O2 + C5H12 = H2O + CO

O_2 oxygen + CH_3(CH_2)_3CH_3 N-pentane ⟶ H_2O water + CO carbon monoxide

Balance the chemical equation algebraically: O_2 + CH_3(CH_2)_3CH_3 ⟶ H_2O + CO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 CH_3(CH_2)_3CH_3 ⟶ c_3 H_2O + c_4 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 + c_4 C: | 5 c_2 = c_4 H: | 12 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 = 11/2 c_2 = 1 c_3 = 6 c_4 = 5 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 11 c_2 = 2 c_3 = 12 c_4 = 10 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 11 O_2 + 2 CH_3(CH_2)_3CH_3 ⟶ 12 H_2O + 10 CO

+ ⟶ +

oxygen + N-pentane ⟶ water + carbon monoxide

Construct the equilibrium constant, K, expression for: O_2 + CH_3(CH_2)_3CH_3 ⟶ H_2O + 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: 11 O_2 + 2 CH_3(CH_2)_3CH_3 ⟶ 12 H_2O + 10 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 | 11 | -11 CH_3(CH_2)_3CH_3 | 2 | -2 H_2O | 12 | 12 CO | 10 | 10 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 11 | -11 | ([O2])^(-11) CH_3(CH_2)_3CH_3 | 2 | -2 | ([CH3(CH2)3CH3])^(-2) H_2O | 12 | 12 | ([H2O])^12 CO | 10 | 10 | ([CO])^10 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])^(-11) ([CH3(CH2)3CH3])^(-2) ([H2O])^12 ([CO])^10 = (([H2O])^12 ([CO])^10)/(([O2])^11 ([CH3(CH2)3CH3])^2)

Construct the rate of reaction expression for: O_2 + CH_3(CH_2)_3CH_3 ⟶ H_2O + 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: 11 O_2 + 2 CH_3(CH_2)_3CH_3 ⟶ 12 H_2O + 10 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 | 11 | -11 CH_3(CH_2)_3CH_3 | 2 | -2 H_2O | 12 | 12 CO | 10 | 10 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 | 11 | -11 | -1/11 (Δ[O2])/(Δt) CH_3(CH_2)_3CH_3 | 2 | -2 | -1/2 (Δ[CH3(CH2)3CH3])/(Δt) H_2O | 12 | 12 | 1/12 (Δ[H2O])/(Δt) CO | 10 | 10 | 1/10 (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 = -1/11 (Δ[O2])/(Δt) = -1/2 (Δ[CH3(CH2)3CH3])/(Δt) = 1/12 (Δ[H2O])/(Δt) = 1/10 (Δ[CO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | N-pentane | water | carbon monoxide formula | O_2 | CH_3(CH_2)_3CH_3 | H_2O | CO Hill formula | O_2 | C_5H_12 | H_2O | CO name | oxygen | N-pentane | water | carbon monoxide IUPAC name | molecular oxygen | pentane | water | carbon monoxide