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H2SO4 + KMnO4 + Zn = H2O + K2SO4 + MnO2 + ZnSO4

Input interpretation

H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + Zn zinc ⟶ H_2O water + K_2SO_4 potassium sulfate + MnO_2 manganese dioxide + ZnSO_4 zinc sulfate
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + Zn zinc ⟶ H_2O water + K_2SO_4 potassium sulfate + MnO_2 manganese dioxide + ZnSO_4 zinc sulfate

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + Zn ⟶ H_2O + K_2SO_4 + MnO_2 + ZnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 Zn ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 MnO_2 + c_7 ZnSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and Zn: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 2 c_6 + 4 c_7 S: | c_1 = c_5 + c_7 K: | c_2 = 2 c_5 Mn: | c_2 = c_6 Zn: | 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 = 4 c_2 = 2 c_3 = 3 c_4 = 4 c_5 = 1 c_6 = 2 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2SO_4 + 2 KMnO_4 + 3 Zn ⟶ 4 H_2O + K_2SO_4 + 2 MnO_2 + 3 ZnSO_4
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + Zn ⟶ H_2O + K_2SO_4 + MnO_2 + ZnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 Zn ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 MnO_2 + c_7 ZnSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and Zn: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 2 c_6 + 4 c_7 S: | c_1 = c_5 + c_7 K: | c_2 = 2 c_5 Mn: | c_2 = c_6 Zn: | 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 = 4 c_2 = 2 c_3 = 3 c_4 = 4 c_5 = 1 c_6 = 2 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2SO_4 + 2 KMnO_4 + 3 Zn ⟶ 4 H_2O + K_2SO_4 + 2 MnO_2 + 3 ZnSO_4

Structures

+ + ⟶ + + +
+ + ⟶ + + +

Names

sulfuric acid + potassium permanganate + zinc ⟶ water + potassium sulfate + manganese dioxide + zinc sulfate
sulfuric acid + potassium permanganate + zinc ⟶ water + potassium sulfate + manganese dioxide + zinc sulfate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + Zn ⟶ H_2O + K_2SO_4 + MnO_2 + ZnSO_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: 4 H_2SO_4 + 2 KMnO_4 + 3 Zn ⟶ 4 H_2O + K_2SO_4 + 2 MnO_2 + 3 ZnSO_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 | 4 | -4 KMnO_4 | 2 | -2 Zn | 3 | -3 H_2O | 4 | 4 K_2SO_4 | 1 | 1 MnO_2 | 2 | 2 ZnSO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 4 | -4 | ([H2SO4])^(-4) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) Zn | 3 | -3 | ([Zn])^(-3) H_2O | 4 | 4 | ([H2O])^4 K_2SO_4 | 1 | 1 | [K2SO4] MnO_2 | 2 | 2 | ([MnO2])^2 ZnSO_4 | 3 | 3 | ([ZnSO4])^3 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])^(-4) ([KMnO4])^(-2) ([Zn])^(-3) ([H2O])^4 [K2SO4] ([MnO2])^2 ([ZnSO4])^3 = (([H2O])^4 [K2SO4] ([MnO2])^2 ([ZnSO4])^3)/(([H2SO4])^4 ([KMnO4])^2 ([Zn])^3)
Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + Zn ⟶ H_2O + K_2SO_4 + MnO_2 + ZnSO_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: 4 H_2SO_4 + 2 KMnO_4 + 3 Zn ⟶ 4 H_2O + K_2SO_4 + 2 MnO_2 + 3 ZnSO_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 | 4 | -4 KMnO_4 | 2 | -2 Zn | 3 | -3 H_2O | 4 | 4 K_2SO_4 | 1 | 1 MnO_2 | 2 | 2 ZnSO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 4 | -4 | ([H2SO4])^(-4) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) Zn | 3 | -3 | ([Zn])^(-3) H_2O | 4 | 4 | ([H2O])^4 K_2SO_4 | 1 | 1 | [K2SO4] MnO_2 | 2 | 2 | ([MnO2])^2 ZnSO_4 | 3 | 3 | ([ZnSO4])^3 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])^(-4) ([KMnO4])^(-2) ([Zn])^(-3) ([H2O])^4 [K2SO4] ([MnO2])^2 ([ZnSO4])^3 = (([H2O])^4 [K2SO4] ([MnO2])^2 ([ZnSO4])^3)/(([H2SO4])^4 ([KMnO4])^2 ([Zn])^3)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + Zn ⟶ H_2O + K_2SO_4 + MnO_2 + ZnSO_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: 4 H_2SO_4 + 2 KMnO_4 + 3 Zn ⟶ 4 H_2O + K_2SO_4 + 2 MnO_2 + 3 ZnSO_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 | 4 | -4 KMnO_4 | 2 | -2 Zn | 3 | -3 H_2O | 4 | 4 K_2SO_4 | 1 | 1 MnO_2 | 2 | 2 ZnSO_4 | 3 | 3 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 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) Zn | 3 | -3 | -1/3 (Δ[Zn])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) MnO_2 | 2 | 2 | 1/2 (Δ[MnO2])/(Δt) ZnSO_4 | 3 | 3 | 1/3 (Δ[ZnSO4])/(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 = -1/4 (Δ[H2SO4])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/3 (Δ[Zn])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[MnO2])/(Δt) = 1/3 (Δ[ZnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + Zn ⟶ H_2O + K_2SO_4 + MnO_2 + ZnSO_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: 4 H_2SO_4 + 2 KMnO_4 + 3 Zn ⟶ 4 H_2O + K_2SO_4 + 2 MnO_2 + 3 ZnSO_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 | 4 | -4 KMnO_4 | 2 | -2 Zn | 3 | -3 H_2O | 4 | 4 K_2SO_4 | 1 | 1 MnO_2 | 2 | 2 ZnSO_4 | 3 | 3 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 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) Zn | 3 | -3 | -1/3 (Δ[Zn])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) MnO_2 | 2 | 2 | 1/2 (Δ[MnO2])/(Δt) ZnSO_4 | 3 | 3 | 1/3 (Δ[ZnSO4])/(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 = -1/4 (Δ[H2SO4])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/3 (Δ[Zn])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[MnO2])/(Δt) = 1/3 (Δ[ZnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | potassium permanganate | zinc | water | potassium sulfate | manganese dioxide | zinc sulfate formula | H_2SO_4 | KMnO_4 | Zn | H_2O | K_2SO_4 | MnO_2 | ZnSO_4 Hill formula | H_2O_4S | KMnO_4 | Zn | H_2O | K_2O_4S | MnO_2 | O_4SZn name | sulfuric acid | potassium permanganate | zinc | water | potassium sulfate | manganese dioxide | zinc sulfate IUPAC name | sulfuric acid | potassium permanganate | zinc | water | dipotassium sulfate | dioxomanganese | zinc sulfate
| sulfuric acid | potassium permanganate | zinc | water | potassium sulfate | manganese dioxide | zinc sulfate formula | H_2SO_4 | KMnO_4 | Zn | H_2O | K_2SO_4 | MnO_2 | ZnSO_4 Hill formula | H_2O_4S | KMnO_4 | Zn | H_2O | K_2O_4S | MnO_2 | O_4SZn name | sulfuric acid | potassium permanganate | zinc | water | potassium sulfate | manganese dioxide | zinc sulfate IUPAC name | sulfuric acid | potassium permanganate | zinc | water | dipotassium sulfate | dioxomanganese | zinc sulfate

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