Cl2 + CH4 = HCl + CCl4 + CH3Cl + CHCl3 + CH2Cl

Cl_2 (chlorine) + CH_4 (methane) ⟶ HCl (hydrogen chloride) + CCl_4 (carbon tetrachloride) + CH_3Cl (methyl chloride) + CHCl_3 (chloroform) + CH2Cl

Balance the chemical equation algebraically: Cl_2 + CH_4 ⟶ HCl + CCl_4 + CH_3Cl + CHCl_3 + CH2Cl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 CH_4 ⟶ c_3 HCl + c_4 CCl_4 + c_5 CH_3Cl + c_6 CHCl_3 + c_7 CH2Cl 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 + 4 c_4 + c_5 + 3 c_6 + c_7 C: | c_2 = c_4 + c_5 + c_6 + c_7 H: | 4 c_2 = c_3 + 3 c_5 + c_6 + 2 c_7 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_4 = 1 and solve the system of equations for the remaining coefficients: c_4 = 1 c_5 = 1/2 + c_1 + (3 c_2)/2 - (3 c_3)/2 c_6 = -3/2 + c_1 - c_2/2 - c_3/2 c_7 = 2 c_3 - 2 c_1 The resulting system of equations is still underdetermined, so additional coefficients must be set arbitrarily. Set c_1 = 11, c_2 = 5 and c_3 = 12 and solve for the remaining coefficients: c_1 = 11 c_2 = 5 c_3 = 12 c_4 = 1 c_5 = 1 c_6 = 1 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 11 Cl_2 + 5 CH_4 ⟶ 12 HCl + CCl_4 + CH_3Cl + CHCl_3 + 2 CH2Cl

+ ⟶ + + + + CH2Cl

chlorine + methane ⟶ hydrogen chloride + carbon tetrachloride + methyl chloride + chloroform + CH2Cl

Construct the equilibrium constant, K, expression for: Cl_2 + CH_4 ⟶ HCl + CCl_4 + CH_3Cl + CHCl_3 + CH2Cl 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: 11 Cl_2 + 5 CH_4 ⟶ 12 HCl + CCl_4 + CH_3Cl + CHCl_3 + 2 CH2Cl 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 | 11 | -11 CH_4 | 5 | -5 HCl | 12 | 12 CCl_4 | 1 | 1 CH_3Cl | 1 | 1 CHCl_3 | 1 | 1 CH2Cl | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cl_2 | 11 | -11 | ([Cl2])^(-11) CH_4 | 5 | -5 | ([CH4])^(-5) HCl | 12 | 12 | ([HCl])^12 CCl_4 | 1 | 1 | [CCl4] CH_3Cl | 1 | 1 | [CH3Cl] CHCl_3 | 1 | 1 | [CHCl3] CH2Cl | 2 | 2 | ([CH2Cl])^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 = ([Cl2])^(-11) ([CH4])^(-5) ([HCl])^12 [CCl4] [CH3Cl] [CHCl3] ([CH2Cl])^2 = (([HCl])^12 [CCl4] [CH3Cl] [CHCl3] ([CH2Cl])^2)/(([Cl2])^11 ([CH4])^5)

Construct the rate of reaction expression for: Cl_2 + CH_4 ⟶ HCl + CCl_4 + CH_3Cl + CHCl_3 + CH2Cl 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: 11 Cl_2 + 5 CH_4 ⟶ 12 HCl + CCl_4 + CH_3Cl + CHCl_3 + 2 CH2Cl 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 | 11 | -11 CH_4 | 5 | -5 HCl | 12 | 12 CCl_4 | 1 | 1 CH_3Cl | 1 | 1 CHCl_3 | 1 | 1 CH2Cl | 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 Cl_2 | 11 | -11 | -1/11 (Δ[Cl2])/(Δt) CH_4 | 5 | -5 | -1/5 (Δ[CH4])/(Δt) HCl | 12 | 12 | 1/12 (Δ[HCl])/(Δt) CCl_4 | 1 | 1 | (Δ[CCl4])/(Δt) CH_3Cl | 1 | 1 | (Δ[CH3Cl])/(Δt) CHCl_3 | 1 | 1 | (Δ[CHCl3])/(Δt) CH2Cl | 2 | 2 | 1/2 (Δ[CH2Cl])/(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 = -1/11 (Δ[Cl2])/(Δt) = -1/5 (Δ[CH4])/(Δt) = 1/12 (Δ[HCl])/(Δt) = (Δ[CCl4])/(Δt) = (Δ[CH3Cl])/(Δt) = (Δ[CHCl3])/(Δt) = 1/2 (Δ[CH2Cl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chlorine | methane | hydrogen chloride | carbon tetrachloride | methyl chloride | chloroform | CH2Cl formula | Cl_2 | CH_4 | HCl | CCl_4 | CH_3Cl | CHCl_3 | CH2Cl Hill formula | Cl_2 | CH_4 | ClH | CCl_4 | CH_3Cl | CHCl_3 | CH2Cl name | chlorine | methane | hydrogen chloride | carbon tetrachloride | methyl chloride | chloroform | IUPAC name | molecular chlorine | methane | hydrogen chloride | carbon tetrachloride | chloromethane | chloroform |