Concept of fugacity.pdf

Description of fugacity

1. Shri Shivaji Science College, Nagpur
Seminar Topic :
Concept of fugacity, Determination offugacity,excess
functionof non-ideal solution
By
BhagyashreeS. bokde
M.ScChemistry (sem2)

2. C0NTENT
➢Concept of fugacity.
➢Fugacity atlow pressure.
➢Determination offugacityofgas.
➢Calculation of fugacity at low pressure.
➢Physical significanceoffugacity.
➢Fugacity ofgasingaseousmixture.
➢Excess function of non-ideal solution.

3. Concept of fugacity
The great American chemist G. N. Lewis (1875-1946)
introduced the concept of Fugacity for representing the actual behavior of real gases
which is distinctly different from the behavior of ideal gases.
Variation of free energy with pressure at constattemperature is given by,
1
??????�
????????????
??????
This equation is applicable to all gases wheterideal or non ideal.
If one mole of gas is under consideration,thrnv-reflects to
moalvolume. For an ideal gas. The above equation may be written as
ⅆ�
??????=2�
ⅆ??????
�
…………………...
and for n moles as,
ⅆ�
??????=�??????�
ⅆ??????
�
2
= nRTd(lnp)………3
Integration of this equation is,
G=�
∗
+ nRTlnp..........................4
=Y .....................

4. �
∗
be the integration constant ,which is the free energy of n moles of the ideal
gas at temperature T, then pressure p is unity .
Integration of eq. 2 is between pressure p1 and p2 at constant temp. is,
G = ׬
�1
�2
�??????�
�??????
??????
= nRT. ln
??????2
??????1
…………..
The corresponding equation for 1 mole of the gas would be,
∆�=??????���
??????2
??????1
……………….
Equation 4 and 6 are not valid for real gases , since v is not exactly equal to
????????????
??????
•In order to make them simple equation applicable to real gases , lewis
Introduced a new fuctionF called fugacity function . It takes the plane of in
equation which for ideal gases may be expressed as
(??????�)
??????= nRTd (lnp) …………………
And equation may be represented as,
G = �
∗
+ nRTlnf………………
Where, �
∗
is the free energy of n moles of a real gas when its fugacity happens
to be 1.
5
6
7
8

5. •Thus, fugacity is a sort of ‘frictiouspressure’ which is used in order to retain for
real gases simple from of equations which are applicable to ideal gases only.
•Eq. 8 eventullygives the free energy of a real gas at temperature T and pressure P
at which its fugacity can be taken as f.
•Eq. 7 an integration between fugacitiesf1 and f2 at constant temp. T yields,
∆�=�??????�??????�
�2
�1
………………
The corresponding equation for 1mole of the gas would be
∆�=??????�??????�(
�2
�1
)……………..
As discussed above, equation 9 and 10 are applicable to real gases.
❖Fugacity at low pressure :-
The ratio f and p , where p is the actual pressure approaches unity where p
approaches zero . Since in that cost a real gas approximates to ideal behavior. The
lugacityfunction therefore may be defined as,
limit
�
�
=1
9
10
p→0

6. •Evidently, at low pressure, fugacity is equal to pressure whreretwo terms
differ martially only at high pressure.
❖Determination of Fugacity of a gas :-
from equation 8 for 1 mole of a gas may be put as,
G = �
∗
+ RT ln f ……………………. 12
•Determination of eq. 12 with respect to pressure at constant temperature and
constatntno of moles of the various constituents , i.e. in closed system gives,
??????�
??????�
??????
= RT
??????(ln�)
????????????
………..13
Since
??????�
??????�
??????
=v
It, follows that
??????ln�
??????
????????????
=
??????
????????????
……………..14
•Thus, at definite temperature equation 14 may written as,
RT d ( ln f ) =v dp……………… 15
Since, one mole of the gas is under consideration. V is the molar
volume of the gas.

7. •Knowing that for an ideal gas ,
v =
????????????
??????
, the quantity d, defined as departure from ideal behavior at a given
temperature is given by,
α=
????????????
??????
-V ……………..16
Multiplying by dpthroughout we get,
α= RT
��
�
-vdp………….17
Combining equation 15 and 17 we have,
RTd(lnf) = RT
��
�
-αdp
Or, d (lnf) = d ( lnp) –αdp(RT) ……………18
Integrating equation 18 between pressure 0 and p we have,
ln
�
�
=
−1
????????????
׬
0
??????
∝(????????????)…………..19

8. ❖Calculation of fugacity at low pressure :-
•It has been found that the experiment value of αat low pressure assumes almost a
constant value under such conditions , therefore eq. 19 gives,
ln
�
�
= -α
�
????????????
………………….. 20
now, at low pressure since gases tend to be ideal f = p
�
�
≈1……….21

9. •Making use of the fact that ln x is approximately equal to -1 , when x
apporachesunity, we have
ln
�
??????
=
�
??????
-p
Hence,
�
�
= 1 + ln
�
??????
………………..22
=1 –α
??????
????????????
=
????????????
????????????
f=
??????
2
??????
????????????
……………………. 23
This equation is useful in calculating fugacity at moderately low pressure.
❖Fugacity of gas in gaseous mixture :-
•Remembering that for one mole of a pure substance,thefree energy (G) is identical with
chemical potential. In eq. 7 for one mole of any gaseous component iof a gaseous
mixture may be written as
d??????
??????= RTd(ln fi ) ………….24
equation8maybewritten as,

10. ??????
??????= ??????
??????
∗
+ RT ln�
??????……………… 25
Where,??????
??????
∗
is the chemical potential of the gaseous component ias its unit fugacity.
❖Physical significance of fugacity :-
In order to understand the physical significance of the term Fugacity,
•A systemconsistingofliquidwaterincontactwithitsvapour.
•Water molecules in the liquid phase will have a tendancyto escapinto the vapour
phase by evaporation.
•While thoseonethevapourphasewillhaveatendancytoescapintotheliquid
phase by condensation.
•At equilibriumthetwoescapingtendancieswillbeequal.
•It is now accepted that each substance in a given state has a tendancyto escap
from that state.
•This escapingtendancywas term buLewis as Fugacity.

11. ❖Excess function of non –ideal solution :-
•The deviation from ideal behavior can be expressed in terms of excess
thermodynamic functions which gives more quantitaveidea abotthe nature of
molecular interaction.
•The difference betweenthermodynamicfunctionofmixingforanon–idealsystem
andthecorresponding value for an ideal system at same temperatrureand pressure
is called ‘thermodynamic excess function’.
•It isdenotedbysubscript E. This quantity represents the excess ( positive or
negative) of a given thermodynamic property of the solution over that in the ideal
solution.
??????
�
= ∆γ�??????????????????��
??????�????????????
-∆γ�??????????????????��
??????��????????????
=∆γ�??????????????????��
(���−??????��????????????)
-∆γ�??????????????????��
??????��????????????
Where,γcan be any thermodynamic function.
•In chemicalthermodynamics, excess property are properties of mixture which
quantify the non-ideal behaviourof real mixture.
•They aredefinedasthedifference betweenthevalueofthepropertyinareal
mixtureandthevaluethatwouldexistinanidealsolutionunderthesamecondition.

12. •When a solution does not obey Roult’slow for all the concentration and temp.
ranges it is known as ‘non-ideal solution’.
•A non-idealsolutionmayshowpositive ornegativedeviationfromRoult’slow.
•∆Hmixand ∆Vmixfor non-ideal solution are not equal to zero.
•The mostfrequentlyusedexcesspropertiesare the excess volume, excess
enthalpy and excess chemical potential.
•The excessvolume,internalenergy and enthalpy are identical to the
corresponding mixing properties.
�
�
=∆Vmix
�
�
= ∆�mix
�
�
= ∆Umix
•This relationshiphold because the volume, internal energy and enthalpy change
of mixing are zero for an ideal solution.

13. ThankYou