2 MnO_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 1 | -1 | ([NaOH])^(-1) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) NaHSO_3 | 3 | -3 | ([NaHSO3])^(-3) H_2O | 2 | 2 | ([H2O])^2 K_2SO_4 | 1 | 1 | [K2SO4] Na_2SO_4 | 2 | 2 | ([Na2SO4])^2 MnO_2 | 2 | 2 | ([MnO2])^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 = ([NaOH])^(-1) ([KMnO4])^(-2) ([NaHSO3])^(-3) ([H2O])^2 [K2SO4] ([Na2SO4])^2 ([MnO2])^2 = (([H2O])^2 [K2SO4] ([Na2SO4])^2 ([MnO2])^2)/([NaOH] ([KMnO4])^2 ([NaHSO3])^3)

Rate of reaction

Construct the rate of reaction expression for: NaOH + KMnO_4 + NaHSO_3 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + MnO_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: NaOH + 2 KMnO_4 + 3 NaHSO_3 ⟶ 2 H_2O + K_2SO_4 + 2 Na_2SO_4 + 2 MnO_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 NaOH | 1 | -1 KMnO_4 | 2 | -2 NaHSO_3 | 3 | -3 H_2O | 2 | 2 K_2SO_4 | 1 | 1 Na_2SO_4 | 2 | 2 MnO_2 | 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 NaOH | 1 | -1 | -(Δ[NaOH])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) NaHSO_3 | 3 | -3 | -1/3 (Δ[NaHSO3])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) Na_2SO_4 | 2 | 2 | 1/2 (Δ[Na2SO4])/(Δt) MnO_2 | 2 | 2 | 1/2 (Δ[MnO2])/(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 = -(Δ[NaOH])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/3 (Δ[NaHSO3])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[Na2SO4])/(Δt) = 1/2 (Δ[MnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: NaOH + KMnO_4 + NaHSO_3 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + MnO_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: NaOH + 2 KMnO_4 + 3 NaHSO_3 ⟶ 2 H_2O + K_2SO_4 + 2 Na_2SO_4 + 2 MnO_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 NaOH | 1 | -1 KMnO_4 | 2 | -2 NaHSO_3 | 3 | -3 H_2O | 2 | 2 K_2SO_4 | 1 | 1 Na_2SO_4 | 2 | 2 MnO_2 | 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 NaOH | 1 | -1 | -(Δ[NaOH])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) NaHSO_3 | 3 | -3 | -1/3 (Δ[NaHSO3])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) Na_2SO_4 | 2 | 2 | 1/2 (Δ[Na2SO4])/(Δt) MnO_2 | 2 | 2 | 1/2 (Δ[MnO2])/(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 = -(Δ[NaOH])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/3 (Δ[NaHSO3])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[Na2SO4])/(Δt) = 1/2 (Δ[MnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sodium hydroxide | potassium permanganate | sodium bisulfite | water | potassium sulfate | sodium sulfate | manganese dioxide formula | NaOH | KMnO_4 | NaHSO_3 | H_2O | K_2SO_4 | Na_2SO_4 | MnO_2 Hill formula | HNaO | KMnO_4 | HNaO_3S | H_2O | K_2O_4S | Na_2O_4S | MnO_2 name | sodium hydroxide | potassium permanganate | sodium bisulfite | water | potassium sulfate | sodium sulfate | manganese dioxide IUPAC name | sodium hydroxide | potassium permanganate | | water | dipotassium sulfate | disodium sulfate | dioxomanganese
| sodium hydroxide | potassium permanganate | sodium bisulfite | water | potassium sulfate | sodium sulfate | manganese dioxide formula | NaOH | KMnO_4 | NaHSO_3 | H_2O | K_2SO_4 | Na_2SO_4 | MnO_2 Hill formula | HNaO | KMnO_4 | HNaO_3S | H_2O | K_2O_4S | Na_2O_4S | MnO_2 name | sodium hydroxide | potassium permanganate | sodium bisulfite | water | potassium sulfate | sodium sulfate | manganese dioxide IUPAC name | sodium hydroxide | potassium permanganate | | water | dipotassium sulfate | disodium sulfate | dioxomanganese

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