O2 + C2H2 = H2O + CO2 + C + CO

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

Balance the chemical equation algebraically: O_2 + C_2H_2 ⟶ H_2O + CO_2 + C + 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 C + c_6 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_6 C: | 2 c_2 = c_4 + c_5 + c_6 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_4 = 1 and solve the system of equations for the remaining coefficients: c_3 = c_2 c_4 = 1 c_5 = 1 - 2 c_1 + 3 c_2 c_6 = -2 + 2 c_1 - c_2 Multiply by the least common denominator, 4, to eliminate fractional coefficients: c_3 = c_2 c_4 = 4 c_5 = 4 - 2 c_1 + 3 c_2 c_6 = -8 + 2 c_1 - c_2 The resulting system of equations is still underdetermined, so additional coefficients must be set arbitrarily. Set c_1 = 9 and c_2 = 6 and solve for the remaining coefficients: c_1 = 9 c_2 = 6 c_3 = 6 c_4 = 4 c_5 = 4 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 9 O_2 + 6 C_2H_2 ⟶ 6 H_2O + 4 CO_2 + 4 C + 4 CO

+ ⟶ + + +

oxygen + acetylene ⟶ water + carbon dioxide + activated charcoal + carbon monoxide

Construct the equilibrium constant, K, expression for: O_2 + C_2H_2 ⟶ H_2O + CO_2 + C + 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: 9 O_2 + 6 C_2H_2 ⟶ 6 H_2O + 4 CO_2 + 4 C + 4 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 | 9 | -9 C_2H_2 | 6 | -6 H_2O | 6 | 6 CO_2 | 4 | 4 C | 4 | 4 CO | 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 | 9 | -9 | ([O2])^(-9) C_2H_2 | 6 | -6 | ([C2H2])^(-6) H_2O | 6 | 6 | ([H2O])^6 CO_2 | 4 | 4 | ([CO2])^4 C | 4 | 4 | ([C])^4 CO | 4 | 4 | ([CO])^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])^(-9) ([C2H2])^(-6) ([H2O])^6 ([CO2])^4 ([C])^4 ([CO])^4 = (([H2O])^6 ([CO2])^4 ([C])^4 ([CO])^4)/(([O2])^9 ([C2H2])^6)

Construct the rate of reaction expression for: O_2 + C_2H_2 ⟶ H_2O + CO_2 + C + 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: 9 O_2 + 6 C_2H_2 ⟶ 6 H_2O + 4 CO_2 + 4 C + 4 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 | 9 | -9 C_2H_2 | 6 | -6 H_2O | 6 | 6 CO_2 | 4 | 4 C | 4 | 4 CO | 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 | 9 | -9 | -1/9 (Δ[O2])/(Δt) C_2H_2 | 6 | -6 | -1/6 (Δ[C2H2])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) CO_2 | 4 | 4 | 1/4 (Δ[CO2])/(Δt) C | 4 | 4 | 1/4 (Δ[C])/(Δt) CO | 4 | 4 | 1/4 (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 = -1/9 (Δ[O2])/(Δt) = -1/6 (Δ[C2H2])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/4 (Δ[CO2])/(Δt) = 1/4 (Δ[C])/(Δt) = 1/4 (Δ[CO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

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