Input interpretation
![H_2O water + KMnO_4 potassium permanganate + SO_2 sulfur dioxide ⟶ H_2SO_4 sulfuric acid + MnSO_4 manganese(II) sulfate + K_2SO_3 potassium sulfite](../image_source/2e159ea482369fc4d86e09c3e8a41c3d.png)
H_2O water + KMnO_4 potassium permanganate + SO_2 sulfur dioxide ⟶ H_2SO_4 sulfuric acid + MnSO_4 manganese(II) sulfate + K_2SO_3 potassium sulfite
Balanced equation
![Balance the chemical equation algebraically: H_2O + KMnO_4 + SO_2 ⟶ H_2SO_4 + MnSO_4 + K_2SO_3 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 K_2SO_3 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 O: | c_1 + 4 c_2 + 2 c_3 = 4 c_4 + 4 c_5 + 3 c_6 K: | c_2 = 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 6 c_4 = 3 c_5 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 2 KMnO_4 + 6 SO_2 ⟶ 3 H_2SO_4 + 2 MnSO_4 + K_2SO_3](../image_source/ee72d051240f1ea889018af47727dc3d.png)
Balance the chemical equation algebraically: H_2O + KMnO_4 + SO_2 ⟶ H_2SO_4 + MnSO_4 + K_2SO_3 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 K_2SO_3 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 O: | c_1 + 4 c_2 + 2 c_3 = 4 c_4 + 4 c_5 + 3 c_6 K: | c_2 = 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 6 c_4 = 3 c_5 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 2 KMnO_4 + 6 SO_2 ⟶ 3 H_2SO_4 + 2 MnSO_4 + K_2SO_3
Structures
![+ + ⟶ + +](../image_source/82a88289552c99008cebcdb67db6409e.png)
+ + ⟶ + +
Names
![water + potassium permanganate + sulfur dioxide ⟶ sulfuric acid + manganese(II) sulfate + potassium sulfite](../image_source/f1dd3a43c1af87ae7e5545bf44be9f3a.png)
water + potassium permanganate + sulfur dioxide ⟶ sulfuric acid + manganese(II) sulfate + potassium sulfite
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2O + KMnO_4 + SO_2 ⟶ H_2SO_4 + MnSO_4 + K_2SO_3 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_2O + 2 KMnO_4 + 6 SO_2 ⟶ 3 H_2SO_4 + 2 MnSO_4 + K_2SO_3 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 | 3 | -3 KMnO_4 | 2 | -2 SO_2 | 6 | -6 H_2SO_4 | 3 | 3 MnSO_4 | 2 | 2 K_2SO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) SO_2 | 6 | -6 | ([SO2])^(-6) H_2SO_4 | 3 | 3 | ([H2SO4])^3 MnSO_4 | 2 | 2 | ([MnSO4])^2 K_2SO_3 | 1 | 1 | [K2SO3] 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])^(-3) ([KMnO4])^(-2) ([SO2])^(-6) ([H2SO4])^3 ([MnSO4])^2 [K2SO3] = (([H2SO4])^3 ([MnSO4])^2 [K2SO3])/(([H2O])^3 ([KMnO4])^2 ([SO2])^6)](../image_source/e20eea969c9d780c24c1b40bef21b6de.png)
Construct the equilibrium constant, K, expression for: H_2O + KMnO_4 + SO_2 ⟶ H_2SO_4 + MnSO_4 + K_2SO_3 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_2O + 2 KMnO_4 + 6 SO_2 ⟶ 3 H_2SO_4 + 2 MnSO_4 + K_2SO_3 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 | 3 | -3 KMnO_4 | 2 | -2 SO_2 | 6 | -6 H_2SO_4 | 3 | 3 MnSO_4 | 2 | 2 K_2SO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) SO_2 | 6 | -6 | ([SO2])^(-6) H_2SO_4 | 3 | 3 | ([H2SO4])^3 MnSO_4 | 2 | 2 | ([MnSO4])^2 K_2SO_3 | 1 | 1 | [K2SO3] 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])^(-3) ([KMnO4])^(-2) ([SO2])^(-6) ([H2SO4])^3 ([MnSO4])^2 [K2SO3] = (([H2SO4])^3 ([MnSO4])^2 [K2SO3])/(([H2O])^3 ([KMnO4])^2 ([SO2])^6)
Rate of reaction
![Construct the rate of reaction expression for: H_2O + KMnO_4 + SO_2 ⟶ H_2SO_4 + MnSO_4 + K_2SO_3 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_2O + 2 KMnO_4 + 6 SO_2 ⟶ 3 H_2SO_4 + 2 MnSO_4 + K_2SO_3 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 | 3 | -3 KMnO_4 | 2 | -2 SO_2 | 6 | -6 H_2SO_4 | 3 | 3 MnSO_4 | 2 | 2 K_2SO_3 | 1 | 1 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 | 3 | -3 | -1/3 (Δ[H2O])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) SO_2 | 6 | -6 | -1/6 (Δ[SO2])/(Δt) H_2SO_4 | 3 | 3 | 1/3 (Δ[H2SO4])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) K_2SO_3 | 1 | 1 | (Δ[K2SO3])/(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[H2O])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/6 (Δ[SO2])/(Δt) = 1/3 (Δ[H2SO4])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = (Δ[K2SO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/6ba9ad3fdcca036942c5daaccd977e95.png)
Construct the rate of reaction expression for: H_2O + KMnO_4 + SO_2 ⟶ H_2SO_4 + MnSO_4 + K_2SO_3 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_2O + 2 KMnO_4 + 6 SO_2 ⟶ 3 H_2SO_4 + 2 MnSO_4 + K_2SO_3 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 | 3 | -3 KMnO_4 | 2 | -2 SO_2 | 6 | -6 H_2SO_4 | 3 | 3 MnSO_4 | 2 | 2 K_2SO_3 | 1 | 1 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 | 3 | -3 | -1/3 (Δ[H2O])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) SO_2 | 6 | -6 | -1/6 (Δ[SO2])/(Δt) H_2SO_4 | 3 | 3 | 1/3 (Δ[H2SO4])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) K_2SO_3 | 1 | 1 | (Δ[K2SO3])/(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[H2O])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/6 (Δ[SO2])/(Δt) = 1/3 (Δ[H2SO4])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = (Δ[K2SO3])/(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 sulfite formula | H_2O | KMnO_4 | SO_2 | H_2SO_4 | MnSO_4 | K_2SO_3 Hill formula | H_2O | KMnO_4 | O_2S | H_2O_4S | MnSO_4 | K_2O_3S name | water | potassium permanganate | sulfur dioxide | sulfuric acid | manganese(II) sulfate | potassium sulfite IUPAC name | water | potassium permanganate | sulfur dioxide | sulfuric acid | manganese(+2) cation sulfate | dipotassium sulfite](../image_source/3fe08ec21e63e55f7c4f60f93c93e06e.png)
| water | potassium permanganate | sulfur dioxide | sulfuric acid | manganese(II) sulfate | potassium sulfite formula | H_2O | KMnO_4 | SO_2 | H_2SO_4 | MnSO_4 | K_2SO_3 Hill formula | H_2O | KMnO_4 | O_2S | H_2O_4S | MnSO_4 | K_2O_3S name | water | potassium permanganate | sulfur dioxide | sulfuric acid | manganese(II) sulfate | potassium sulfite IUPAC name | water | potassium permanganate | sulfur dioxide | sulfuric acid | manganese(+2) cation sulfate | dipotassium sulfite