HF + F2 + CCl4 = HCl + Cl2 + CF4

HF hydrogen fluoride + F_2 fluorine + CCl_4 carbon tetrachloride ⟶ HCl hydrogen chloride + Cl_2 chlorine + CF_4 tetrafluoromethane

Balance the chemical equation algebraically: HF + F_2 + CCl_4 ⟶ HCl + Cl_2 + CF_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HF + c_2 F_2 + c_3 CCl_4 ⟶ c_4 HCl + c_5 Cl_2 + c_6 CF_4 Set the number of atoms in the reactants equal to the number of atoms in the products for F, H, C and Cl: F: | c_1 + 2 c_2 = 4 c_6 H: | c_1 = c_4 C: | c_3 = c_6 Cl: | 4 c_3 = c_4 + 2 c_5 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_2 = 1 c_3 = c_1/4 + 1/2 c_4 = c_1 c_5 = 1 c_6 = c_1/4 + 1/2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 2 and solve for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HF + F_2 + CCl_4 ⟶ 2 HCl + Cl_2 + CF_4

+ + ⟶ + +

hydrogen fluoride + fluorine + carbon tetrachloride ⟶ hydrogen chloride + chlorine + tetrafluoromethane

Construct the equilibrium constant, K, expression for: HF + F_2 + CCl_4 ⟶ HCl + Cl_2 + CF_4 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 HF + F_2 + CCl_4 ⟶ 2 HCl + Cl_2 + CF_4 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 HF | 2 | -2 F_2 | 1 | -1 CCl_4 | 1 | -1 HCl | 2 | 2 Cl_2 | 1 | 1 CF_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HF | 2 | -2 | ([HF])^(-2) F_2 | 1 | -1 | ([F2])^(-1) CCl_4 | 1 | -1 | ([CCl4])^(-1) HCl | 2 | 2 | ([HCl])^2 Cl_2 | 1 | 1 | [Cl2] CF_4 | 1 | 1 | [CF4] 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 = ([HF])^(-2) ([F2])^(-1) ([CCl4])^(-1) ([HCl])^2 [Cl2] [CF4] = (([HCl])^2 [Cl2] [CF4])/(([HF])^2 [F2] [CCl4])

Construct the rate of reaction expression for: HF + F_2 + CCl_4 ⟶ HCl + Cl_2 + CF_4 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 HF + F_2 + CCl_4 ⟶ 2 HCl + Cl_2 + CF_4 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 HF | 2 | -2 F_2 | 1 | -1 CCl_4 | 1 | -1 HCl | 2 | 2 Cl_2 | 1 | 1 CF_4 | 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 HF | 2 | -2 | -1/2 (Δ[HF])/(Δt) F_2 | 1 | -1 | -(Δ[F2])/(Δt) CCl_4 | 1 | -1 | -(Δ[CCl4])/(Δt) HCl | 2 | 2 | 1/2 (Δ[HCl])/(Δt) Cl_2 | 1 | 1 | (Δ[Cl2])/(Δt) CF_4 | 1 | 1 | (Δ[CF4])/(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[HF])/(Δt) = -(Δ[F2])/(Δt) = -(Δ[CCl4])/(Δt) = 1/2 (Δ[HCl])/(Δt) = (Δ[Cl2])/(Δt) = (Δ[CF4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen fluoride | fluorine | carbon tetrachloride | hydrogen chloride | chlorine | tetrafluoromethane formula | HF | F_2 | CCl_4 | HCl | Cl_2 | CF_4 Hill formula | FH | F_2 | CCl_4 | ClH | Cl_2 | CF_4 name | hydrogen fluoride | fluorine | carbon tetrachloride | hydrogen chloride | chlorine | tetrafluoromethane IUPAC name | hydrogen fluoride | molecular fluorine | carbon tetrachloride | hydrogen chloride | molecular chlorine | tetrafluoromethane