Zn + CrCl3 = ZnCl2 + Cr

Zn zinc + CrCl_3 chromic chloride ⟶ ZnCl_2 zinc chloride + Cr chromium

Balance the chemical equation algebraically: Zn + CrCl_3 ⟶ ZnCl_2 + Cr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Zn + c_2 CrCl_3 ⟶ c_3 ZnCl_2 + c_4 Cr Set the number of atoms in the reactants equal to the number of atoms in the products for Zn, Cl and Cr: Zn: | c_1 = c_3 Cl: | 3 c_2 = 2 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 Zn + 2 CrCl_3 ⟶ 3 ZnCl_2 + 2 Cr

+ ⟶ +

zinc + chromic chloride ⟶ zinc chloride + chromium

| zinc | chromic chloride | zinc chloride | chromium molecular enthalpy | 0 kJ/mol | -556.5 kJ/mol | -415.1 kJ/mol | 0 kJ/mol total enthalpy | 0 kJ/mol | -1113 kJ/mol | -1245 kJ/mol | 0 kJ/mol | H_initial = -1113 kJ/mol | | H_final = -1245 kJ/mol | ΔH_rxn^0 | -1245 kJ/mol - -1113 kJ/mol = -132.3 kJ/mol (exothermic) | | |

Construct the equilibrium constant, K, expression for: Zn + CrCl_3 ⟶ ZnCl_2 + Cr 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 Zn + 2 CrCl_3 ⟶ 3 ZnCl_2 + 2 Cr 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 Zn | 3 | -3 CrCl_3 | 2 | -2 ZnCl_2 | 3 | 3 Cr | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Zn | 3 | -3 | ([Zn])^(-3) CrCl_3 | 2 | -2 | ([CrCl3])^(-2) ZnCl_2 | 3 | 3 | ([ZnCl2])^3 Cr | 2 | 2 | ([Cr])^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 = ([Zn])^(-3) ([CrCl3])^(-2) ([ZnCl2])^3 ([Cr])^2 = (([ZnCl2])^3 ([Cr])^2)/(([Zn])^3 ([CrCl3])^2)

Construct the rate of reaction expression for: Zn + CrCl_3 ⟶ ZnCl_2 + Cr 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 Zn + 2 CrCl_3 ⟶ 3 ZnCl_2 + 2 Cr 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 Zn | 3 | -3 CrCl_3 | 2 | -2 ZnCl_2 | 3 | 3 Cr | 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 Zn | 3 | -3 | -1/3 (Δ[Zn])/(Δt) CrCl_3 | 2 | -2 | -1/2 (Δ[CrCl3])/(Δt) ZnCl_2 | 3 | 3 | 1/3 (Δ[ZnCl2])/(Δt) Cr | 2 | 2 | 1/2 (Δ[Cr])/(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[Zn])/(Δt) = -1/2 (Δ[CrCl3])/(Δt) = 1/3 (Δ[ZnCl2])/(Δt) = 1/2 (Δ[Cr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| zinc | chromic chloride | zinc chloride | chromium formula | Zn | CrCl_3 | ZnCl_2 | Cr Hill formula | Zn | Cl_3Cr | Cl_2Zn | Cr name | zinc | chromic chloride | zinc chloride | chromium IUPAC name | zinc | trichlorochromium | zinc dichloride | chromium

| zinc | chromic chloride | zinc chloride | chromium molar mass | 65.38 g/mol | 158.3 g/mol | 136.3 g/mol | 51.9961 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 420 °C | 1152 °C | 293 °C | 1857 °C boiling point | 907 °C | | | 2672 °C density | 7.14 g/cm^3 | 2.87 g/cm^3 | | 7.14 g/cm^3 solubility in water | insoluble | slightly soluble | soluble | insoluble odor | odorless | | odorless | odorless