Cl2 + CH4 = HCl + CHCl3

Cl_2 chlorine + CH_4 methane ⟶ HCl hydrogen chloride + CHCl_3 chloroform

Balance the chemical equation algebraically: Cl_2 + CH_4 ⟶ HCl + CHCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 CH_4 ⟶ c_3 HCl + c_4 CHCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, C and H: Cl: | 2 c_1 = c_3 + 3 c_4 C: | c_2 = c_4 H: | 4 c_2 = c_3 + 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 c_2 = 1 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Cl_2 + CH_4 ⟶ 3 HCl + CHCl_3

+ ⟶ +

chlorine + methane ⟶ hydrogen chloride + chloroform

| chlorine | methane | hydrogen chloride | chloroform molecular free energy | 0 kJ/mol | -51 kJ/mol | -95.3 kJ/mol | -73.7 kJ/mol total free energy | 0 kJ/mol | -51 kJ/mol | -285.9 kJ/mol | -73.7 kJ/mol | G_initial = -51 kJ/mol | | G_final = -359.6 kJ/mol | ΔG_rxn^0 | -359.6 kJ/mol - -51 kJ/mol = -308.6 kJ/mol (exergonic) | | |

Construct the equilibrium constant, K, expression for: Cl_2 + CH_4 ⟶ HCl + CHCl_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 Cl_2 + CH_4 ⟶ 3 HCl + CHCl_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 Cl_2 | 3 | -3 CH_4 | 1 | -1 HCl | 3 | 3 CHCl_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cl_2 | 3 | -3 | ([Cl2])^(-3) CH_4 | 1 | -1 | ([CH4])^(-1) HCl | 3 | 3 | ([HCl])^3 CHCl_3 | 1 | 1 | [CHCl3] 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 = ([Cl2])^(-3) ([CH4])^(-1) ([HCl])^3 [CHCl3] = (([HCl])^3 [CHCl3])/(([Cl2])^3 [CH4])

Construct the rate of reaction expression for: Cl_2 + CH_4 ⟶ HCl + CHCl_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 Cl_2 + CH_4 ⟶ 3 HCl + CHCl_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 Cl_2 | 3 | -3 CH_4 | 1 | -1 HCl | 3 | 3 CHCl_3 | 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 Cl_2 | 3 | -3 | -1/3 (Δ[Cl2])/(Δt) CH_4 | 1 | -1 | -(Δ[CH4])/(Δt) HCl | 3 | 3 | 1/3 (Δ[HCl])/(Δt) CHCl_3 | 1 | 1 | (Δ[CHCl3])/(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[Cl2])/(Δt) = -(Δ[CH4])/(Δt) = 1/3 (Δ[HCl])/(Δt) = (Δ[CHCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chlorine | methane | hydrogen chloride | chloroform formula | Cl_2 | CH_4 | HCl | CHCl_3 Hill formula | Cl_2 | CH_4 | ClH | CHCl_3 name | chlorine | methane | hydrogen chloride | chloroform IUPAC name | molecular chlorine | methane | hydrogen chloride | chloroform