# 化学势

HA ⇌ H+ + A

## 热力学的定义

${\displaystyle dU=TdS-PdV+\sum _{i=1}^{n}\mu _{i}dN_{i}}$

${\displaystyle \mu _{i}=\left({\frac {\partial U}{\partial N_{i}}}\right)_{S,V,N_{j\neq i}}}$

${\displaystyle dG=-SdT+VdP+\sum _{i=1}^{n}\mu _{i}dN_{i}}$

${\displaystyle \mu _{i}=\left({\frac {\partial G}{\partial N_{i}}}\right)_{T,P,N_{j\neq i}}}$

${\displaystyle dG=\sum _{i=1}^{n}\mu _{i}dN_{i}}$

${\displaystyle dG=\mu _{1}dN_{1}+\mu _{2}dN_{2}+...=0}$

${\displaystyle \mu _{i}=\left({\frac {\partial H}{\partial N_{i}}}\right)_{S,P,N_{j\neq i}}\qquad \mu _{i}=\left({\frac {\partial F}{\partial N_{i}}}\right)_{T,V,N_{j\neq i}}}$

## 应用

Gibbs–Duhem方程描述了一个热力学系统中的组分的化学势变化之间的关系。例如一种由两种物质组成的混合物，在确定的温度和压强下，这两种物质的化学势满足如下关系：

${\displaystyle d\mu _{\mathrm {B} }=-{\frac {n_{\mathrm {A} }}{n_{\mathrm {B} }}}d\mu _{\mathrm {A} }}$

## 历史

"If to any homogeneous mass in a state of hydrostatic stress we suppose an infinitesimal quantity of any substance to be added, the mass remaining homogeneous and its entropy and volume remaining unchanged, the increase of the energy of the mass divided by the quantity of the substance added is the potential for that substance in the mass considered."

1873年，吉布斯在他的论文《物质热力学性质的几何面表示法》（A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces）中，提出了他的新方程及其基本原理，用于讨论当不同系统相互接触时发生的自发过程。对于相互接触的均匀物质（如固、液、气组分），通过三维的体积-熵-内能图，吉布斯定义了三种状态：“必要稳定（necessarily stable）”，“中性（neutral）”，“不稳定（unstable）”，并借之理解某个变化过程能否自发进行。1876年，吉布斯在此理论基础之上引入了化学势的概念用于理解化学反应过程。他对此总结道：

${\displaystyle \delta (\epsilon -T\eta +P\nu )=0}$

"If we wish to express in a single equation the necessary and sufficient condition of thermodynamic equilibrium for a substance when surrounded by a medium of constant pressure P and temperature T, this equation may be written:

${\displaystyle \delta (\epsilon -T\eta +P\nu )=0}$

where δ refers to the variation produced by any variations in the state of the parts of the body, and (when different parts of the body are in different states) in the proportion in which the body is divided between the different states. The condition of stable equilibrium is that the value of the expression in the parenthesis shall be a minimum."

## 电化学，内部/外部/总化学势

${\displaystyle \mu _{\mathrm {tot} }=\mu _{\mathrm {int} }+\mu _{\mathrm {ext} }}$

${\displaystyle \mu _{\mathrm {ext} }=qV+mgh+\cdots }$

## 理想和非理想溶液中的化学势

(左）理想溶液（右）实际溶液中某组分的化学势

${\displaystyle \mu _{i}=\mu _{i}^{\text{ideal}}+\mu _{i}^{\text{excess}}}$

${\displaystyle \mu _{i}=\mu _{i0}(T,P)+RT\ln(x_{i})}$

${\displaystyle \mu _{i}=\mu _{i0}(T,P)+RT\ln(\gamma _{i}x_{i})=\mu _{i0}(T,P)+RT\ln(\gamma _{i})+RT\ln(x_{i})}$

## 文献

1. ^ Opacity, Walter F. Huebner, W. David Barfield, ISBN 1461487978, p. 105, https://books.google.de/books?id=ib-8BAAAQBAJ&pg=PA105&dq=partial+molar+free+energy+%22molar+chemical+potential%22&hl=de&sa=X&ved=0ahUKEwi9lbXjosnYAhUCzaQKHap3ChQQ6AEIKDAA#v=onepage&q=partial%20molar%20free%20energy%20%22molar%20chemical%20potential%22&f=false
2. ^ Atkins, Peter; de Paula, Julio. Atkins' Physical Chemistry 8th. Oxford University Press. 2006. ISBN 978-0-19-870072-2. Page references in this article refer specifically to the 8th edition of this book.
3. ^ Baierlein, Ralph. The elusive chemical potential (PDF). American Journal of Physics. April 2001, 69 (4): 423–434. Bibcode:2001AmJPh..69..423B. doi:10.1119/1.1336839.
4. ^ Job, G.; Herrmann, F. Chemical potential–a quantity in search of recognition (PDF). European Journal of Physics. February 2006, 27 (2): 353–371 [2018-04-30]. Bibcode:2006EJPh...27..353J. doi:10.1088/0143-0807/27/2/018. （原始内容 (PDF)存档于2015-09-24）.
5. ^ Kittel, Charles; Herbert Kroemer. Thermal Physics (2nd Edition). W. H. Freeman. 1980-01-15: 357. ISBN 978-0-7167-1088-2.
6. ^ Statistical Physics, F Mandl, (Wiley, London, 11971) ISBN 0 471 56658 6, page 88
7. ^ Atkins, Section 4.1, p 126
8. ^ Atkins, Section 5.5, pp 150-155
9. ^ Atkins, Section 5.3, pp 143-145
10. Thermal Physics by Kittel and Kroemer, second edition, page 124.
11. ^ Thermodynamics in Earth and Planetary Sciences by Jibamitra Ganguly, google books link. This text uses "internal", "external", and "total chemical potential" as in this article.
12. ^ Electrochemical Methods by Bard and Faulkner, 2nd edition, Section 2.2.4(a),4-5.
13. ^ Electrochemistry at Metal and Semiconductor Electrodes, by Norio Sato, pages 4-5, google books link
15. ^ The Physics of Solids: Essentials and Beyond, by Eleftherios N. Economou, page 140, google books link. In this text, total chemical potential is usually called "electrochemical potential", but sometimes just "chemical potential". The internal chemical potential is referred to by the unwieldy phrase "chemical potential in the absence of the [electric] field".
16. ^ Solid State Physics by Ashcroft and Mermin, page 257 note 36. Page 593 of the same book uses, instead, an unusual "flipped" definition where "chemical potential" is the total chemical potential which is constant in equilibrium, and "electrochemical potential" is the internal chemical potential; presumably this unusual terminology was an unintentional mistake.
17. ^ Morell, Christophe, Introduction to Density Functional Theory of Chemical Reactivity: The so-called Conceptual DFT (http://inac.cea.fr/Phocea/file.php?class=pisp&reload=1261486766&file=christophe.morell/files/98/introduction_to_Density_Functional_Theory_of_Chemical_Reactivity.pdf 页面存档备份，存于互联网档案馆), retrieved May 2016
18. ^ Baierlein, Ralph. Thermal Physics. Cambridge University Press. 2003. ISBN 0-521-65838-1. OCLC 39633743.
19. ^ Hadrons and Quark-Gluon Plasma, by Jean Letessier, Johann Rafelski, p91