Ag + CuCl2 = Cu + AgCl

Ag silver + CuCl_2 copper(II) chloride ⟶ Cu copper + AgCl silver chloride

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

+ ⟶ +

silver + copper(II) chloride ⟶ copper + silver chloride

| silver | copper(II) chloride | copper | silver chloride molecular enthalpy | 0 kJ/mol | -220.1 kJ/mol | 0 kJ/mol | -127 kJ/mol total enthalpy | 0 kJ/mol | -220.1 kJ/mol | 0 kJ/mol | -254 kJ/mol | H_initial = -220.1 kJ/mol | | H_final = -254 kJ/mol | ΔH_rxn^0 | -254 kJ/mol - -220.1 kJ/mol = -33.9 kJ/mol (exothermic) | | |

Construct the equilibrium constant, K, expression for: Ag + CuCl_2 ⟶ Cu + AgCl 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 Ag + CuCl_2 ⟶ Cu + 2 AgCl 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 Ag | 2 | -2 CuCl_2 | 1 | -1 Cu | 1 | 1 AgCl | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Ag | 2 | -2 | ([Ag])^(-2) CuCl_2 | 1 | -1 | ([CuCl2])^(-1) Cu | 1 | 1 | [Cu] AgCl | 2 | 2 | ([AgCl])^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 = ([Ag])^(-2) ([CuCl2])^(-1) [Cu] ([AgCl])^2 = ([Cu] ([AgCl])^2)/(([Ag])^2 [CuCl2])

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

| silver | copper(II) chloride | copper | silver chloride formula | Ag | CuCl_2 | Cu | AgCl Hill formula | Ag | Cl_2Cu | Cu | AgCl name | silver | copper(II) chloride | copper | silver chloride IUPAC name | silver | dichlorocopper | copper | chlorosilver

| silver | copper(II) chloride | copper | silver chloride molar mass | 107.8682 g/mol | 134.4 g/mol | 63.546 g/mol | 143.32 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 960 °C | 620 °C | 1083 °C | 455 °C boiling point | 2212 °C | | 2567 °C | 1554 °C density | 10.49 g/cm^3 | 3.386 g/cm^3 | 8.96 g/cm^3 | 5.56 g/cm^3 solubility in water | insoluble | | insoluble | odor | | | odorless |