O2 + C2H3Cl = H2O + HCl + CO2

O_2 oxygen + H_2C=CHCl vinyl chloride ⟶ H_2O water + HCl hydrogen chloride + CO_2 carbon dioxide

Balance the chemical equation algebraically: O_2 + H_2C=CHCl ⟶ H_2O + HCl + CO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 H_2C=CHCl ⟶ c_3 H_2O + c_4 HCl + c_5 CO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for O, C, Cl and H: O: | 2 c_1 = c_3 + 2 c_5 C: | 2 c_2 = c_5 Cl: | c_2 = c_4 H: | 3 c_2 = 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 = 5/2 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 5 c_2 = 2 c_3 = 2 c_4 = 2 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 O_2 + 2 H_2C=CHCl ⟶ 2 H_2O + 2 HCl + 4 CO_2

+ ⟶ + +

oxygen + vinyl chloride ⟶ water + hydrogen chloride + carbon dioxide

| oxygen | vinyl chloride | water | hydrogen chloride | carbon dioxide molecular free energy | 231.7 kJ/mol | 53.6 kJ/mol | -237.1 kJ/mol | -95.3 kJ/mol | -394.4 kJ/mol total free energy | 1159 kJ/mol | 107.2 kJ/mol | -474.2 kJ/mol | -190.6 kJ/mol | -1578 kJ/mol | G_initial = 1266 kJ/mol | | G_final = -2242 kJ/mol | | ΔG_rxn^0 | -2242 kJ/mol - 1266 kJ/mol = -3508 kJ/mol (exergonic) | | | |

Construct the equilibrium constant, K, expression for: O_2 + H_2C=CHCl ⟶ H_2O + HCl + CO_2 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: 5 O_2 + 2 H_2C=CHCl ⟶ 2 H_2O + 2 HCl + 4 CO_2 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 O_2 | 5 | -5 H_2C=CHCl | 2 | -2 H_2O | 2 | 2 HCl | 2 | 2 CO_2 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 5 | -5 | ([O2])^(-5) H_2C=CHCl | 2 | -2 | ([H2C=CHCl])^(-2) H_2O | 2 | 2 | ([H2O])^2 HCl | 2 | 2 | ([HCl])^2 CO_2 | 4 | 4 | ([CO2])^4 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 = ([O2])^(-5) ([H2C=CHCl])^(-2) ([H2O])^2 ([HCl])^2 ([CO2])^4 = (([H2O])^2 ([HCl])^2 ([CO2])^4)/(([O2])^5 ([H2C=CHCl])^2)

Construct the rate of reaction expression for: O_2 + H_2C=CHCl ⟶ H_2O + HCl + CO_2 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: 5 O_2 + 2 H_2C=CHCl ⟶ 2 H_2O + 2 HCl + 4 CO_2 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 O_2 | 5 | -5 H_2C=CHCl | 2 | -2 H_2O | 2 | 2 HCl | 2 | 2 CO_2 | 4 | 4 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 O_2 | 5 | -5 | -1/5 (Δ[O2])/(Δt) H_2C=CHCl | 2 | -2 | -1/2 (Δ[H2C=CHCl])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) HCl | 2 | 2 | 1/2 (Δ[HCl])/(Δt) CO_2 | 4 | 4 | 1/4 (Δ[CO2])/(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 = -1/5 (Δ[O2])/(Δt) = -1/2 (Δ[H2C=CHCl])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[HCl])/(Δt) = 1/4 (Δ[CO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | vinyl chloride | water | hydrogen chloride | carbon dioxide formula | O_2 | H_2C=CHCl | H_2O | HCl | CO_2 Hill formula | O_2 | C_2H_3Cl | H_2O | ClH | CO_2 name | oxygen | vinyl chloride | water | hydrogen chloride | carbon dioxide IUPAC name | molecular oxygen | chloroethylene | water | hydrogen chloride | carbon dioxide