HBr + NaMnO4 = H2O + Br2 + NaBr + MnBr2

HBr hydrogen bromide + NaMnO_4 sodium permanganate ⟶ H_2O water + Br_2 bromine + NaBr sodium bromide + MnBr_2 manganese(II) bromide

Balance the chemical equation algebraically: HBr + NaMnO_4 ⟶ H_2O + Br_2 + NaBr + MnBr_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HBr + c_2 NaMnO_4 ⟶ c_3 H_2O + c_4 Br_2 + c_5 NaBr + c_6 MnBr_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Br, H, Mn, Na and O: Br: | c_1 = 2 c_4 + c_5 + 2 c_6 H: | c_1 = 2 c_3 Mn: | c_2 = c_6 Na: | c_2 = c_5 O: | 4 c_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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 1 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 = 16 c_2 = 2 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: | | 16 HBr + 2 NaMnO_4 ⟶ 8 H_2O + 5 Br_2 + 2 NaBr + 2 MnBr_2

+ ⟶ + + +

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

Construct the equilibrium constant, K, expression for: HBr + NaMnO_4 ⟶ H_2O + Br_2 + NaBr + 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: 16 HBr + 2 NaMnO_4 ⟶ 8 H_2O + 5 Br_2 + 2 NaBr + 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 HBr | 16 | -16 NaMnO_4 | 2 | -2 H_2O | 8 | 8 Br_2 | 5 | 5 NaBr | 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 HBr | 16 | -16 | ([HBr])^(-16) NaMnO_4 | 2 | -2 | ([NaMnO4])^(-2) H_2O | 8 | 8 | ([H2O])^8 Br_2 | 5 | 5 | ([Br2])^5 NaBr | 2 | 2 | ([NaBr])^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 = ([HBr])^(-16) ([NaMnO4])^(-2) ([H2O])^8 ([Br2])^5 ([NaBr])^2 ([MnBr2])^2 = (([H2O])^8 ([Br2])^5 ([NaBr])^2 ([MnBr2])^2)/(([HBr])^16 ([NaMnO4])^2)

Construct the rate of reaction expression for: HBr + NaMnO_4 ⟶ H_2O + Br_2 + NaBr + 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: 16 HBr + 2 NaMnO_4 ⟶ 8 H_2O + 5 Br_2 + 2 NaBr + 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 HBr | 16 | -16 NaMnO_4 | 2 | -2 H_2O | 8 | 8 Br_2 | 5 | 5 NaBr | 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 HBr | 16 | -16 | -1/16 (Δ[HBr])/(Δt) NaMnO_4 | 2 | -2 | -1/2 (Δ[NaMnO4])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) Br_2 | 5 | 5 | 1/5 (Δ[Br2])/(Δt) NaBr | 2 | 2 | 1/2 (Δ[NaBr])/(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 = -1/16 (Δ[HBr])/(Δt) = -1/2 (Δ[NaMnO4])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/5 (Δ[Br2])/(Δt) = 1/2 (Δ[NaBr])/(Δt) = 1/2 (Δ[MnBr2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen bromide | sodium permanganate | water | bromine | sodium bromide | manganese(II) bromide formula | HBr | NaMnO_4 | H_2O | Br_2 | NaBr | MnBr_2 Hill formula | BrH | MnNaO_4 | H_2O | Br_2 | BrNa | Br_2Mn name | hydrogen bromide | sodium permanganate | water | bromine | sodium bromide | manganese(II) bromide IUPAC name | hydrogen bromide | sodium permanganate | water | molecular bromine | sodium bromide | dibromomanganese