HCl + CrO3 = H2O + Cl2 + CrCl3

HCl (hydrogen chloride) + CrO_3 (chromium trioxide) ⟶ H_2O (water) + Cl_2 (chlorine) + CrCl_3 (chromic chloride)

Balance the chemical equation algebraically: HCl + CrO_3 ⟶ H_2O + Cl_2 + CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 CrO_3 ⟶ c_3 H_2O + c_4 Cl_2 + c_5 CrCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Cr and O: Cl: | c_1 = 2 c_4 + 3 c_5 H: | c_1 = 2 c_3 Cr: | c_2 = c_5 O: | 3 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 = 6 c_2 = 1 c_3 = 3 c_4 = 3/2 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 12 c_2 = 2 c_3 = 6 c_4 = 3 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 HCl + 2 CrO_3 ⟶ 6 H_2O + 3 Cl_2 + 2 CrCl_3

+ ⟶ + +

hydrogen chloride + chromium trioxide ⟶ water + chlorine + chromic chloride

| hydrogen chloride | chromium trioxide | water | chlorine | chromic chloride molecular free energy | -95.3 kJ/mol | -502 kJ/mol | -237.1 kJ/mol | 0 kJ/mol | -486.1 kJ/mol total free energy | -1144 kJ/mol | -1004 kJ/mol | -1423 kJ/mol | 0 kJ/mol | -972.2 kJ/mol | G_initial = -2148 kJ/mol | | G_final = -2395 kJ/mol | | ΔG_rxn^0 | -2395 kJ/mol - -2148 kJ/mol = -247.2 kJ/mol (exergonic) | | | |

Construct the equilibrium constant, K, expression for: HCl + CrO_3 ⟶ H_2O + Cl_2 + 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: 12 HCl + 2 CrO_3 ⟶ 6 H_2O + 3 Cl_2 + 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 HCl | 12 | -12 CrO_3 | 2 | -2 H_2O | 6 | 6 Cl_2 | 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 HCl | 12 | -12 | ([HCl])^(-12) CrO_3 | 2 | -2 | ([CrO3])^(-2) H_2O | 6 | 6 | ([H2O])^6 Cl_2 | 3 | 3 | ([Cl2])^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 = ([HCl])^(-12) ([CrO3])^(-2) ([H2O])^6 ([Cl2])^3 ([CrCl3])^2 = (([H2O])^6 ([Cl2])^3 ([CrCl3])^2)/(([HCl])^12 ([CrO3])^2)

Construct the rate of reaction expression for: HCl + CrO_3 ⟶ H_2O + Cl_2 + 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: 12 HCl + 2 CrO_3 ⟶ 6 H_2O + 3 Cl_2 + 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 HCl | 12 | -12 CrO_3 | 2 | -2 H_2O | 6 | 6 Cl_2 | 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 HCl | 12 | -12 | -1/12 (Δ[HCl])/(Δt) CrO_3 | 2 | -2 | -1/2 (Δ[CrO3])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) Cl_2 | 3 | 3 | 1/3 (Δ[Cl2])/(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 = -1/12 (Δ[HCl])/(Δt) = -1/2 (Δ[CrO3])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/3 (Δ[Cl2])/(Δt) = 1/2 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | chromium trioxide | water | chlorine | chromic chloride formula | HCl | CrO_3 | H_2O | Cl_2 | CrCl_3 Hill formula | ClH | CrO_3 | H_2O | Cl_2 | Cl_3Cr name | hydrogen chloride | chromium trioxide | water | chlorine | chromic chloride IUPAC name | hydrogen chloride | trioxochromium | water | molecular chlorine | trichlorochromium