For the adsorption of nitrogen molecules on a certain sample...

For the adsorption of nitrogen molecules on a certain sample of carbon, the pressure required to half-saturate the surface at $298 \mathrm{K}$ is $2 \times 10^{-5}$ Pa. If the enthalpy of adsorption is $-10 \mathrm{kJ} \mathrm{mol}^{-1}$ and the sticking coefficient $s^{*}$ is unity, what is the rate constant of desorption $k_{\mathrm{d}} ?$

Key Concepts

Enthalpy of Adsorption

This thermodynamic parameter represents the heat released during the adsorption process. A negative enthalpy value indicates that the process is exothermic. It is closely related to the activation energy for desorption and thus plays a crucial role in determining the desorption rate constant within kinetic models.

Desorption Rate Constant

This constant quantifies the rate at which adsorbed species leave the surface. It is central to desorption kinetics and is typically modeled with an Arrhenius expression, implying that the rate of desorption is influenced by both temperature and the activation energy associated with the process.

Sticking Coefficient

The sticking coefficient is the probability that a molecule, upon colliding with a surface, will adhere to it. A value of unity indicates that every molecule hitting the surface sticks, which simplifies the modeling of adsorption kinetics and directly affects the rate of adsorption.

Adsorption-Desorption Equilibrium

This concept describes the dynamic balance between the processes of adsorption (molecules attaching to a surface) and desorption (molecules detaching from a surface). At equilibrium, the rate at which molecules adsorb equals the rate at which they desorb. Understanding this balance is fundamental in surface science and reaction kinetics.

Equilibrium Pressure (Half-Saturation Pressure)

This is the pressure at which a specific fractional coverage of the adsorption sites is achieved, such as half-saturation. It provides important information about the affinity between the adsorbate and the surface and is used to infer kinetic and thermodynamic properties of the adsorption process.

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