Thermal Physics Help: Argon Adsorption Equilibrium

In summary, we need to find an expression for the number of adsorbed atoms per unit area in an ideal gas of argon atoms in equilibrium with argon atoms adsorbed on a plane surface. This can be done by setting the chemical potentials of the gas and adsorbed atoms equal and using the ideal gas law to simplify the expression. The final expression takes into account the quantum concentration of the gas, pressure, temperature, number of sites for adsorption, and energy per absorbed atom.
  • #1
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Thermal Physics Help??

Please - any help is appreciated. I kind of have an idea of where to start but would like any input. Thanks in advance.

Consider an ideal gas of argon atoms in equilibrium with argon atoms adsorbed on a plane surface. (Ps) is the # of sites per unit surface area at which the atoms can be adsorbed, and when they are, their energy is -E per absorbed atom. Find an expression for the # of adsorbed atoms per unit area, (Pad), in terms of the quantum concentration of the argon gas (nQ), the pressure of the gas (P), the termperature (t), (Ps) and E.

Hint: (1) Chemical potentials are equal in equalibrium
(2) The atoms do not interact on adjacent adsorbed sites, so you may study a single site and generalize to the many site problem.
 
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  • #2


Hello! I can definitely help you with this problem. Let's break it down step by step:

1. First, let's define our variables:
nQ = quantum concentration of argon gas
P = pressure of gas
t = temperature
Ps = number of sites per unit surface area for adsorption
E = energy per absorbed atom

2. We know that in equilibrium, the chemical potential of the gas (μg) is equal to the chemical potential of the adsorbed atoms (μa). This can be written as:
μg = μa

3. The chemical potential of the gas can be expressed as:
μg = kT ln(nQ/V)
where k is the Boltzmann constant and V is the volume of the gas.

4. The chemical potential of the adsorbed atoms can be expressed as:
μa = -E + kT ln(Pad/Ps)
where Pad is the number of adsorbed atoms per unit area.

5. Setting μg = μa and rearranging the equations, we get:
Pad = Ps * exp(-E/kT) * (nQ/V)

6. We can simplify this expression by using the ideal gas law: PV = nRT
where n is the number of moles of gas and R is the gas constant. We can rewrite this as:
V = nRT/P

7. Substituting this into our previous equation, we get the final expression for Pad:
Pad = Ps * exp(-E/kT) * (nQ/PRT)

8. This expression gives us the number of adsorbed atoms per unit area, taking into account the quantum concentration of the gas, pressure, temperature, number of sites for adsorption, and energy per absorbed atom.

I hope this helps! Let me know if you have any other questions or need further clarification. Good luck with your problem!
 

1. What is thermal physics?

Thermal physics is the branch of physics that deals with the study of heat and temperature and their relationship to energy and work. It also involves the analysis of the behavior of materials at the microscopic level and the transfer of thermal energy between systems.

2. What is Argon Adsorption Equilibrium?

Argon Adsorption Equilibrium is a phenomenon that occurs when argon gas molecules are absorbed onto the surface of a solid material. This equilibrium state is achieved when the rate of adsorption (gas molecules sticking to the surface) is equal to the rate of desorption (gas molecules leaving the surface).

3. Why is Argon used in thermal physics experiments?

Argon is a commonly used gas in thermal physics experiments because it is inert, meaning it does not react with other substances. This allows for more accurate measurements and observations of thermal properties without interference from chemical reactions.

4. How does Argon Adsorption Equilibrium impact thermal properties?

Argon Adsorption Equilibrium can significantly impact the thermal properties of a material by affecting its heat capacity, thermal conductivity, and thermal expansion. The adsorption of argon molecules can also alter the surface energy and surface tension of a material.

5. What factors affect Argon Adsorption Equilibrium?

The factors that affect Argon Adsorption Equilibrium include temperature, pressure, and surface characteristics of the material. The type of material and the amount of available surface area also play a role in determining the extent of argon adsorption and desorption.

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