O2 + C2H2 = CO + HO

O_2 oxygen + C_2H_2 acetylene ⟶ CO carbon monoxide + (HO)^• hydroxyl radical

Balance the chemical equation algebraically: O_2 + C_2H_2 ⟶ CO + (HO)^• Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 C_2H_2 ⟶ c_3 CO + c_4 HO^• 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 + c_4 C: | 2 c_2 = c_3 H: | 2 c_2 = 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 = 2 c_2 = 1 c_3 = 2 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 O_2 + C_2H_2 ⟶ 2 CO + 2 HO^•

+ ⟶ + (HO)^•

oxygen + acetylene ⟶ carbon monoxide + hydroxyl radical

Construct the equilibrium constant, K, expression for: O_2 + C_2H_2 ⟶ CO + (HO)^• 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 ⟶ 2 CO + 2 HO^• 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 CO | 2 | 2 HO^• | 2 | 2 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) CO | 2 | 2 | ([CO])^2 HO^• | 2 | 2 | ([HO•])^2 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) ([CO])^2 ([HO•])^2 = (([CO])^2 ([HO•])^2)/(([O2])^2 [C2H2])

Construct the rate of reaction expression for: O_2 + C_2H_2 ⟶ CO + (HO)^• 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 ⟶ 2 CO + 2 HO^• 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 CO | 2 | 2 HO^• | 2 | 2 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) CO | 2 | 2 | 1/2 (Δ[CO])/(Δt) HO^• | 2 | 2 | 1/2 (Δ[HO•])/(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) = 1/2 (Δ[CO])/(Δt) = 1/2 (Δ[HO•])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | acetylene | carbon monoxide | hydroxyl radical formula | O_2 | C_2H_2 | CO | (HO)^• name | oxygen | acetylene | carbon monoxide | hydroxyl radical IUPAC name | molecular oxygen | acetylene | carbon monoxide |

| oxygen | acetylene | carbon monoxide | hydroxyl radical molar mass | 31.998 g/mol | 26.038 g/mol | 28.01 g/mol | 17.0073 g/mol phase | gas (at STP) | gas (at STP) | gas (at STP) | melting point | -218 °C | -81 °C | -205 °C | boiling point | -183 °C | -75 °C | -191.5 °C | density | 0.001429 g/cm^3 (at 0 °C) | 0.618 g/cm^3 (at -55 °C) | 0.001145 g/cm^3 (at 25 °C) | surface tension | 0.01347 N/m | 0.01431 N/m | | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | | 1.772×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless |