# Chemical potential on a solid and its vapor pressure

• I
• Physics_Student_2018
In summary, the conversation discusses the formula μv - μ∞ = -kTlnP∞ and how it relates to the equilibrium vapor pressure of a flat solid surface. It is agreed that at equilibrium, μv should equal μ∞. The formula is derived using μv0, the chemical potential of vapor in the standard state, and at the sublimation point, μv equals μ∞ and P∞ equals 1. The physics behind this concept is still being discussed.
Physics_Student_2018
I have been reading the book "Nanostructures and Nanomaterials" by G. Cao and Y. Yang, and was intrigued by the following passage in page 33:
"Assuming the vapor of solid phase obeys the ideal gas law, for the flat surface one can easily arrive at:
μvμ = −kTlnP, where μv is the chemical potential of a vapor atom, μ, the chemical potential of an atom on the flat surface, k, the Boltzmann constant, P, the equilibrium vapor pressure of flat solid surface, and T, temperature."

My first impression is that the two chemical potentials should be equal for the solid and its vapor pressure at equilibrium. Could somebody please explain to me how this formula is derived?

Thank you.

My impression is that by μv they mean μv0, the chemical potential of vapour in the standard state (P=1). Then if the vapour at P is in equilibrium with the solid:
μv = μv0 + kTlnP = μ
and hence μv0 - μ = -kTlnP
If μv = μ then P = 1 and the solid sublimes.

mjc123 said:
My impression is that by μv they mean μv0, the chemical potential of vapour in the standard state (P=1). Then if the vapour at P is in equilibrium with the solid:
μv = μv0 + kTlnP = μ
and hence μv0 - μ = -kTlnP
If μv = μ then P = 1 and the solid sublimes.

Thanks for your reply. I see that you agree with me that we should have μv = μ at equilibrium. In the last line, did you mean "μv0 = μ then..."? I am still not understanding the physics behind it.

Yes, I must have done. μv = μ always at equilibrium; at the sublimation point μv = μ = μv0.

## 1. What is chemical potential on a solid?

The chemical potential on a solid is a measure of the energy required to add one mole of a substance to a solid at constant temperature and pressure. It is a thermodynamic property that is influenced by factors such as temperature, pressure, and composition.

## 2. How does chemical potential affect the vapor pressure of a solid?

The chemical potential of a solid is directly related to its vapor pressure. As the chemical potential increases, the vapor pressure of the solid also increases. This means that a higher chemical potential leads to a greater tendency for molecules to escape from the solid and enter the gas phase.

## 3. Can the chemical potential on a solid change?

Yes, the chemical potential on a solid can change depending on external factors such as temperature and pressure. For example, increasing the temperature of a solid will also increase its chemical potential, causing an increase in its vapor pressure.

## 4. How is the chemical potential on a solid measured?

The chemical potential on a solid can be measured using various techniques, such as equilibrium vapor pressure measurements, isothermal adsorption measurements, or calorimetry. These methods allow for the determination of the chemical potential at different temperatures and pressures.

## 5. Can the chemical potential on a solid be used to predict its reactivity?

Yes, the chemical potential on a solid can provide important information about its reactivity. A higher chemical potential indicates a greater driving force for reactions to occur, while a lower chemical potential suggests a more stable and less reactive solid.

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