查看“逸度”的源代码

'''逸度'''（英语：Fugacity）在[[化学热力学]]中表示[[实际气体]]的有效[[压力]]，用 <math>f</math> 表示。它等于相同条件下具有相同[[化学势]]的[[理想气体]]的压强。在与化学势有关的描述[[理想气体]]性质的热力学式子中用逸度代替活度，即可得到相应的描述[[实际气体]]性质的关系式。例如 0°C 下 100个大气压的氮气的逸度为 97.03 个大气压<ref>Peter Atkins and Julio de Paula, Atkins' Physical Chemistry (8th edn, W.H. Freeman 2006),  p.112</ref>，这意味着它与 97.03 个大气压下的氮气理想气体有着相同的化学势。逸度可以通过实验测定，也可以用[[范德瓦尔斯方程|范德华气体]]模型估算。逸度与压强的比值称为'''逸度系数'''<math> \phi \,</math>，它是无量纲量。<ref>{{Cite book
| edition = 7th
| publisher = Oxford University Press
| isbn = 0-19-879285-9
| last = Atkins
| first = Peter
| coauthors = John W. Locke
| title = Atkins' Physical Chemistry
| date = 2002-01
}}</ref>如下式所示。

<center><math> \phi = f/P \,</math></center>

例如，100个大气压下氮气的[[逸度系数]]为0.9763，理想气体的逸度系数为1。

<!--
The fugacity is closely related to the [[activity (chemistry)|thermodynamic activity]]. For a gas, the activity is simply the fugacity divided by a reference pressure to give a dimensionless quantity. This reference pressure is called the [[standard state]] and normally chosen as 1 [[atmosphere (unit)|atmosphere]] or 1 [[bar (unit)|bar]], Again using nitrogen at 100 atm as an example, since the fugacity is 97.03 atm, the activity is just 97.03 without units.

Accurate calculations of [[chemical equilibrium]] for real gases should use the fugacity rather than the pressure. The thermodynamic condition for chemical equilibrium is that the total chemical potential of reactants is equal to that of products. If the chemical potential of each gas is expressed as a function of fugacity, the equilibrium condition may be transformed into the familiar [[reaction quotient]] form (or [[law of mass action]]) except that the pressures are replaced by fugacities.

For a condensed phase (liquid or solid), the chemical potential is equal to that of the vapor in equilibrium with the condensed phase, and therefore the fugacity is equal to the fugacity of the vapor. This fugacity is approximately equal to the [[vapor pressure]] when the vapor pressure is not too high.

The word "fugacity" is derived from the Latin for "fleetness", which is often interpreted as “the tendency to flee or escape”.  The concept of fugacity was introduced by American chemist [[Gilbert N. Lewis]] in 1901.<ref>{{Cite journal
| doi = 10.1021/ja01947a002
| volume = 30
| issue = 5
| pages = 668–683
| last = Lewis
| first = Gilbert Newton
| title = The Osmotic Pressure of Concentrated Solutions, and the Laws of Perfect Solution.
| journal = Journal of the American Chemical Society
| date = 1908-05-01
| unused_data = DUPLICATE DATA: doi = 10.1021/ja01947a002
}}</ref>
-->

==用化学势定义逸度==
逸度定义的出发点是化学势与理想气体的压强的关系。

根据热力学基本方程：
<center><math>{\rm d}\mu  = {\rm d}G = -S{\rm d}T + V{\rm d}P</math></center>
定温下对压强从[[一般条件|参考态]]压强（1 [[巴]]）开始作定积分：
<center><math>\int_{\mu^\ominus }^\mu  {\rm d}\mu   = \int_{P^\ominus }^P {\bar V{\rm d}P}</math></center>
<!--
For any pure substance, the chemical potential (μ) is equal to the molar [[Gibbs free energy]], whose variation with temperature (T) and pressure (P) is given by <math>{d\mu } = dG = -SdT + VdP</math>. At constant temperature, this expression can be integrated as a function of <math>P</math>. We must also set a [[standard state|reference state]]. For an ideal gas the reference state depends only on pressure, and we set <math>P</math> = 1 [[bar (unit)|bar]] so that -->

对于理想气体有
<center><math>\bar V = \frac{{RT}}{P}</math></center>

整理后，得：

<center><math>\mu  = \mu ^\ominus  + RT\ln \frac{P}
{{P^\ominus }}</math></center>

上式给出了理想气体等温过程中化学势与压强的关系。

对于实际气体，因为上述状态方程式計算複雜，上述定積分難於處理計算，因此引入逸度的概念，逸度為修正因子，从而将实际气体的化学势表达式与理想气体统一起来。
<!--For a real gas, we cannot calculate <math>\int_{P^\circ }^P {\bar VdP}</math> because we do not have a simple expression for a real gas’ molar volume.  Even if using an approximate expression such as the [[van der Waals equation]], the [[Redlich-Kwong equation of state|Redlich-Kwong]] or any other [[equation of state]], it would depend on the substance being studied and would be therefore of very limited utility.

We would like the expression for a real gas’ chemical potential to be similar to the one for an ideal gas. We therefore define a magnitude, called '''fugacity''', so that the chemical potential for a real gas becomes -->

<center><math>\mu  = \mu ^\ominus  + RT\ln \frac{f}
{{f^\ominus }}</math></center>

一般把上式作为逸度的定义式，也可以明确地将<math>f</math>解出：
<!--with a given reference state to be discussed later. This is the usual form of the definition, but it may be solved for f to obtain the equivalent explicit form-->

<center><math>f = {{f^\ominus }} \exp \left(\frac{\mu  - \mu ^\ominus}{RT}\right)</math></center>

<!--
==Evaluation of fugacity for a real gas==

Fugacity is used to better approximate the chemical potential of real gases than estimations made using the [[ideal gas law]].  Yet fugacity allows the use of many of the relationships developed for an idealized system.

In the real world, gases approach [[ideal gas]] behavior at low pressures and high temperatures; under such conditions the value of fugacity approaches the value of [[pressure]].  Yet no substance is truly ideal.  At moderate pressures real gases have attractive interactions and at high pressures intermolecular repulsions become important.  Both interactions result in a deviation from "ideal" behavior for which interactions between gas atoms or molecules are ignored. 

For a given temperature <math> T\,</math>, the fugacity <math> f\,</math> satisfies the following differential relation:

:<math> d \ln {f \over f_0} = {dG \over RT} = {{\bar V dP} \over RT} \,</math>

where <math>G\,</math> is the [[Gibbs free energy]], <math>R\,</math> is the [[gas constant]], <math>\bar V\,</math> is the fluid's [[molar volume]], and <math>f_0\,</math> is a reference fugacity which is generally taken as 1 bar. For an ideal gas, when <math>f=P</math>, this equation reduces to the [[ideal gas law]].

Thus, for any two physical states at the same temperature, represented by subscripts 1 and 2, the ratio of the two fugacities is as follows:

:<math> {f_2 \over f_1} = \exp \left ({1 \over RT} \int_{G_1}^{G_2} dG \right) = \exp \left ({1 \over RT} \int_{P_1}^{P_2} \bar V\,dP \right) \,</math>

For an ideal gas, this becomes simply <math>{f_2 \over f_1} = {p_2 \over p_1}</math>  or  <math>f = P</math>

But for <math>P \to 0</math>, every gas is an ideal gas. Therefore, fugacity must obey the [[Limit of a function|limit]] equation

:<math>\mathop {\lim }_{P \to 0} \frac{f}
{P} = 1</math>

We determine <math>f</math> by defining a function

:<math>\Phi  = \frac{{P\bar V - RT}}
{P}</math>

We can obtain values for <math>\Phi</math> experimentally easily by measuring <math>V</math>, <math>T</math> and <math>P</math>.

From the expression above we have

:<math>\bar V = \frac{{RT}}
{P} + \Phi</math>

We can then write

:<math>\int_{\mu ^\circ }^\mu  {d\mu }  = \int_{P^\circ }^P {\bar VdP}  = \int_{P^\circ }^P {\frac{{RT}}
{P}dP}  + \int_{P^\circ }^P {\Phi dP}</math>

Where

:<math>\mu  = \mu ^\circ  + RT\ln \frac{P}
{{P^\circ }} + \int_{P^\circ }^P {\Phi dP}</math>

Since the expression for an ideal gas was chosen to be <math>\mu  = \mu ^\circ  + RT\ln \frac{f}
{{f^\circ }}</math>,we must have

:<math>\mu ^\circ  + RT\ln \frac{f}
{{f^\circ }} = \mu ^\circ  + RT\ln \frac{P}
{{P^\circ }} + \int_{P^\circ }^P {\Phi dP}</math>

:<math> \Rightarrow RT\ln \frac{f}
{{f^\circ }} - RT\ln \frac{P}
{{P^\circ }} = \int_{P^\circ }^P {\Phi dP}</math>

:<math>RT\ln \frac{{fP^\circ }}
{{Pf^\circ }} = \int_{P^\circ }^P {\Phi dP}</math>

Suppose we choose <math>P^\circ \to 0</math>. Since <math>\mathop {\lim }_{P^\circ \to 0} f^\circ = P^\circ</math>, we obtain

:<math>RT\ln \frac{f}
{P} = \int_0^P {\Phi dP}</math>

The fugacity coefficient is defined as <math>\phi</math> = f/P (note that for an ideal gas, <math>\phi</math> = 1.0), and
it will then verify

:<math>\ln \phi  = \frac{1}
{{RT}}\int_0^P {\Phi dP}</math>

The integral can be evaluated via graphical integration if we experimentally measure values for <math>\Phi</math> while varying <math>P</math>.

We can then find the fugacity coefficient of a gas at a given pressure <math>P</math> and calculate

:<math>f = \phi P\,</math>

The reference state for the expression of a real gas’ chemical potential is taken to be “ideal gas, at <math>P</math> = 1 bar and temperature <math>T</math>”. Since in the reference state the gas is considered to be ideal (it is an hypothetical reference state), we can write that for the real gas

:<math>\mu  = \mu ^\circ  + RT\ln \frac{f}
{{P^\circ }}</math>
-->

==参见==
*[[活度]]
*[[化学平衡]]
*[[热力学平衡]]

==参考文献==

{{Reflist}}


[[Category:物理化学]]
[[Category:化学热力学]]
[[Category:热力学性质]]
[[Category:状态函数]]