CuCl2 + Cr = Cu + CrCl2

CuCl_2 copper(II) chloride + Cr chromium ⟶ Cu copper + CrCl_2 chromous chloride

Balance the chemical equation algebraically: CuCl_2 + Cr ⟶ Cu + CrCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CuCl_2 + c_2 Cr ⟶ c_3 Cu + c_4 CrCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, Cu and Cr: Cl: | 2 c_1 = 2 c_4 Cu: | c_1 = c_3 Cr: | 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: | | CuCl_2 + Cr ⟶ Cu + CrCl_2

+ ⟶ +

copper(II) chloride + chromium ⟶ copper + chromous chloride

| copper(II) chloride | chromium | copper | chromous chloride molecular enthalpy | -220.1 kJ/mol | 0 kJ/mol | 0 kJ/mol | -395.4 kJ/mol total enthalpy | -220.1 kJ/mol | 0 kJ/mol | 0 kJ/mol | -395.4 kJ/mol | H_initial = -220.1 kJ/mol | | H_final = -395.4 kJ/mol | ΔH_rxn^0 | -395.4 kJ/mol - -220.1 kJ/mol = -175.3 kJ/mol (exothermic) | | |

Construct the equilibrium constant, K, expression for: CuCl_2 + Cr ⟶ Cu + CrCl_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: CuCl_2 + Cr ⟶ Cu + CrCl_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 CuCl_2 | 1 | -1 Cr | 1 | -1 Cu | 1 | 1 CrCl_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CuCl_2 | 1 | -1 | ([CuCl2])^(-1) Cr | 1 | -1 | ([Cr])^(-1) Cu | 1 | 1 | [Cu] CrCl_2 | 1 | 1 | [CrCl2] 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 = ([CuCl2])^(-1) ([Cr])^(-1) [Cu] [CrCl2] = ([Cu] [CrCl2])/([CuCl2] [Cr])

Construct the rate of reaction expression for: CuCl_2 + Cr ⟶ Cu + CrCl_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: CuCl_2 + Cr ⟶ Cu + CrCl_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 CuCl_2 | 1 | -1 Cr | 1 | -1 Cu | 1 | 1 CrCl_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 CuCl_2 | 1 | -1 | -(Δ[CuCl2])/(Δt) Cr | 1 | -1 | -(Δ[Cr])/(Δt) Cu | 1 | 1 | (Δ[Cu])/(Δt) CrCl_2 | 1 | 1 | (Δ[CrCl2])/(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[CuCl2])/(Δt) = -(Δ[Cr])/(Δt) = (Δ[Cu])/(Δt) = (Δ[CrCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| copper(II) chloride | chromium | copper | chromous chloride formula | CuCl_2 | Cr | Cu | CrCl_2 Hill formula | Cl_2Cu | Cr | Cu | Cl_2Cr name | copper(II) chloride | chromium | copper | chromous chloride IUPAC name | dichlorocopper | chromium | copper | dichlorochromium

| copper(II) chloride | chromium | copper | chromous chloride molar mass | 134.4 g/mol | 51.9961 g/mol | 63.546 g/mol | 122.9 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 620 °C | 1857 °C | 1083 °C | 824 °C boiling point | | 2672 °C | 2567 °C | 1302 °C density | 3.386 g/cm^3 | 7.14 g/cm^3 | 8.96 g/cm^3 | 2.9 g/cm^3 solubility in water | | insoluble | insoluble | soluble odor | | odorless | odorless |