Question

Be sure to answer all parts. The catalytic destruction of ozone occurs via a two-step mechanism, where X can be any of several species: (1) X + O3 → XO + O2 [slow] (2) XO + O → X + O2 [fast] (a) Write the overall reaction. O3 + O → 2 O2 O3 + XO → X + 2 O2 XO + X + O3 + O → XO + X + 2 O2 X + O3 → XO + O2 (b) Write the rate law for each step (using k for the rate constant). Reaction 1: Reaction 2: k[X][O2] k[XO][O2] k[X][O3] k[XO][O3] k[XO][O2] k[X][O] k[X][O2] k[XO][O] (c) X acts as a and XO acts as a catalyst intermediate intermediate catalyst (d) High-flying aircraft release NO into the stratosphere, which catalyzes this process. When O3 and NO concentrations are 3 Ă— 1012 molecule/cm3 and 9.9 Ă— 109 molecule/cm3, respectively, what is the rate of O3 depletion? The rate constant k for the rate-determining step is 6 Ă— 10â’15 (cm3)2/molecule·s. Give your answer in scientific notation. Use one significant figure in your answer. Ă— 10 molecule/s

Answer 1

a) O₃ + O → 2 O₂.

b) For reaction 1: Rate = k₁ [X][O₃] & For reaction 2: Rate = k₂ [XO][O].

c) X acts as a catalyst and XO acts as an intermediate.

d) rate of depletion of O₃ = 2 x 10⁸ molecule/cm³.s.

Step-by-step explanation:

a) To obtain the overall reaction, we add the two mentioned steps and cancel the particles appear the same at both sides.

• The overall reaction is: O₃ + O → 2 O₂.

b) The rate law of both steps:

• For reaction 1: Rate = k₁ [X][O₃].

• For reaction 2: Rate = k₂ [XO][O].

c) X acts as a catalyst and XO acts as an intermediate.

• X begins the reaction as a reactant in the first step and finally appears as a product in the second step and does not appear in the overall reaction, so it is considered as a catalyst.

• XO is produced in the first step and consumed within the second step and does not appear in the overall reaction, so it os considered as an intermediate.

d) The rate determining step is the slowest step (step 1) and in this step the depletion of O₃ occurs.

• The rate law for this step is (rate of O₃ depletion):

• Rate of depletion of O₃ = k[NO][O₃] = (6 x 10⁻¹⁵ cm³/molecule.s) (3 x 10¹² molecule/cm³) (9.9 x 10⁹ molecule/cm³) = 1.782 x 10⁸ molecule/cm³.s = 2 x 10⁸ molecule/cm³.s. "one significant figure"