Input interpretation
H_2O water + KMnO_4 potassium permanganate + SO_2 sulfur dioxide ⟶ H_2SO_4 sulfuric acid + MnSO_4 manganese(II) sulfate + KHSO_4 potassium bisulfate
Balanced equation
Balance the chemical equation algebraically: H_2O + KMnO_4 + SO_2 ⟶ H_2SO_4 + MnSO_4 + KHSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KMnO_4 + c_3 SO_2 ⟶ c_4 H_2SO_4 + c_5 MnSO_4 + c_6 KHSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K, Mn and S: H: | 2 c_1 = 2 c_4 + c_6 O: | c_1 + 4 c_2 + 2 c_3 = 4 c_4 + 4 c_5 + 4 c_6 K: | c_2 = c_6 Mn: | c_2 = c_5 S: | c_3 = c_4 + 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 5 c_4 = 1 c_5 = 2 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 2 KMnO_4 + 5 SO_2 ⟶ H_2SO_4 + 2 MnSO_4 + 2 KHSO_4
Structures
+ + ⟶ + +
Names
water + potassium permanganate + sulfur dioxide ⟶ sulfuric acid + manganese(II) sulfate + potassium bisulfate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2O + KMnO_4 + SO_2 ⟶ H_2SO_4 + MnSO_4 + KHSO_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: 2 H_2O + 2 KMnO_4 + 5 SO_2 ⟶ H_2SO_4 + 2 MnSO_4 + 2 KHSO_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_2O | 2 | -2 KMnO_4 | 2 | -2 SO_2 | 5 | -5 H_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 KHSO_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_2O | 2 | -2 | ([H2O])^(-2) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) SO_2 | 5 | -5 | ([SO2])^(-5) H_2SO_4 | 1 | 1 | [H2SO4] MnSO_4 | 2 | 2 | ([MnSO4])^2 KHSO_4 | 2 | 2 | ([KHSO4])^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 = ([H2O])^(-2) ([KMnO4])^(-2) ([SO2])^(-5) [H2SO4] ([MnSO4])^2 ([KHSO4])^2 = ([H2SO4] ([MnSO4])^2 ([KHSO4])^2)/(([H2O])^2 ([KMnO4])^2 ([SO2])^5)](../image_source/b79a866493fbba36c705e30268c4a105.png)
Construct the equilibrium constant, K, expression for: H_2O + KMnO_4 + SO_2 ⟶ H_2SO_4 + MnSO_4 + KHSO_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: 2 H_2O + 2 KMnO_4 + 5 SO_2 ⟶ H_2SO_4 + 2 MnSO_4 + 2 KHSO_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_2O | 2 | -2 KMnO_4 | 2 | -2 SO_2 | 5 | -5 H_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 KHSO_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_2O | 2 | -2 | ([H2O])^(-2) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) SO_2 | 5 | -5 | ([SO2])^(-5) H_2SO_4 | 1 | 1 | [H2SO4] MnSO_4 | 2 | 2 | ([MnSO4])^2 KHSO_4 | 2 | 2 | ([KHSO4])^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 = ([H2O])^(-2) ([KMnO4])^(-2) ([SO2])^(-5) [H2SO4] ([MnSO4])^2 ([KHSO4])^2 = ([H2SO4] ([MnSO4])^2 ([KHSO4])^2)/(([H2O])^2 ([KMnO4])^2 ([SO2])^5)
Rate of reaction
![Construct the rate of reaction expression for: H_2O + KMnO_4 + SO_2 ⟶ H_2SO_4 + MnSO_4 + KHSO_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: 2 H_2O + 2 KMnO_4 + 5 SO_2 ⟶ H_2SO_4 + 2 MnSO_4 + 2 KHSO_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_2O | 2 | -2 KMnO_4 | 2 | -2 SO_2 | 5 | -5 H_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 KHSO_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_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) SO_2 | 5 | -5 | -1/5 (Δ[SO2])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) KHSO_4 | 2 | 2 | 1/2 (Δ[KHSO4])/(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[H2O])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/5 (Δ[SO2])/(Δt) = (Δ[H2SO4])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = 1/2 (Δ[KHSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/bb95fef6c02537870580c22393a2f76e.png)
Construct the rate of reaction expression for: H_2O + KMnO_4 + SO_2 ⟶ H_2SO_4 + MnSO_4 + KHSO_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: 2 H_2O + 2 KMnO_4 + 5 SO_2 ⟶ H_2SO_4 + 2 MnSO_4 + 2 KHSO_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_2O | 2 | -2 KMnO_4 | 2 | -2 SO_2 | 5 | -5 H_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 KHSO_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_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) SO_2 | 5 | -5 | -1/5 (Δ[SO2])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) KHSO_4 | 2 | 2 | 1/2 (Δ[KHSO4])/(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[H2O])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/5 (Δ[SO2])/(Δt) = (Δ[H2SO4])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = 1/2 (Δ[KHSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| water | potassium permanganate | sulfur dioxide | sulfuric acid | manganese(II) sulfate | potassium bisulfate formula | H_2O | KMnO_4 | SO_2 | H_2SO_4 | MnSO_4 | KHSO_4 Hill formula | H_2O | KMnO_4 | O_2S | H_2O_4S | MnSO_4 | HKO_4S name | water | potassium permanganate | sulfur dioxide | sulfuric acid | manganese(II) sulfate | potassium bisulfate IUPAC name | water | potassium permanganate | sulfur dioxide | sulfuric acid | manganese(+2) cation sulfate | potassium hydrogen sulfate