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HCl + KMnO4 + K2SO3 = H2O + K2SO4 + KCl + MnO2

Input interpretation

HCl hydrogen chloride + KMnO_4 potassium permanganate + K_2SO_3 potassium sulfite ⟶ H_2O water + K_2SO_4 potassium sulfate + KCl potassium chloride + MnO_2 manganese dioxide
HCl hydrogen chloride + KMnO_4 potassium permanganate + K_2SO_3 potassium sulfite ⟶ H_2O water + K_2SO_4 potassium sulfate + KCl potassium chloride + MnO_2 manganese dioxide

Balanced equation

Balance the chemical equation algebraically: HCl + KMnO_4 + K_2SO_3 ⟶ H_2O + K_2SO_4 + KCl + MnO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 KMnO_4 + c_3 K_2SO_3 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 KCl + c_7 MnO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, K, Mn, O and S: Cl: | c_1 = c_6 H: | c_1 = 2 c_4 K: | c_2 + 2 c_3 = 2 c_5 + c_6 Mn: | c_2 = c_7 O: | 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 2 c_7 S: | 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 3 c_4 = 1 c_5 = 3 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HCl + 2 KMnO_4 + 3 K_2SO_3 ⟶ H_2O + 3 K_2SO_4 + 2 KCl + 2 MnO_2
Balance the chemical equation algebraically: HCl + KMnO_4 + K_2SO_3 ⟶ H_2O + K_2SO_4 + KCl + MnO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 KMnO_4 + c_3 K_2SO_3 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 KCl + c_7 MnO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, K, Mn, O and S: Cl: | c_1 = c_6 H: | c_1 = 2 c_4 K: | c_2 + 2 c_3 = 2 c_5 + c_6 Mn: | c_2 = c_7 O: | 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 2 c_7 S: | 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 3 c_4 = 1 c_5 = 3 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HCl + 2 KMnO_4 + 3 K_2SO_3 ⟶ H_2O + 3 K_2SO_4 + 2 KCl + 2 MnO_2

Structures

+ + ⟶ + + +
+ + ⟶ + + +

Names

hydrogen chloride + potassium permanganate + potassium sulfite ⟶ water + potassium sulfate + potassium chloride + manganese dioxide
hydrogen chloride + potassium permanganate + potassium sulfite ⟶ water + potassium sulfate + potassium chloride + manganese dioxide

Equilibrium constant

Construct the equilibrium constant, K, expression for: HCl + KMnO_4 + K_2SO_3 ⟶ H_2O + K_2SO_4 + KCl + 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: 2 HCl + 2 KMnO_4 + 3 K_2SO_3 ⟶ H_2O + 3 K_2SO_4 + 2 KCl + 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 HCl | 2 | -2 KMnO_4 | 2 | -2 K_2SO_3 | 3 | -3 H_2O | 1 | 1 K_2SO_4 | 3 | 3 KCl | 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 HCl | 2 | -2 | ([HCl])^(-2) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) K_2SO_3 | 3 | -3 | ([K2SO3])^(-3) H_2O | 1 | 1 | [H2O] K_2SO_4 | 3 | 3 | ([K2SO4])^3 KCl | 2 | 2 | ([KCl])^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 = ([HCl])^(-2) ([KMnO4])^(-2) ([K2SO3])^(-3) [H2O] ([K2SO4])^3 ([KCl])^2 ([MnO2])^2 = ([H2O] ([K2SO4])^3 ([KCl])^2 ([MnO2])^2)/(([HCl])^2 ([KMnO4])^2 ([K2SO3])^3)
Construct the equilibrium constant, K, expression for: HCl + KMnO_4 + K_2SO_3 ⟶ H_2O + K_2SO_4 + KCl + 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: 2 HCl + 2 KMnO_4 + 3 K_2SO_3 ⟶ H_2O + 3 K_2SO_4 + 2 KCl + 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 HCl | 2 | -2 KMnO_4 | 2 | -2 K_2SO_3 | 3 | -3 H_2O | 1 | 1 K_2SO_4 | 3 | 3 KCl | 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 HCl | 2 | -2 | ([HCl])^(-2) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) K_2SO_3 | 3 | -3 | ([K2SO3])^(-3) H_2O | 1 | 1 | [H2O] K_2SO_4 | 3 | 3 | ([K2SO4])^3 KCl | 2 | 2 | ([KCl])^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 = ([HCl])^(-2) ([KMnO4])^(-2) ([K2SO3])^(-3) [H2O] ([K2SO4])^3 ([KCl])^2 ([MnO2])^2 = ([H2O] ([K2SO4])^3 ([KCl])^2 ([MnO2])^2)/(([HCl])^2 ([KMnO4])^2 ([K2SO3])^3)

Rate of reaction

Construct the rate of reaction expression for: HCl + KMnO_4 + K_2SO_3 ⟶ H_2O + K_2SO_4 + KCl + 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: 2 HCl + 2 KMnO_4 + 3 K_2SO_3 ⟶ H_2O + 3 K_2SO_4 + 2 KCl + 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 HCl | 2 | -2 KMnO_4 | 2 | -2 K_2SO_3 | 3 | -3 H_2O | 1 | 1 K_2SO_4 | 3 | 3 KCl | 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 HCl | 2 | -2 | -1/2 (Δ[HCl])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) K_2SO_3 | 3 | -3 | -1/3 (Δ[K2SO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) K_2SO_4 | 3 | 3 | 1/3 (Δ[K2SO4])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(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 = -1/2 (Δ[HCl])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/3 (Δ[K2SO3])/(Δt) = (Δ[H2O])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/2 (Δ[MnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: HCl + KMnO_4 + K_2SO_3 ⟶ H_2O + K_2SO_4 + KCl + 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: 2 HCl + 2 KMnO_4 + 3 K_2SO_3 ⟶ H_2O + 3 K_2SO_4 + 2 KCl + 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 HCl | 2 | -2 KMnO_4 | 2 | -2 K_2SO_3 | 3 | -3 H_2O | 1 | 1 K_2SO_4 | 3 | 3 KCl | 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 HCl | 2 | -2 | -1/2 (Δ[HCl])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) K_2SO_3 | 3 | -3 | -1/3 (Δ[K2SO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) K_2SO_4 | 3 | 3 | 1/3 (Δ[K2SO4])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(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 = -1/2 (Δ[HCl])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/3 (Δ[K2SO3])/(Δt) = (Δ[H2O])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/2 (Δ[MnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| hydrogen chloride | potassium permanganate | potassium sulfite | water | potassium sulfate | potassium chloride | manganese dioxide formula | HCl | KMnO_4 | K_2SO_3 | H_2O | K_2SO_4 | KCl | MnO_2 Hill formula | ClH | KMnO_4 | K_2O_3S | H_2O | K_2O_4S | ClK | MnO_2 name | hydrogen chloride | potassium permanganate | potassium sulfite | water | potassium sulfate | potassium chloride | manganese dioxide IUPAC name | hydrogen chloride | potassium permanganate | dipotassium sulfite | water | dipotassium sulfate | potassium chloride | dioxomanganese
| hydrogen chloride | potassium permanganate | potassium sulfite | water | potassium sulfate | potassium chloride | manganese dioxide formula | HCl | KMnO_4 | K_2SO_3 | H_2O | K_2SO_4 | KCl | MnO_2 Hill formula | ClH | KMnO_4 | K_2O_3S | H_2O | K_2O_4S | ClK | MnO_2 name | hydrogen chloride | potassium permanganate | potassium sulfite | water | potassium sulfate | potassium chloride | manganese dioxide IUPAC name | hydrogen chloride | potassium permanganate | dipotassium sulfite | water | dipotassium sulfate | potassium chloride | dioxomanganese

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