Equilibrio Homogéneo en Fase Líquida

!"#"$%&'"("$)*
!"#$%&'%()$*$+,-%.)/0120,-%
+&'","-."%*/%(%012+%*+2*!)#+*,3&'"4)*
*
!"# %-5+6"7%*4+,*6.)-)5%*8.)$6"$%*
! "#$%&%'!%(!)*(+'!,%!(*!-+&.$*&$%!,%!%/01(1#'1+!9:;<!,%!(*!'%*--12&!%&!3*.%!*-0+.*4!
! ! ! ! ! ! !
5 79,1.: + 56 ⇔ 5 8 6 !
! ! 9)<!
*
!!"#"26.%4'$$"=2*
!!"$#! ;(*&$%*&,+! (*!-+&,1-12&!,%!%/01(1#'1+!<*'*!%.$*!'%*--12&!/0=>1-*!?!*,+<$*&,+!%(@(+.!%.$*,+.!
,%!'%3%'%&-1*!?!(*@(*.!%.-*(*.!,%!-+&-%&$'*-1+&%.!>A.!*,%-0*,*.!<*'*!.0!%.$0,1+B!.%!-+&-(0?%!/0%4!
! ! ! ! ! ! ! !
* C5 D6
6% =
8
CD
57
* E * C56D
! ! ! 9><!
! F+>+!.%!$'*#*G*!-+&!.+(0-1+&%.!,1(0=,*.!.%!<0%,%!*-%<$*'!/0%4!
γ C5 D6
8
*! ! ! ! ! ! ! ! ! !
γ E γ C56D
CD
57
≈ H!
! 9?<*
/0%,*&,+!'%,0-1,*!(*!9H:!*4!
*! ! ! ! ! ! ! !
6% =
-C5 D6
8
CD
57
- E -C56D
! ! ! 9@<*
! I(! /0%'%'! ,%$%'>1&*'! %(! )*(+'! ,%! :;! >%,1*&$%! (+.! )*(+'%.! ,%! (*.! -+&-%&$'*-1+&%.! ,%! %/01(1#'1+!
*<*'%-%! %(! <'+#(%>*! /0%! &+! .%! <0%,%! J-+&K%(*'L! %.$%! %.$*,+! ?! >%,1'! -*,*! -+&-%&$'*-12&B! ?*! /0%!
*($%'*'!0&*!,%!%((*.!9>%,1*&$%!(*!$1$0(*-12&!,%(!"?B!<+'!%G%><(+:!1><(1-*!>+,131-*'!.1>0($A&%*>%&$%!
(*!-+&-%&$'*-12&!,%!(*.!,%>A.!%.<%-1%.!/0%!%.$A&!%&!%/01(1#'1+B!.%KM&!(*!'%*--12&!9)<E!
! N(! <'+#(%>*! .%! '%.0%()%! *K'%K*&,+! 0&! .+()%&$%! +'KA&1-+! 1&>1.-1#(%! -+&! %(! *K0*B! %&! %(! -0*(! &+!
<0%,*!$%&%'!(0K*'!(*!'%*--12&!9)<B!<%'+!.=!(*!.1K01%&$%4!
! ! ! ! ! ! ! !
5β79,1.: ⇔ 5 α79,1.: !
! 9-<* * α!O!3*.%!+'KA&1-*P!β!O!3*.%!*-0+.*!
! N(!%.$0,1+!,%(!%/01(1#'1+!,%!,1.$'1#0-12&!.%!)%'A!%&*""A*!?!(*!,%$%'>1&*-12&!,%!(*!-+&.$*&$%!:B!%&!
"""ACE!N(!.1.$%>*!.%!<0%,%!'%<'%.%&$*'!-+>+4!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!5 β79 ,1.
! : !+ 56
! ⇔
!
!5 α !
β O!3*.%!*-0+.*!
5 86
!
!
79 ,1. :
!
!
!
!
!
!
α O!3*.%!+'KA&1-*
! Q%!<0%,%!*R+'*B!.%<*'*&,+!(*.!3*.%.B!$1$0(*&,+!(*!+'KA&1-*B!?!R*-1%&,+!0.+!,%!:BB!,%$%'>1&*'!%(!
)*(+'!,%!(*!-+&-%&$'*-12&!,%!%/01(1#'1+!,%(!"?!%&!3*.%!*-0+.*E!
! F0*&,+!.%!$1$0(%!,1-R*!3*.%B!%(!%/01(1#'1+!'%<'%.%&$*,+!<+'!(*!'%*--12&!9)<B!*(!,%.*<*'%-%'!%(!"?B!.%!
,%.<(*S*'A!R*-1*!(*!1S/01%',*B!,*&,+!-+>+!'%.0($*,+!(*!-+&-%&$'*-12&!,%!"?!J1&1-1*(L!/0%!-+''%.<+&T
,%'=*!*(!%.$*,+!,%!%/01(1#'1+!*(-*&S*,+!%&!(*!%U<%'1%&-1*E!
! ;(*&$%*&,+! <*'*! (*! '%*--12&! 9)<! (*! )*'1*-12&! ,%! -+&-%&$'*-1+&%.! %&$'%! %(! %.$*,+! 1&1-1*(! ?! %(! ,%!
%/01(1#'1+B!?!((*>*&,+4!
!
!
FU = !
! ! -+&-%&$'*-12&!JV&1-1*(L,%!"?!%&!3*.%!*-0+.*E!
!
F5 = !
! ! -+&-%&$'*-12&!,%!"?!%&!3*.%!+'KA&1-*!9,%!%/01(1#'1+:E!
!
F5
= F55 = ! -+&-%&$'*-12&!,%!"?!%&!3*.%!*-0+.*!9,%!%/01(1#'1+:E!
6,
!
F? = !
! ! -+&-%&$'*-12&!1&1-1*(!,%!":!9-+&+-1,*:E!
!
/0%,*'AB!'%%><(*S*&,+!%.$+.!)*(+'%.!%&!(*!98:4!
!
! ! ! ! ! !
6% =
F U − F 55
!
F 55 (F ? − (F U − F 55 ))
! 9D<*
!
!
!!"%#! Q1!*!0&!.1.$%>*!-+><0%.$+!<+'!,+.!3*.%.!(=/01,*.!1&>1.-1#(%.!%&$'%!.=B!.%!(%!*K'%K*!0&*!$%'-%'*!
.0.$*&-1*!.+(0#(%!%&!*>#*.!3*.%.B!.%!+#.%')*!/0%!,1-R*!.0.$*&-1*!.%!,1.$'1#0?%!%&$'%!(*.!,+.!-*<*.!,%!
>*&%'*!,%31&1,*E!
⇔ 5 α79,1.: !!
β
! ! ! ! ! ! ! ! ! !!!!!!! 5 79,1.:
9-<!
! ;(*&$%*&,+!%.$%!%/01(1#'1+!<*'*!%(!579,1.:!/0%!.%!,1.$'1#0?%!%&$'%!*K0*!?!$%$'*-(+'0'+!,%!-*'#+&+B!?!
*,+<$*&,+! (+.! %.$*,+.! ,%! '%3%'%&-1*! ?! %.-*(*.! ,%! -+&-%&$'*-1+&%.! >A.! -+&)%&1%&$%.B! .%! -+&-(0?%!
/0%4!
! ! ! ! ! ! ! ! ! !
* C5 WWα
6 , = C WWβ !
*5
7
! 9E<!
7
! F+>+!.%!$'*#*G*!-+&!.+(0-1+&%.!,1(0=,*.B!.%!<0%,%!*-%<$*'!/0%4!
*! ! ! ! ! ! ! ! ! ! !
γ C5 D
α
7
γ
CDβ
57
≈ H!
! 9F<*
/0%,*&,+!'%,0-1,*!(*!9E<!*4!
! ! ! ! ! ! ! ! ! !
6, =
Fα5
7
F
β
57
!! ! 9G<!
! N.$*! -+&-(0.12&! -+&.$1$0?%! (+! /0%! .%! ,%&+>1&*!,;H* B;* 4IJKLIMNOIPQB! $*>#1X&! ((*>*,*! ,;H* B;*
.;RCLKSB!?!*!(*!-+&.$*&$%!:B!.%!(*!-+&+-%!-+>+!OS;TIOI;QK;*B;*L;RCLKS!+!,%!BIJKLIMNOIPQE!
!
7!
! Y*!*<(1-*-12&!,%!%.$%!%/01(1#'1+!$1%&%!1><+'$*&-1*!%&!(*!+#$%&-12&!?@+!<0'131-*-12&!,%!<'+,0-$+.!
/0=>1-+.!+'KA&1-+.!%!1&+'KA&1-+.!?!-+&.$1$0?%!(*!#*.%!,%!(*!-'+>*$+K'*3=*E!
! Y*!0$1(1,*,!/0%!$%&,'A!%&!%.$%!Z'*#*G+!;'A-$1-+!.%'A!<+.1#1(1$*'!%(!%.$0,1+!,%(!%/01(1#'1+!,%!(*!'%T
*--12&!9)<E!
!
!
!!!"#* 6+$2"$)*%8+.)6%.")!
!!!"$# 4;K;LUIQCOIPQ*B;*VC*OSQJKCQK;*B;*BIJKLIMNOIPQ*9:B<!
! N&!0&!#*(2&!,%!HECCC!>(!,%!-*<*-1,*,B!.%!-+(+-*&!8C!>(!,%!.+(0-12&!.*$0'*,*!,%!"?!%&!$%$'*-(+'0T
'+!,%!-*'#+&+!?![CC!>(!,%!*K0*E!Q%!*K1$*!3'%-0%&$%>%&$%!,0'*&$%!H!R+'*B!-+&!%(!+#G%$+!,%!*0>%&$*'!
(*!.0<%'31-1%!,%!.%<*'*-12&!%&$'%!(*.!3*.%.!*-0+.*!?!+'KA&1-*B!(+!-0*(!1&-'%>%&$*!(*!)%(+-1,*,!,%!,1T
30.12&!,%(!"?!%&$'%!*>#*.!3*.%.!?!<%'>1$%!((%K*'!*(!%/01(1#'1+!%&!>%&+'!$1%><+E!
! Q%!<*.*!(0%K+!*!0&*!*><+((*!,%!,%-*&$*-12&B!.%!.%<*'*&!(*.!3*.%.!?!.%!$1$0(*&!-+&!2C?#?%@!CBH!\E!
! ;*'*!(*.!$1$0(*-1+&%.!$+>*'4!![!>(!,%!(*!-*<*!+'KA&1-*!?!7CC!>(!,%!(*!-*<*!*-0+.*E!
! ]%*(1S*'!<+'!,0<(1-*,+E!
!
!!!"%# 4;K;LUIQCOIPQ*B;*VC*OSQJKCQK;*B;*;WNIVIMLIS*B;*VC*L;COOIPQ*9:;<!
! N&!0&!#*(2&!,%!HECCC!>(!,%!-*<*-1,*,B!.%!-+(+-*&!8C!>(!,%!.+(0-12&!.*$0'*,*!,%!"?!%&!$%$'*-(+'0T
'+!,%!-*'#+&+!?![CC!>(!,%!.+(0-12&!CBH!\!,%!":B!?!.%!<'+-%,%!,%!1K0*(!>*&%'*!/0%!%&!%(!<0&$+!*&$%T
'1+'E!
! ;*'*!(*.!$1$0(*-1+&%.!$+>*'4!!HC!>(!,%!(*!-*<*!+'KA&1-*!?!HCC!>(!,%!(*!-*<*!*-0+.*E!
! ]%*(1S*'!<+'!,0<(1-*,+E!
!
!!!"&# 4;K;LUIQCOIPQ*B;V*TCOKSL*B;V*2C?#?%@*XY>*2*
!!!"'# 4;K;LUIQCOIPQ*B;V*TCOKSL*B;V*":*XY>*2*
! ;*'*!(+.!<0&$+.!"""AO!?*"""AB!<'+-%,%'!,%!*-0%',+!-+&!(*!$X-&1-*!0$1(1S*,*!%&!%(!$'*#*G+!<'A-$1-+!
7%,'(+6.")E!
! ;*'*!(*.!$1$0(*-1+&%.!,%!"?!%&!3*.%!+'KA&1-*!.%!'%-+>1%&,*!*K'%K*'!0&*!<%/0%^*!-*&$1,*,!,%!.+(0T
-12&!,%!":!<*'*!3*)+'%-%'!%(!<*.*G%!,%!"?!*!(*!3*.%!*-0+.*E!
!
!
!("# $),$',%#*Z*.+#',6)4%#!
! F+&!(+.!,*$+.!,%!(*.!$1$0(*-1+&%.B!-*(-0(*'!(*.!-+&-%&$'*-1+&%.!-+''%.<+&,1%&$%.B!'%%><(*S*'!*,%T
-0*,*>%&$%!%&!(*!9D<!?!9G<B!+#$%&1%&,+!(+.!)*(+'%.!,%!:B!?!:;E!
! 5&3+'>*'!*,%>A.!(*!$%><%'*$0'*!*!(*!-0*(!30%!'%*(1S*,*!(*!%U<%'1%&-1*E!
!
!
$'+#6"%2)."%*
>A! I!<*'$1'!,%!(*!-+&,1-12&!,%!%/01(1#'1+!31.1-+/0=>1-+B!,%,0S-*!(*.!%U<'%.1+&%.!,%!(*!-+&.$*&$%!,%!
%/01(1#'1+!9:;:!?!-+&.$*&$%!,%!,1.$'1#0-12&!9:B:E!Y*!%U<'%.12&!*!(*!/0%!.%!*''1#%!,%#%'A!<%'>1$1'!-*(T
!
8!
-0(*'!%(!)*(+'!&0>X'1-+!,%!-*,*!-+&.$*&$%B!R*-1%&,+!0.+!,%!(+.!,*$+.!+#$%&1,+.!,%!(*!%U<%'1%&-1*E!
I,+<$%!(+.!%.$*,+.!,%!'%3%'%&-1*!?!%.$*,+.!$1<+!>A.!*,%-0*,+.B!G0.$131-*&,+!.0!%(%--12&E!
?A! Y+.!'%.0($*,+.!+#$%&1,+.!%&!%(!$'*#*G+!<'A-$1-+!.+&!<0&$0*(%.!%!1><(1-*&!0&*!.%'1%!,%!.0<+.1-1+T
&%.E!NU<(1/0%!-2>+!<'+-%,%'=*!%U<%'1>%&$*(>%&$%!<*'*!+#$%&%'!%(!)*(+'!>A.!%U*-$+!,%!(*.!-+&.$*&T
$%.!,%!%/01(1#'1+!?!,%!,1.$'1#0-12&E!
@A* I&*(1-%!%(!$'*$*>1%&$+!,%(!%/01(1#'1+!,%!,1.$'1#0-12&!,%!0&!.+(0$+!%&$'%!,+.!(=/01,+.!1&>1.-1#(%.B!
-0*&,+!*/0X(!.%!%&-0%&$'*!<*'-1*(>%&$%!,1>%'1S*,+!%&!0&*!,%!(*.!3*.%.E!
DA* Y*!%U$'*--12&!,%!0&!.+(0$+!,%!0&*!.+(0-12&!-+&!0&!.+()%&$%!1&>1.-1#(%!%&!%((*!%.!0&*!+<%'*-12&!
,%!>0-R+!0.+E!`%'1)%!(*!32'>0(*!K%&%'*(1S*,*!/0%!(%!<%'>1$*!-+&+-%'!(*!3'*--12&!/0%!<%'>*&%-%!.1&!
%U$'*%'!,%.<0X.!,%!Q!+<%'*-1+&%.!%&!-+''1%&$%!-'0S*,*B!-+&![!K'E!,%!.+()%&$%B!<*'$1%&,+!,%!(!K'E!,%!
.+(0-12&!/0%!-+&$1%&%&!\X!>+(%.!,%!.+(0$+E!NU<(1/0%!/0X!'%.0($*!>A.!-+&)%&1%&$%4!%3%-$0*'!0&*!%UT
$'*--12&!-+&!0&*!>*.*![!K'E!,%!.+()%&$%!%&!0&*!.+(*!%$*<*B!+!Q!%U$'*--1+&%.!-+&![]Q!K'E!
!
!
!
-"-,"%0.)!3)*
T! !"#$%&$'() *+) ,&(&$-./01&$'2) ! a1&,(*?B! I(%U*&,%'B! N,1$+'1*(! bX,1-+Tc01'M'K1-*B! d0%&+.! I1'%.B!
He[[E)
T!34/5%+()*+)6#%+*"'E!
T!7"'%'*-)*+)8/01&$'),0(&$'2)!f(*..$+&%B!Q*>0%(B!N,E!IK01(*'B!b*,'1,B!He[8E!
!
!
3$)4,5%6776%
!
_!