O2 + C2H8 = H2O + CO2

O_2 oxygen + C_2H_8 terminal dimethyl ⟶ H_2O water + CO_2 carbon dioxide

Balance the chemical equation algebraically: O_2 + C_2H_8 ⟶ H_2O + CO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 C_2H_8 ⟶ c_3 H_2O + c_4 CO_2 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: | 2 c_2 = c_4 H: | 8 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_1 = 4 c_2 = 1 c_3 = 4 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 O_2 + C_2H_8 ⟶ 4 H_2O + 2 CO_2

+ ⟶ +

oxygen + terminal dimethyl ⟶ water + carbon dioxide

Construct the equilibrium constant, K, expression for: O_2 + C_2H_8 ⟶ H_2O + 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: 4 O_2 + C_2H_8 ⟶ 4 H_2O + 2 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 | 4 | -4 C_2H_8 | 1 | -1 H_2O | 4 | 4 CO_2 | 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 | 4 | -4 | ([O2])^(-4) C_2H_8 | 1 | -1 | ([C2H8])^(-1) H_2O | 4 | 4 | ([H2O])^4 CO_2 | 2 | 2 | ([CO2])^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])^(-4) ([C2H8])^(-1) ([H2O])^4 ([CO2])^2 = (([H2O])^4 ([CO2])^2)/(([O2])^4 [C2H8])

Construct the rate of reaction expression for: O_2 + C_2H_8 ⟶ H_2O + 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: 4 O_2 + C_2H_8 ⟶ 4 H_2O + 2 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 | 4 | -4 C_2H_8 | 1 | -1 H_2O | 4 | 4 CO_2 | 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 | 4 | -4 | -1/4 (Δ[O2])/(Δt) C_2H_8 | 1 | -1 | -(Δ[C2H8])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) CO_2 | 2 | 2 | 1/2 (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 = -1/4 (Δ[O2])/(Δt) = -(Δ[C2H8])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[CO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | terminal dimethyl | water | carbon dioxide formula | O_2 | C_2H_8 | H_2O | CO_2 name | oxygen | terminal dimethyl | water | carbon dioxide IUPAC name | molecular oxygen | methane | water | carbon dioxide