O2 + C2H2 = H2O + CO2 + CO

O_2 oxygen + C_2H_2 acetylene ⟶ H_2O water + CO_2 carbon dioxide + CO carbon monoxide

Balance the chemical equation algebraically: O_2 + C_2H_2 ⟶ H_2O + CO_2 + CO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 C_2H_2 ⟶ c_3 H_2O + c_4 CO_2 + c_5 CO Set the number of atoms in the reactants equal to the number of atoms in the products for O, C and H: O: | 2 c_1 = c_3 + 2 c_4 + c_5 C: | 2 c_2 = c_4 + c_5 H: | 2 c_2 = 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_2 = 1 c_3 = 1 c_4 = 2 c_1 - 3 c_5 = 5 - 2 c_1 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 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 O_2 + C_2H_2 ⟶ H_2O + CO_2 + CO

+ ⟶ + +

oxygen + acetylene ⟶ water + carbon dioxide + carbon monoxide

| oxygen | acetylene | water | carbon dioxide | carbon monoxide molecular enthalpy | 0 kJ/mol | 227.4 kJ/mol | -285.8 kJ/mol | -393.5 kJ/mol | -110.5 kJ/mol total enthalpy | 0 kJ/mol | 227.4 kJ/mol | -285.8 kJ/mol | -393.5 kJ/mol | -110.5 kJ/mol | H_initial = 227.4 kJ/mol | | H_final = -789.8 kJ/mol | | ΔH_rxn^0 | -789.8 kJ/mol - 227.4 kJ/mol = -1017 kJ/mol (exothermic) | | | |

| oxygen | acetylene | water | carbon dioxide | carbon monoxide molecular free energy | 231.7 kJ/mol | 209.9 kJ/mol | -237.1 kJ/mol | -394.4 kJ/mol | -137 kJ/mol total free energy | 463.4 kJ/mol | 209.9 kJ/mol | -237.1 kJ/mol | -394.4 kJ/mol | -137 kJ/mol | G_initial = 673.3 kJ/mol | | G_final = -768.5 kJ/mol | | ΔG_rxn^0 | -768.5 kJ/mol - 673.3 kJ/mol = -1442 kJ/mol (exergonic) | | | |

| oxygen | acetylene | water | carbon dioxide | carbon monoxide molecular entropy | 205 J/(mol K) | 201 J/(mol K) | 69.91 J/(mol K) | 214 J/(mol K) | 198 J/(mol K) total entropy | 410 J/(mol K) | 201 J/(mol K) | 69.91 J/(mol K) | 214 J/(mol K) | 198 J/(mol K) | S_initial = 611 J/(mol K) | | S_final = 481.9 J/(mol K) | | ΔS_rxn^0 | 481.9 J/(mol K) - 611 J/(mol K) = -129.1 J/(mol K) (exoentropic) | | | |

Construct the equilibrium constant, K, expression for: O_2 + C_2H_2 ⟶ H_2O + CO_2 + CO 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 O_2 + C_2H_2 ⟶ H_2O + CO_2 + CO 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 | 2 | -2 C_2H_2 | 1 | -1 H_2O | 1 | 1 CO_2 | 1 | 1 CO | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 2 | -2 | ([O2])^(-2) C_2H_2 | 1 | -1 | ([C2H2])^(-1) H_2O | 1 | 1 | [H2O] CO_2 | 1 | 1 | [CO2] CO | 1 | 1 | [CO] 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])^(-2) ([C2H2])^(-1) [H2O] [CO2] [CO] = ([H2O] [CO2] [CO])/(([O2])^2 [C2H2])

Construct the rate of reaction expression for: O_2 + C_2H_2 ⟶ H_2O + CO_2 + CO 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 O_2 + C_2H_2 ⟶ H_2O + CO_2 + CO 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 | 2 | -2 C_2H_2 | 1 | -1 H_2O | 1 | 1 CO_2 | 1 | 1 CO | 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 O_2 | 2 | -2 | -1/2 (Δ[O2])/(Δt) C_2H_2 | 1 | -1 | -(Δ[C2H2])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) CO | 1 | 1 | (Δ[CO])/(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[O2])/(Δt) = -(Δ[C2H2])/(Δt) = (Δ[H2O])/(Δt) = (Δ[CO2])/(Δt) = (Δ[CO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | acetylene | water | carbon dioxide | carbon monoxide formula | O_2 | C_2H_2 | H_2O | CO_2 | CO name | oxygen | acetylene | water | carbon dioxide | carbon monoxide IUPAC name | molecular oxygen | acetylene | water | carbon dioxide | carbon monoxide