Input interpretation
H_2SO_4 sulfuric acid + MnO_2 manganese dioxide + KBr2 ⟶ H_2O water + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + Br_2 bromine
Balanced equation
Balance the chemical equation algebraically: H_2SO_4 + MnO_2 + KBr2 ⟶ H_2O + K_2SO_4 + MnSO_4 + Br_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 MnO_2 + c_3 KBr2 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 MnSO_4 + c_7 Br_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Mn, K and Br: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 2 c_2 = c_4 + 4 c_5 + 4 c_6 S: | c_1 = c_5 + c_6 Mn: | c_2 = c_6 K: | c_3 = 2 c_5 Br: | 2 c_3 = 2 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_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 = 1 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + MnO_2 + 2 KBr2 ⟶ 2 H_2O + K_2SO_4 + MnSO_4 + 2 Br_2
Structures
+ + KBr2 ⟶ + + +
Names
sulfuric acid + manganese dioxide + KBr2 ⟶ water + potassium sulfate + manganese(II) sulfate + bromine
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2SO_4 + MnO_2 + KBr2 ⟶ H_2O + K_2SO_4 + MnSO_4 + Br_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 H_2SO_4 + MnO_2 + 2 KBr2 ⟶ 2 H_2O + K_2SO_4 + MnSO_4 + 2 Br_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 H_2SO_4 | 2 | -2 MnO_2 | 1 | -1 KBr2 | 2 | -2 H_2O | 2 | 2 K_2SO_4 | 1 | 1 MnSO_4 | 1 | 1 Br_2 | 2 | 2 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) MnO_2 | 1 | -1 | ([MnO2])^(-1) KBr2 | 2 | -2 | ([KBr2])^(-2) H_2O | 2 | 2 | ([H2O])^2 K_2SO_4 | 1 | 1 | [K2SO4] MnSO_4 | 1 | 1 | [MnSO4] Br_2 | 2 | 2 | ([Br2])^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 = ([H2SO4])^(-2) ([MnO2])^(-1) ([KBr2])^(-2) ([H2O])^2 [K2SO4] [MnSO4] ([Br2])^2 = (([H2O])^2 [K2SO4] [MnSO4] ([Br2])^2)/(([H2SO4])^2 [MnO2] ([KBr2])^2)](../image_source/616ec79e016cc37d9151ca039e09ba75.png)
Construct the equilibrium constant, K, expression for: H_2SO_4 + MnO_2 + KBr2 ⟶ H_2O + K_2SO_4 + MnSO_4 + Br_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 H_2SO_4 + MnO_2 + 2 KBr2 ⟶ 2 H_2O + K_2SO_4 + MnSO_4 + 2 Br_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 H_2SO_4 | 2 | -2 MnO_2 | 1 | -1 KBr2 | 2 | -2 H_2O | 2 | 2 K_2SO_4 | 1 | 1 MnSO_4 | 1 | 1 Br_2 | 2 | 2 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) MnO_2 | 1 | -1 | ([MnO2])^(-1) KBr2 | 2 | -2 | ([KBr2])^(-2) H_2O | 2 | 2 | ([H2O])^2 K_2SO_4 | 1 | 1 | [K2SO4] MnSO_4 | 1 | 1 | [MnSO4] Br_2 | 2 | 2 | ([Br2])^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 = ([H2SO4])^(-2) ([MnO2])^(-1) ([KBr2])^(-2) ([H2O])^2 [K2SO4] [MnSO4] ([Br2])^2 = (([H2O])^2 [K2SO4] [MnSO4] ([Br2])^2)/(([H2SO4])^2 [MnO2] ([KBr2])^2)
Rate of reaction
![Construct the rate of reaction expression for: H_2SO_4 + MnO_2 + KBr2 ⟶ H_2O + K_2SO_4 + MnSO_4 + Br_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 H_2SO_4 + MnO_2 + 2 KBr2 ⟶ 2 H_2O + K_2SO_4 + MnSO_4 + 2 Br_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 H_2SO_4 | 2 | -2 MnO_2 | 1 | -1 KBr2 | 2 | -2 H_2O | 2 | 2 K_2SO_4 | 1 | 1 MnSO_4 | 1 | 1 Br_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 H_2SO_4 | 2 | -2 | -1/2 (Δ[H2SO4])/(Δt) MnO_2 | 1 | -1 | -(Δ[MnO2])/(Δt) KBr2 | 2 | -2 | -1/2 (Δ[KBr2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) MnSO_4 | 1 | 1 | (Δ[MnSO4])/(Δt) Br_2 | 2 | 2 | 1/2 (Δ[Br2])/(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[MnO2])/(Δt) = -1/2 (Δ[KBr2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[MnSO4])/(Δt) = 1/2 (Δ[Br2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/ab8bd0a607b69bcc688eaa46767054b6.png)
Construct the rate of reaction expression for: H_2SO_4 + MnO_2 + KBr2 ⟶ H_2O + K_2SO_4 + MnSO_4 + Br_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 H_2SO_4 + MnO_2 + 2 KBr2 ⟶ 2 H_2O + K_2SO_4 + MnSO_4 + 2 Br_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 H_2SO_4 | 2 | -2 MnO_2 | 1 | -1 KBr2 | 2 | -2 H_2O | 2 | 2 K_2SO_4 | 1 | 1 MnSO_4 | 1 | 1 Br_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 H_2SO_4 | 2 | -2 | -1/2 (Δ[H2SO4])/(Δt) MnO_2 | 1 | -1 | -(Δ[MnO2])/(Δt) KBr2 | 2 | -2 | -1/2 (Δ[KBr2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) MnSO_4 | 1 | 1 | (Δ[MnSO4])/(Δt) Br_2 | 2 | 2 | 1/2 (Δ[Br2])/(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[MnO2])/(Δt) = -1/2 (Δ[KBr2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[MnSO4])/(Δt) = 1/2 (Δ[Br2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sulfuric acid | manganese dioxide | KBr2 | water | potassium sulfate | manganese(II) sulfate | bromine formula | H_2SO_4 | MnO_2 | KBr2 | H_2O | K_2SO_4 | MnSO_4 | Br_2 Hill formula | H_2O_4S | MnO_2 | Br2K | H_2O | K_2O_4S | MnSO_4 | Br_2 name | sulfuric acid | manganese dioxide | | water | potassium sulfate | manganese(II) sulfate | bromine IUPAC name | sulfuric acid | dioxomanganese | | water | dipotassium sulfate | manganese(+2) cation sulfate | molecular bromine