KMnO4 + HBr = H2O + Br2 + KBr + MnBr2

KMnO_4 (potassium permanganate) + HBr (hydrogen bromide) ⟶ H_2O (water) + Br_2 (bromine) + KBr (potassium bromide) + MnBr_2 (manganese(II) bromide)

Balance the chemical equation algebraically: KMnO_4 + HBr ⟶ H_2O + Br_2 + KBr + MnBr_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 + c_2 HBr ⟶ c_3 H_2O + c_4 Br_2 + c_5 KBr + c_6 MnBr_2 Set the number of atoms in the reactants equal to the number of atoms in the products for K, Mn, O, Br and H: K: | c_1 = c_5 Mn: | c_1 = c_6 O: | 4 c_1 = c_3 Br: | c_2 = 2 c_4 + c_5 + 2 c_6 H: | c_2 = 2 c_3 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 8 c_3 = 4 c_4 = 5/2 c_5 = 1 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 16 c_3 = 8 c_4 = 5 c_5 = 2 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KMnO_4 + 16 HBr ⟶ 8 H_2O + 5 Br_2 + 2 KBr + 2 MnBr_2

+ ⟶ + + +

potassium permanganate + hydrogen bromide ⟶ water + bromine + potassium bromide + manganese(II) bromide

Construct the equilibrium constant, K, expression for: KMnO_4 + HBr ⟶ H_2O + Br_2 + KBr + MnBr_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 KMnO_4 + 16 HBr ⟶ 8 H_2O + 5 Br_2 + 2 KBr + 2 MnBr_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 KMnO_4 | 2 | -2 HBr | 16 | -16 H_2O | 8 | 8 Br_2 | 5 | 5 KBr | 2 | 2 MnBr_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KMnO_4 | 2 | -2 | ([KMnO4])^(-2) HBr | 16 | -16 | ([HBr])^(-16) H_2O | 8 | 8 | ([H2O])^8 Br_2 | 5 | 5 | ([Br2])^5 KBr | 2 | 2 | ([KBr])^2 MnBr_2 | 2 | 2 | ([MnBr2])^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 = ([KMnO4])^(-2) ([HBr])^(-16) ([H2O])^8 ([Br2])^5 ([KBr])^2 ([MnBr2])^2 = (([H2O])^8 ([Br2])^5 ([KBr])^2 ([MnBr2])^2)/(([KMnO4])^2 ([HBr])^16)

Construct the rate of reaction expression for: KMnO_4 + HBr ⟶ H_2O + Br_2 + KBr + MnBr_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 KMnO_4 + 16 HBr ⟶ 8 H_2O + 5 Br_2 + 2 KBr + 2 MnBr_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 KMnO_4 | 2 | -2 HBr | 16 | -16 H_2O | 8 | 8 Br_2 | 5 | 5 KBr | 2 | 2 MnBr_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 KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) HBr | 16 | -16 | -1/16 (Δ[HBr])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) Br_2 | 5 | 5 | 1/5 (Δ[Br2])/(Δt) KBr | 2 | 2 | 1/2 (Δ[KBr])/(Δt) MnBr_2 | 2 | 2 | 1/2 (Δ[MnBr2])/(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[KMnO4])/(Δt) = -1/16 (Δ[HBr])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/5 (Δ[Br2])/(Δt) = 1/2 (Δ[KBr])/(Δt) = 1/2 (Δ[MnBr2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium permanganate | hydrogen bromide | water | bromine | potassium bromide | manganese(II) bromide formula | KMnO_4 | HBr | H_2O | Br_2 | KBr | MnBr_2 Hill formula | KMnO_4 | BrH | H_2O | Br_2 | BrK | Br_2Mn name | potassium permanganate | hydrogen bromide | water | bromine | potassium bromide | manganese(II) bromide IUPAC name | potassium permanganate | hydrogen bromide | water | molecular bromine | potassium bromide | dibromomanganese