Cl2 + KBr + C6H6 = KCl + HBr + C6H5Br

Cl_2 chlorine + KBr potassium bromide + C_6H_6 benzene ⟶ KCl potassium chloride + HBr hydrogen bromide + C_6H_5Br bromobenzene

Balance the chemical equation algebraically: Cl_2 + KBr + C_6H_6 ⟶ KCl + HBr + C_6H_5Br Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 KBr + c_3 C_6H_6 ⟶ c_4 KCl + c_5 HBr + c_6 C_6H_5Br Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, Br, K, C and H: Cl: | 2 c_1 = c_4 Br: | c_2 = c_5 + c_6 K: | c_2 = c_4 C: | 6 c_3 = 6 c_6 H: | 6 c_3 = c_5 + 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Cl_2 + 2 KBr + C_6H_6 ⟶ 2 KCl + HBr + C_6H_5Br

+ + ⟶ + +

chlorine + potassium bromide + benzene ⟶ potassium chloride + hydrogen bromide + bromobenzene

Construct the equilibrium constant, K, expression for: Cl_2 + KBr + C_6H_6 ⟶ KCl + HBr + C_6H_5Br 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: Cl_2 + 2 KBr + C_6H_6 ⟶ 2 KCl + HBr + C_6H_5Br 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 Cl_2 | 1 | -1 KBr | 2 | -2 C_6H_6 | 1 | -1 KCl | 2 | 2 HBr | 1 | 1 C_6H_5Br | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cl_2 | 1 | -1 | ([Cl2])^(-1) KBr | 2 | -2 | ([KBr])^(-2) C_6H_6 | 1 | -1 | ([C6H6])^(-1) KCl | 2 | 2 | ([KCl])^2 HBr | 1 | 1 | [HBr] C_6H_5Br | 1 | 1 | [C6H5Br] 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 = ([Cl2])^(-1) ([KBr])^(-2) ([C6H6])^(-1) ([KCl])^2 [HBr] [C6H5Br] = (([KCl])^2 [HBr] [C6H5Br])/([Cl2] ([KBr])^2 [C6H6])

Construct the rate of reaction expression for: Cl_2 + KBr + C_6H_6 ⟶ KCl + HBr + C_6H_5Br 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: Cl_2 + 2 KBr + C_6H_6 ⟶ 2 KCl + HBr + C_6H_5Br 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 Cl_2 | 1 | -1 KBr | 2 | -2 C_6H_6 | 1 | -1 KCl | 2 | 2 HBr | 1 | 1 C_6H_5Br | 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 Cl_2 | 1 | -1 | -(Δ[Cl2])/(Δt) KBr | 2 | -2 | -1/2 (Δ[KBr])/(Δt) C_6H_6 | 1 | -1 | -(Δ[C6H6])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) HBr | 1 | 1 | (Δ[HBr])/(Δt) C_6H_5Br | 1 | 1 | (Δ[C6H5Br])/(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 = -(Δ[Cl2])/(Δt) = -1/2 (Δ[KBr])/(Δt) = -(Δ[C6H6])/(Δt) = 1/2 (Δ[KCl])/(Δt) = (Δ[HBr])/(Δt) = (Δ[C6H5Br])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chlorine | potassium bromide | benzene | potassium chloride | hydrogen bromide | bromobenzene formula | Cl_2 | KBr | C_6H_6 | KCl | HBr | C_6H_5Br Hill formula | Cl_2 | BrK | C_6H_6 | ClK | BrH | C_6H_5Br name | chlorine | potassium bromide | benzene | potassium chloride | hydrogen bromide | bromobenzene IUPAC name | molecular chlorine | potassium bromide | benzene | potassium chloride | hydrogen bromide | bromobenzene