Chemistry - Surface Chemistry Question with Solution | TestHub
If two atoms collide in interstellar space, the energy of the resulting molecule is so great that it rapidly dissociates. Hydrogen atoms only react to give stable H₂ molecules on the surface of dust particles. The dust particles absorb most of the excess energy, and the newly formed H₂ rapidly desorbs. This question examines two kinetic models for H₂ formation on the surface of a dust particle.
In both models, the rate constant for adsorption of H atoms onto the surface of dust particles is . The typical number density of H atoms (number of H atoms per unit volume) in interstellar space is .
Note: In the following, you may treat numbers of surface-adsorbed atoms and number densities of gas-phase atoms in the same way as you would normally use concentrations in the rate equations. As a result, the units of the rate constants may be unfamiliar to you. Reaction rates have units of numbers of atoms or molecules per unit time.
You may assume that this rate is constant throughout.
Desorption of H atoms is first order with respect to the number of adsorbed atoms. The rate constant for the desorption step is .
The H atoms are mobile on the surface. When they meet, they react to form H₂, which then desorbs. The kinetic models under consideration differ in the way the reaction is modeled but share the same rate constants , , and for adsorption, desorption, and bimolecular reaction, respectively, as given below.
Reaction to form H₂ is assumed to be second order. On a dust particle, the rate of removal of H atoms by reaction is .
[where = steady-state number of H-atoms on the surface of a dust particle]
If the rate of production of H₂ per dust particle in this model is , then what is the value of ?
Answer:
Solution:
∴ rate of production of rate of removal of H -atoms
∴ rate of production of