Input interpretation
H_2SO_4 sulfuric acid + K_2MnO_4 potassium manganate + Na_2SO_3 sodium sulfite ⟶ H_2O water + K_2SO_4 potassium sulfate + Na_2SO_4 sodium sulfate + MnSO_4 manganese(II) sulfate
Balanced equation
Balance the chemical equation algebraically: H_2SO_4 + K_2MnO_4 + Na_2SO_3 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + MnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 K_2MnO_4 + c_3 Na_2SO_3 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Na_2SO_4 + c_7 MnSO_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 Na: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 4 c_6 + 4 c_7 S: | c_1 + c_3 = c_5 + c_6 + c_7 K: | 2 c_2 = 2 c_5 Mn: | c_2 = c_7 Na: | 2 c_3 = 2 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 2 c_5 = 1 c_6 = 2 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + K_2MnO_4 + 2 Na_2SO_3 ⟶ 2 H_2O + K_2SO_4 + 2 Na_2SO_4 + MnSO_4
Structures
+ + ⟶ + + +
Names
sulfuric acid + potassium manganate + sodium sulfite ⟶ water + potassium sulfate + sodium sulfate + manganese(II) sulfate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2SO_4 + K_2MnO_4 + Na_2SO_3 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + MnSO_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_2SO_4 + K_2MnO_4 + 2 Na_2SO_3 ⟶ 2 H_2O + K_2SO_4 + 2 Na_2SO_4 + MnSO_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 | 2 | -2 K_2MnO_4 | 1 | -1 Na_2SO_3 | 2 | -2 H_2O | 2 | 2 K_2SO_4 | 1 | 1 Na_2SO_4 | 2 | 2 MnSO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 2 | -2 | ([H2SO4])^(-2) K_2MnO_4 | 1 | -1 | ([K2MnO4])^(-1) Na_2SO_3 | 2 | -2 | ([Na2SO3])^(-2) H_2O | 2 | 2 | ([H2O])^2 K_2SO_4 | 1 | 1 | [K2SO4] Na_2SO_4 | 2 | 2 | ([Na2SO4])^2 MnSO_4 | 1 | 1 | [MnSO4] 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])^(-2) ([K2MnO4])^(-1) ([Na2SO3])^(-2) ([H2O])^2 [K2SO4] ([Na2SO4])^2 [MnSO4] = (([H2O])^2 [K2SO4] ([Na2SO4])^2 [MnSO4])/(([H2SO4])^2 [K2MnO4] ([Na2SO3])^2)](../image_source/37aa41f6d9a7d422e5cfb6bb1dfcbb45.png)
Construct the equilibrium constant, K, expression for: H_2SO_4 + K_2MnO_4 + Na_2SO_3 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + MnSO_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_2SO_4 + K_2MnO_4 + 2 Na_2SO_3 ⟶ 2 H_2O + K_2SO_4 + 2 Na_2SO_4 + MnSO_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 | 2 | -2 K_2MnO_4 | 1 | -1 Na_2SO_3 | 2 | -2 H_2O | 2 | 2 K_2SO_4 | 1 | 1 Na_2SO_4 | 2 | 2 MnSO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 2 | -2 | ([H2SO4])^(-2) K_2MnO_4 | 1 | -1 | ([K2MnO4])^(-1) Na_2SO_3 | 2 | -2 | ([Na2SO3])^(-2) H_2O | 2 | 2 | ([H2O])^2 K_2SO_4 | 1 | 1 | [K2SO4] Na_2SO_4 | 2 | 2 | ([Na2SO4])^2 MnSO_4 | 1 | 1 | [MnSO4] 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])^(-2) ([K2MnO4])^(-1) ([Na2SO3])^(-2) ([H2O])^2 [K2SO4] ([Na2SO4])^2 [MnSO4] = (([H2O])^2 [K2SO4] ([Na2SO4])^2 [MnSO4])/(([H2SO4])^2 [K2MnO4] ([Na2SO3])^2)
Rate of reaction
![Construct the rate of reaction expression for: H_2SO_4 + K_2MnO_4 + Na_2SO_3 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + MnSO_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_2SO_4 + K_2MnO_4 + 2 Na_2SO_3 ⟶ 2 H_2O + K_2SO_4 + 2 Na_2SO_4 + MnSO_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 | 2 | -2 K_2MnO_4 | 1 | -1 Na_2SO_3 | 2 | -2 H_2O | 2 | 2 K_2SO_4 | 1 | 1 Na_2SO_4 | 2 | 2 MnSO_4 | 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_2SO_4 | 2 | -2 | -1/2 (Δ[H2SO4])/(Δt) K_2MnO_4 | 1 | -1 | -(Δ[K2MnO4])/(Δt) Na_2SO_3 | 2 | -2 | -1/2 (Δ[Na2SO3])/(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) MnSO_4 | 1 | 1 | (Δ[MnSO4])/(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[H2SO4])/(Δt) = -(Δ[K2MnO4])/(Δt) = -1/2 (Δ[Na2SO3])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[Na2SO4])/(Δt) = (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/c25d3ac0f11df8d08e61441912a40cf3.png)
Construct the rate of reaction expression for: H_2SO_4 + K_2MnO_4 + Na_2SO_3 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + MnSO_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_2SO_4 + K_2MnO_4 + 2 Na_2SO_3 ⟶ 2 H_2O + K_2SO_4 + 2 Na_2SO_4 + MnSO_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 | 2 | -2 K_2MnO_4 | 1 | -1 Na_2SO_3 | 2 | -2 H_2O | 2 | 2 K_2SO_4 | 1 | 1 Na_2SO_4 | 2 | 2 MnSO_4 | 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_2SO_4 | 2 | -2 | -1/2 (Δ[H2SO4])/(Δt) K_2MnO_4 | 1 | -1 | -(Δ[K2MnO4])/(Δt) Na_2SO_3 | 2 | -2 | -1/2 (Δ[Na2SO3])/(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) MnSO_4 | 1 | 1 | (Δ[MnSO4])/(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[H2SO4])/(Δt) = -(Δ[K2MnO4])/(Δt) = -1/2 (Δ[Na2SO3])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[Na2SO4])/(Δt) = (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sulfuric acid | potassium manganate | sodium sulfite | water | potassium sulfate | sodium sulfate | manganese(II) sulfate formula | H_2SO_4 | K_2MnO_4 | Na_2SO_3 | H_2O | K_2SO_4 | Na_2SO_4 | MnSO_4 Hill formula | H_2O_4S | K_2MnO_4 | Na_2O_3S | H_2O | K_2O_4S | Na_2O_4S | MnSO_4 name | sulfuric acid | potassium manganate | sodium sulfite | water | potassium sulfate | sodium sulfate | manganese(II) sulfate IUPAC name | sulfuric acid | dipotassium dioxido-dioxomanganese | disodium sulfite | water | dipotassium sulfate | disodium sulfate | manganese(+2) cation sulfate