Cl2 + CH4 = HCl + C

Cl_2 chlorine + CH_4 methane ⟶ HCl hydrogen chloride + C activated charcoal

Balance the chemical equation algebraically: Cl_2 + CH_4 ⟶ HCl + C Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 CH_4 ⟶ c_3 HCl + c_4 C 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 C: | c_2 = c_4 H: | 4 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 = 2 c_2 = 1 c_3 = 4 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Cl_2 + CH_4 ⟶ 4 HCl + C

+ ⟶ +

chlorine + methane ⟶ hydrogen chloride + activated charcoal

Construct the equilibrium constant, K, expression for: Cl_2 + CH_4 ⟶ HCl + C 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 Cl_2 + CH_4 ⟶ 4 HCl + C 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 | 2 | -2 CH_4 | 1 | -1 HCl | 4 | 4 C | 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 | 2 | -2 | ([Cl2])^(-2) CH_4 | 1 | -1 | ([CH4])^(-1) HCl | 4 | 4 | ([HCl])^4 C | 1 | 1 | [C] 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])^(-2) ([CH4])^(-1) ([HCl])^4 [C] = (([HCl])^4 [C])/(([Cl2])^2 [CH4])

Construct the rate of reaction expression for: Cl_2 + CH_4 ⟶ HCl + C 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 Cl_2 + CH_4 ⟶ 4 HCl + C 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 | 2 | -2 CH_4 | 1 | -1 HCl | 4 | 4 C | 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 | 2 | -2 | -1/2 (Δ[Cl2])/(Δt) CH_4 | 1 | -1 | -(Δ[CH4])/(Δt) HCl | 4 | 4 | 1/4 (Δ[HCl])/(Δt) C | 1 | 1 | (Δ[C])/(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[Cl2])/(Δt) = -(Δ[CH4])/(Δt) = 1/4 (Δ[HCl])/(Δt) = (Δ[C])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chlorine | methane | hydrogen chloride | activated charcoal formula | Cl_2 | CH_4 | HCl | C Hill formula | Cl_2 | CH_4 | ClH | C name | chlorine | methane | hydrogen chloride | activated charcoal IUPAC name | molecular chlorine | methane | hydrogen chloride | carbon

| chlorine | methane | hydrogen chloride | activated charcoal molar mass | 70.9 g/mol | 16.04 g/mol | 36.46 g/mol | 12.011 g/mol phase | gas (at STP) | gas (at STP) | gas (at STP) | solid (at STP) melting point | -101 °C | -182.47 °C | -114.17 °C | 3550 °C boiling point | -34 °C | -161.48 °C | -85 °C | 4027 °C density | 0.003214 g/cm^3 (at 0 °C) | 6.67151×10^-4 g/cm^3 (at 20 °C) | 0.00149 g/cm^3 (at 25 °C) | 2.26 g/cm^3 solubility in water | | soluble | miscible | insoluble surface tension | | 0.0137 N/m | | dynamic viscosity | | 1.114×10^-5 Pa s (at 25 °C) | | odor | | odorless | |