CrCl3 + Cr = CrCl2

CrCl_3 chromic chloride + Cr chromium ⟶ CrCl_2 chromous chloride

Balance the chemical equation algebraically: CrCl_3 + Cr ⟶ CrCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CrCl_3 + c_2 Cr ⟶ c_3 CrCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl and Cr: Cl: | 3 c_1 = 2 c_3 Cr: | c_1 + 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 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 CrCl_3 + Cr ⟶ 3 CrCl_2

+ ⟶

chromic chloride + chromium ⟶ chromous chloride

| chromic chloride | chromium | chromous chloride molecular enthalpy | -556.5 kJ/mol | 0 kJ/mol | -395.4 kJ/mol total enthalpy | -1113 kJ/mol | 0 kJ/mol | -1186 kJ/mol | H_initial = -1113 kJ/mol | | H_final = -1186 kJ/mol ΔH_rxn^0 | -1186 kJ/mol - -1113 kJ/mol = -73.2 kJ/mol (exothermic) | |

Construct the equilibrium constant, K, expression for: CrCl_3 + Cr ⟶ 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: 2 CrCl_3 + Cr ⟶ 3 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 CrCl_3 | 2 | -2 Cr | 1 | -1 CrCl_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CrCl_3 | 2 | -2 | ([CrCl3])^(-2) Cr | 1 | -1 | ([Cr])^(-1) CrCl_2 | 3 | 3 | ([CrCl2])^3 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 = ([CrCl3])^(-2) ([Cr])^(-1) ([CrCl2])^3 = ([CrCl2])^3/(([CrCl3])^2 [Cr])

Construct the rate of reaction expression for: CrCl_3 + Cr ⟶ 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: 2 CrCl_3 + Cr ⟶ 3 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 CrCl_3 | 2 | -2 Cr | 1 | -1 CrCl_2 | 3 | 3 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 CrCl_3 | 2 | -2 | -1/2 (Δ[CrCl3])/(Δt) Cr | 1 | -1 | -(Δ[Cr])/(Δt) CrCl_2 | 3 | 3 | 1/3 (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 = -1/2 (Δ[CrCl3])/(Δt) = -(Δ[Cr])/(Δt) = 1/3 (Δ[CrCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chromic chloride | chromium | chromous chloride formula | CrCl_3 | Cr | CrCl_2 Hill formula | Cl_3Cr | Cr | Cl_2Cr name | chromic chloride | chromium | chromous chloride IUPAC name | trichlorochromium | chromium | dichlorochromium

| chromic chloride | chromium | chromous chloride molar mass | 158.3 g/mol | 51.9961 g/mol | 122.9 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) melting point | 1152 °C | 1857 °C | 824 °C boiling point | | 2672 °C | 1302 °C density | 2.87 g/cm^3 | 7.14 g/cm^3 | 2.9 g/cm^3 solubility in water | slightly soluble | insoluble | soluble odor | | odorless |