Br2 + CuCl2 = Cl2 + CuBr2

Br_2 bromine + CuCl_2 copper(II) chloride ⟶ Cl_2 chlorine + CuBr_2 cupric bromide

Balance the chemical equation algebraically: Br_2 + CuCl_2 ⟶ Cl_2 + CuBr_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Br_2 + c_2 CuCl_2 ⟶ c_3 Cl_2 + c_4 CuBr_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Br, Cl and Cu: Br: | 2 c_1 = 2 c_4 Cl: | 2 c_2 = 2 c_3 Cu: | c_2 = c_4 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 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Br_2 + CuCl_2 ⟶ Cl_2 + CuBr_2

+ ⟶ +

bromine + copper(II) chloride ⟶ chlorine + cupric bromide

| bromine | copper(II) chloride | chlorine | cupric bromide molecular enthalpy | 0 kJ/mol | -220.1 kJ/mol | 0 kJ/mol | -141.8 kJ/mol total enthalpy | 0 kJ/mol | -220.1 kJ/mol | 0 kJ/mol | -141.8 kJ/mol | H_initial = -220.1 kJ/mol | | H_final = -141.8 kJ/mol | ΔH_rxn^0 | -141.8 kJ/mol - -220.1 kJ/mol = 78.3 kJ/mol (endothermic) | | |

Construct the equilibrium constant, K, expression for: Br_2 + CuCl_2 ⟶ Cl_2 + CuBr_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: Br_2 + CuCl_2 ⟶ Cl_2 + CuBr_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 Br_2 | 1 | -1 CuCl_2 | 1 | -1 Cl_2 | 1 | 1 CuBr_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Br_2 | 1 | -1 | ([Br2])^(-1) CuCl_2 | 1 | -1 | ([CuCl2])^(-1) Cl_2 | 1 | 1 | [Cl2] CuBr_2 | 1 | 1 | [CuBr2] 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 = ([Br2])^(-1) ([CuCl2])^(-1) [Cl2] [CuBr2] = ([Cl2] [CuBr2])/([Br2] [CuCl2])

Construct the rate of reaction expression for: Br_2 + CuCl_2 ⟶ Cl_2 + CuBr_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: Br_2 + CuCl_2 ⟶ Cl_2 + CuBr_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 Br_2 | 1 | -1 CuCl_2 | 1 | -1 Cl_2 | 1 | 1 CuBr_2 | 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 Br_2 | 1 | -1 | -(Δ[Br2])/(Δt) CuCl_2 | 1 | -1 | -(Δ[CuCl2])/(Δt) Cl_2 | 1 | 1 | (Δ[Cl2])/(Δt) CuBr_2 | 1 | 1 | (Δ[CuBr2])/(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[Br2])/(Δt) = -(Δ[CuCl2])/(Δt) = (Δ[Cl2])/(Δt) = (Δ[CuBr2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| bromine | copper(II) chloride | chlorine | cupric bromide formula | Br_2 | CuCl_2 | Cl_2 | CuBr_2 Hill formula | Br_2 | Cl_2Cu | Cl_2 | Br_2Cu name | bromine | copper(II) chloride | chlorine | cupric bromide IUPAC name | molecular bromine | dichlorocopper | molecular chlorine | dibromocopper

| bromine | copper(II) chloride | chlorine | cupric bromide molar mass | 159.81 g/mol | 134.4 g/mol | 70.9 g/mol | 223.35 g/mol phase | liquid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | -7.2 °C | 620 °C | -101 °C | 498 °C boiling point | 58.8 °C | | -34 °C | 900 °C density | 3.119 g/cm^3 | 3.386 g/cm^3 | 0.003214 g/cm^3 (at 0 °C) | 4.77 g/cm^3 solubility in water | insoluble | | | very soluble surface tension | 0.0409 N/m | | | dynamic viscosity | 9.44×10^-4 Pa s (at 25 °C) | | |