CuCl2 + Cr = Cu + CrCl3

CuCl_2 copper(II) chloride + Cr chromium ⟶ Cu copper + CrCl_3 chromic chloride

Balance the chemical equation algebraically: CuCl_2 + Cr ⟶ Cu + CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CuCl_2 + c_2 Cr ⟶ c_3 Cu + c_4 CrCl_3 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 = 3 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_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 CuCl_2 + 2 Cr ⟶ 3 Cu + 2 CrCl_3

+ ⟶ +

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

| copper(II) chloride | chromium | copper | chromic chloride molecular enthalpy | -220.1 kJ/mol | 0 kJ/mol | 0 kJ/mol | -556.5 kJ/mol total enthalpy | -660.3 kJ/mol | 0 kJ/mol | 0 kJ/mol | -1113 kJ/mol | H_initial = -660.3 kJ/mol | | H_final = -1113 kJ/mol | ΔH_rxn^0 | -1113 kJ/mol - -660.3 kJ/mol = -452.7 kJ/mol (exothermic) | | |

Construct the equilibrium constant, K, expression for: CuCl_2 + Cr ⟶ Cu + CrCl_3 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 CuCl_2 + 2 Cr ⟶ 3 Cu + 2 CrCl_3 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 | 3 | -3 Cr | 2 | -2 Cu | 3 | 3 CrCl_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CuCl_2 | 3 | -3 | ([CuCl2])^(-3) Cr | 2 | -2 | ([Cr])^(-2) Cu | 3 | 3 | ([Cu])^3 CrCl_3 | 2 | 2 | ([CrCl3])^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 = ([CuCl2])^(-3) ([Cr])^(-2) ([Cu])^3 ([CrCl3])^2 = (([Cu])^3 ([CrCl3])^2)/(([CuCl2])^3 ([Cr])^2)

Construct the rate of reaction expression for: CuCl_2 + Cr ⟶ Cu + CrCl_3 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 CuCl_2 + 2 Cr ⟶ 3 Cu + 2 CrCl_3 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 | 3 | -3 Cr | 2 | -2 Cu | 3 | 3 CrCl_3 | 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 CuCl_2 | 3 | -3 | -1/3 (Δ[CuCl2])/(Δt) Cr | 2 | -2 | -1/2 (Δ[Cr])/(Δt) Cu | 3 | 3 | 1/3 (Δ[Cu])/(Δt) CrCl_3 | 2 | 2 | 1/2 (Δ[CrCl3])/(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[CuCl2])/(Δt) = -1/2 (Δ[Cr])/(Δt) = 1/3 (Δ[Cu])/(Δt) = 1/2 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| copper(II) chloride | chromium | copper | chromic chloride formula | CuCl_2 | Cr | Cu | CrCl_3 Hill formula | Cl_2Cu | Cr | Cu | Cl_3Cr name | copper(II) chloride | chromium | copper | chromic chloride IUPAC name | dichlorocopper | chromium | copper | trichlorochromium

| copper(II) chloride | chromium | copper | chromic chloride molar mass | 134.4 g/mol | 51.9961 g/mol | 63.546 g/mol | 158.3 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 620 °C | 1857 °C | 1083 °C | 1152 °C boiling point | | 2672 °C | 2567 °C | density | 3.386 g/cm^3 | 7.14 g/cm^3 | 8.96 g/cm^3 | 2.87 g/cm^3 solubility in water | | insoluble | insoluble | slightly soluble odor | | odorless | odorless |