Cu + AuCl3 = CuCl2 + Au

Cu (copper) + AuCl_3 (gold(III) chloride) ⟶ CuCl_2 (copper(II) chloride) + Au (gold)

Balance the chemical equation algebraically: Cu + AuCl_3 ⟶ CuCl_2 + Au Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cu + c_2 AuCl_3 ⟶ c_3 CuCl_2 + c_4 Au Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, Au and Cl: Cu: | c_1 = c_3 Au: | c_2 = c_4 Cl: | 3 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3/2 c_2 = 1 c_3 = 3/2 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Cu + 2 AuCl_3 ⟶ 3 CuCl_2 + 2 Au

+ ⟶ +

copper + gold(III) chloride ⟶ copper(II) chloride + gold

Construct the equilibrium constant, K, expression for: Cu + AuCl_3 ⟶ CuCl_2 + Au 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: 3 Cu + 2 AuCl_3 ⟶ 3 CuCl_2 + 2 Au 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 Cu | 3 | -3 AuCl_3 | 2 | -2 CuCl_2 | 3 | 3 Au | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cu | 3 | -3 | ([Cu])^(-3) AuCl_3 | 2 | -2 | ([AuCl3])^(-2) CuCl_2 | 3 | 3 | ([CuCl2])^3 Au | 2 | 2 | ([Au])^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 = ([Cu])^(-3) ([AuCl3])^(-2) ([CuCl2])^3 ([Au])^2 = (([CuCl2])^3 ([Au])^2)/(([Cu])^3 ([AuCl3])^2)

Construct the rate of reaction expression for: Cu + AuCl_3 ⟶ CuCl_2 + Au 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: 3 Cu + 2 AuCl_3 ⟶ 3 CuCl_2 + 2 Au 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 Cu | 3 | -3 AuCl_3 | 2 | -2 CuCl_2 | 3 | 3 Au | 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 Cu | 3 | -3 | -1/3 (Δ[Cu])/(Δt) AuCl_3 | 2 | -2 | -1/2 (Δ[AuCl3])/(Δt) CuCl_2 | 3 | 3 | 1/3 (Δ[CuCl2])/(Δt) Au | 2 | 2 | 1/2 (Δ[Au])/(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 = -1/3 (Δ[Cu])/(Δt) = -1/2 (Δ[AuCl3])/(Δt) = 1/3 (Δ[CuCl2])/(Δt) = 1/2 (Δ[Au])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| copper | gold(III) chloride | copper(II) chloride | gold formula | Cu | AuCl_3 | CuCl_2 | Au Hill formula | Cu | AuCl_3 | Cl_2Cu | Au name | copper | gold(III) chloride | copper(II) chloride | gold IUPAC name | copper | trichlorogold | dichlorocopper | gold

| copper | gold(III) chloride | copper(II) chloride | gold molar mass | 63.546 g/mol | 303.3 g/mol | 134.4 g/mol | 196.966569 g/mol phase | solid (at STP) | | solid (at STP) | solid (at STP) melting point | 1083 °C | | 620 °C | 1063 °C boiling point | 2567 °C | | | 2856 °C density | 8.96 g/cm^3 | | 3.386 g/cm^3 | 19.3 g/cm^3 solubility in water | insoluble | | | insoluble odor | odorless | | |