INSTITUTO POLITECNICO NACIONAL ESCUELA SUPERIOR DE INGENIERIA QUÍMICA E INDUSTRIAS EXTRACTIVAS EXTRACTIVAS
LABORATORIO DE TERMODINÁMICA DEL EQUILIBRIO DE FASES
Práctica 4. “Equilibrio Liquido-Vapor Liquido-Vapor de una solución no ideal a baja presión”
Doctor: Gustao P!r"# L$%"# Gru%o: &IV'( E)u*%o: + INTEGRANTES: • • • •
Go,#-."# /"r,-,0"# C!sar Au1usto Ra23r"# Sa.a#ar Ga4r*".a Cora. Ru3# S"1u,0o Pa.o2a M*c5".." V-#)u"# S-,c5"# 6or1" 6"s7s
PRACTICA No8 + “Equilibrio Liquido-Vapor Liquido-Vapor de una solución no ideal a baja presión” Objetivos:
98 Pr"%arar u,a s"r*" 0" so.uc*o,"s 0" c.oro;or2o<9= > 2"ta,o.<&=? 2"0*r a ca0a u,a su t"2%"ratura 0" 4ur4u@a > .a co2%os*c*$, 0" .os a%or"s a %r"s*$, at2os;!r*ca8
&8 A %art*r 0" .os 0atos "%"r*2",ta."s 0"t"r2*,ar ". co";*c*",t" co" ;*c*",t" 0" act**0a0 <1*= 0" ca0a co2%o,",t" ", ca0a so.uc*$,8
'8 I,"st*1ar ". 2o0".o 0" so.uc*$,
+8 Corro4orar ". %u,to ' ".a4ora,0o .os c-.cu.os corr"s%o,0*",t"s > co2%ara,0o .os r"su.ta0os co, .os 0atos "%"r*2",ta."s8
ntroducción teórica:
PRACTICA No8 + “Equilibrio Liquido-Vapor Liquido-Vapor de una solución no ideal a baja presión” Objetivos:
98 Pr"%arar u,a s"r*" 0" so.uc*o,"s 0" c.oro;or2o<9= > 2"ta,o.<&=? 2"0*r a ca0a u,a su t"2%"ratura 0" 4ur4u@a > .a co2%os*c*$, 0" .os a%or"s a %r"s*$, at2os;!r*ca8
&8 A %art*r 0" .os 0atos "%"r*2",ta."s 0"t"r2*,ar ". co";*c*",t" co" ;*c*",t" 0" act**0a0 <1*= 0" ca0a co2%o,",t" ", ca0a so.uc*$,8
'8 I,"st*1ar ". 2o0".o 0" so.uc*$,
+8 Corro4orar ". %u,to ' ".a4ora,0o .os c-.cu.os corr"s%o,0*",t"s > co2%ara,0o .os r"su.ta0os co, .os 0atos "%"r*2",ta."s8
ntroducción teórica:
S* u, r"c*%*",t" c"rra0o ", ". )u" %r"*a2",t" s" 5a 5"c5o ac3o s" ..",a %arc*a.2",t" co, u,a susta,c*a .3)u*0a A !sta s" "a%orar- %arc*a.2",t"
"sta,0o ta4u.a0os .os co";*c*",t"s A B > C %ara
Su%$,1as" a5ora u, r"c*%*",t" ..",o 0" .3)u*0o A a u,a t"2%"ratura T 0" 2o0o )u" u,a 0" sus %ar"0"s "s 2$*.8 S* .a %r"s*$, "t"r,a so4r" "..a "s P < > s" ." a%orta ca.or s" au2",tar- .a t"2%"ratura 0". .3)u*0o > su %r"s*$, 0" a%or 0" 2o0o )u" a24as %r"s*o,"s t*",0", a *1ua.ars"8 Cua,0o "so suc"0" s" ;or2ar- .a %r*2"ra 4ur4u@a 0" a%or "s 0"c*r co2*",#a .a "4u..*c*$,8 La t"2%"ratura a .a cua. s" *1ua.a, a24as %r"s*o,"s "s ". punto de ebullición a .a %r"s*$, P8 S* !sta "s 9 at2 t",0r"2os ". %u,to 0" "4u..*c*$, ,or2a.8 S* s" s*1u" a%orta,0o ca.or "sta t"2%"ratura %"r2a,"c" co,sta,t" ",tr" ta,to 5a>a .3)u*0o au2",ta,0o 0" ,u"o cua,0o to0a .a susta,c*a "st! ", ;as" 1as"osa8 Co,s*0"r"2os a5ora u,a 2"#c.a *0"a. 0" 0os susta,c*as ", ;as" .3)u*0a A > B8 Eso )u*"r" 0"c*r ",tr" otras cosas )u": a= .a *,t"racc*$, 0" 2o.!cu.as 0" A co, 2o.!cu.as 2o.!cu.as 0" B "s *0!,t*ca a .a )u" s" 0a ",tr" .as 2o.!cu.as 2o.!cu.as 0" A o ",tr" .as 0" B? 4= ". o.u2", 0" 2"#c.a "s .a su2a 0" .os o.72","s 0" A > B %or s"%ara0o? c= ". ca.or 0" 2"#c.a "s ,u.o? 0= ". ")u*.*4r*o .3)u*0oa%or o4"0"c" .a ."> 0" Raou.t8 La ."> 0" Raou.t "sta4."c" )u" ", ". ")u*.*4r*o .a %r"s*$, %arc*a. 0" u,a susta,c*a "s *1ua. a su %r"s*$, 0" a%or %or .a ;racc*$, 2o.ar ", .a ;as" .3)u*0a "s 0"c*r: > ta24*!,
<9'89=
S* s" *,tro0uc" u,a 2"#c.a 0" A > B ", u, r"c*%*",t" ", ". )u" s" 5a 5"c5o ". ac3o > ", ". )u" s" 2a,t*"," u,a t"2%"ratura co,sta,t" s" a%or*#ar-, A > B 5asta a.ca,#ar u, "sta0o 0" ")u*.*4r*o ", ". )u" .a %r"s*$, r"*,a,t" s"r- .a %r"s*$, tota. 0" a%or 0" .a 2"#c.a P )u" 0" acu"r0o co, .a ."> 0" Raou.t t",0r- ". a.or: <9'8&=
S*",0o X A .a co2%os*c*$, 0" .a ;as" .3)u*0a ", ". ")u*.*4r*o 0*;"r",t" 0" .a co2%os*c*$, *,*c*a. 0" .a 2"#c.a8 La %r"s*$, tota. "s 2",or )u"
.a %r"s*$, 0"
a%or 0". 2-s o.-t*. > 2a>or )u" .a %r"s*$, 0" a%or 0". co2%o,",t" %"sa0o8 La ;*1ura 9'89 2u"stra ". 0*a1ra2a 0" ")u*.*4r*o a u,a t"2%"ratura T co,sta,t"8
F*18 9'898 E)u*.*4r*o LV a T ct"8 M"#c.as *0"a."s
4a. 9' %%8'=8
F*18 9'8&8 E)u*.*4r*o LV a P ct"8 M"#c.as *0"a."s 4a. 9' %%8'9=8
Co,s*0!r"s" 0" ,u"o u,a c-2ara co, .a ta%a 0"s%.a#a4." ", .a )u" s" 2a,t*"," u,a %r"s*$, P co,sta,t"8 Su%$,1as" )u" "st- ..",a 0" u,a 2"#c.a 0" A > B 0" co2%os*c*$, X A8 A. a%ortar ca.or s" *r- "."a,0o .a t"2%"ratura > s" .."1ar- u, 2o2",to ", ". )u" .a %r"s*$, 0" a%or 0" .a 2"#c.a *1ua." a P8 A "sta t"2%"ratura s" ..a2a punto de burbuja a P > a "..a s" ;or2a .a %r*2"ra 4ur4u@a 0" a%or8 La co2%os*c*$, 0". a%or s"17, .a ."> 0" Da.to, s"r-:
<9'8'= S* A "s ". co2%o,",t" 2-s o.-t*. "s c.aro )u" "s 2a>or )u" P > co,s"cu",t"2",t" H A "s 2a>or )u" X A8 S" 0*c" )u" ". a%or "st- ",r*)u"c*0o ", ". co2%o,",t" 2-s o.-t*. s* 4*", "s o4*o )u" "..o ,o *2%.*ca )u" H A s"a 2a>or )u" HB8 Para ". co2%o,",t" %"sa0o s" cu2%." )u" H B"s 2",or )u" XB8 S* s" s*1u" a%orta,0o ca.or .a t"2%"ratura ,o s" 2a,t*"," co,sta,t" s*,o )u" a au2",ta,0o? "..o s" 0"4" a )u" ". .3)u*0o s" a "2%o4r"c*",0o ", co2%o,",t" o.-t*. %or .o )u" %ara a.ca,#ar .a %r"s*$, tota. t",0r- )u" au2",tar > <"cuac*$, 9'8&=8 E. ca.or a%orta0o ,o so.o s" *,*"rt" ", a%or*#ar s*,o ta24*!, ", "."ar .a t"2%"ratura 0" a24as ;as"s8 F*,a.2",t" .."1a u, 2o2",to ", ". )u" )u"0a u,a 7.t*2a 1ota 0" 2"#c.a? "sta 2"#c.a "star- ", ")u*.*4r*o co, u, a%or cu>a co2%os*c*$, s"r- o4*a2",t" *1ua. a .a 0" .a 2"#c.a .3)u*0a 0" %art*0a? %or ta,to a%.*ca,0o .a ."> 0" Raou.t s" %u"0" "scr*4*r:
S*",0o H A X A8 R"so.*",0o "st" s*st"2a 0" "cuac*o,"s s" o4t*"," T R .a ..a2a0a te!peratura de roc"o# > X A .a co2%os*c*$, 0" .a 7.t*2a 1ota 0" .a 2"#c.a .a 2-s %o4r" ", ". co2%o,",t" 2-s o.-t*. A8 Co,*"," ac.arar )u" T R ta24*!, "s .a t"2%"ratura a .a cua. s" %ro0uc*r3a .a %r*2"ra 1ota 0" .3)u*0o a %art*r 0" u,a 2"#c.a 0" a%or"s 0" A > B 0" co2%os*c*$, H A X A? 0" a53 ". ,o24r" 0" t"2%"ratura 0" roc3o8 La ;*1ura 9'8&8 R"co1" ". 0*a1ra2a 0" ")u*.*4r*o 0" ;as"s a %r"s*$, co,sta,t" %ara "st" t*%o 0" 2"#c.as8
A5ora 4*", ,o to0as .as 2"#c.as s" co2%orta, 0" "st" 2o0o8 As3 %or "@"2%.o .a 2"#c.a "ta,o.a1ua ,o "s *0"a. ,o cu2%." .a ."> 0" Raou.t8 Las 0"s*ac*o,"s r"s%"cto a "sta ."> %u"0", s"r %os*t*as o ,"1at*as <;*1uras 9'8' > 9'8+= s"17, )u" .a %r"s*$, %arc*a. 0" ca0a co2%o,",t" s"a su%"r*or o *,;"r*or a .a o4t",*0a %or .a 2",c*o,a0a .">8
F*18 9'8'8 D"s*ac*o,"s %os*t*as8
F*18 9'8+8 D"s*ac*o,"s ,"1at*as E, ". ",tor,o 0" A %uro "sto "s %ara s" cu2%." .a ."> 0" Raou.t %ara A au,)u" .a 2"#c.a s"a ,o *0"a.8 E, "s" 2*s2o ra,1o s" sat*s;ac" .a ."> 0" /",r> %ara B: P B /B 8 XB 0o,0" / B "s .a co,sta,t" 0" /",r> )u" s$.o 0"%",0" 0" .a t"2%"ratura8 S* .as 0"s*ac*o,"s so, 2-s acusa0as %u"0", .."1ar a ;or2ars" Ja#"$tro%osJ "s 0"c*r 2"#c.as 0" 0os co2%o,",t"s )u" 5*"r", co2o s* ;u"s" u,a susta,c*a %ura co, u, %u,to 0" "4u..*c*$, co,sta,t" > or*1*,a,0o u, a%or 0" *1ua.
co2%os*c*$, )u" .a 2"#c.a .3)u*0a 0" %art*0a8 Es "*0",t" )u" %ara "stas 2"#c.as ,o %u"0" co,s"1u*rs" ,*,1u,a s"%arac*$, 2"0*a,t" ". "2%."o 0" .a 0"st*.ac*$,8
S* .os .3)u*0os so, *,2*sc*4."s sus 2o.!cu.as ,o *,t"racc*o,a, ",tr" s3 > s" a%or*#a, > co,0",sa, 0" ;or2a *,0"%",0*",t"? s" %u"0" 0"c*r a to0os .os ";"ctos )u" .a 2"#c.a s" co2%orta co2o s* 5u4*"ra u, ta4*)u" 0" s"%arac*$, ",tr" .os .3)u*0os A > B > co2%art*"ra, u, "s%ac*o co27, %ara .os a%or"s8 E, ". ")u*.*4r*o ca0a co2%o,",t" s" co2%orta co2o u,a susta,c*a %ura? ", co,s"cu",c*a .a %r"s*$, %arc*a. 0" ")u*.*4r*o s"r- *1ua. a .a %r"s*$, 0" a%or %ara ca0a co2%o,",t"8
S* s" *,tro0uc", 0os 0" "stos .3)u*0os ", u, r"c*%*",t" ", ". )u" s" 5a 5"c5o ". ac3o s" 2a,t*"," u,a t"2%"ratura co,sta,t" > s" a1*ta %ara "*tar .a 0"ca,tac*$, 0" u,o 0" .os co2%o,",t"s a24os %asar-, a. "sta0o 0" a%or 5asta a.ca,#ar u, "sta0o 0" ")u*.*4r*o ", ". )u" .a %r"s*$, tota. s"r- .a su2a 0" .as %r"s*o,"s %arc*a."s 0" a%or 0" .os co2%o,",t"s %uros 2*",tras "*sta, a24os ", "sta0o .3)u*0o ,o *2%orta,0o .as ca,t*0a0"s %r"s",t"s 0" u,o u otro: <9'8+= S* s" *,tro0uc", a24os ", u, r"c*%*",t" co, u, !24o.o a %r"s*$, co,sta,t" > s" a%orta ca.or %art*",0o 0" u,a t"2%"ratura 4a@a !sta au2",tar- %ro0uc*!,0os" .a %r*2"ra 4ur4u@a 0" a%or cua,0o P s*",0o TB .a t"2%"ratura 0" "4u..*c*$,8 La co2%os*c*$, 0" "sa 4ur4u@a 0" a%or "s:
> Esto s*1,*;*ca )u" %u"0", o4t","rs" a%or"s 0" A > B a u,a t"2%"ratura *,;"r*or a .a 0" sus %u,tos 0" "4u..*c*$, r"s%"ct*os: T B < TBA > TB < TBB S* s" s*1u" a%orta,0o ca.or .a t"2%"ratura > .a co2%os*c*$, 0". a%or %"r2a,"c", co,sta,t"s 2*",tras 5a>a A > B .3)u*0os8 Cua,0o s" aca4" u,o 0" .os 0os .a t"2%"ratura au2",ta 0" ,u"o 5asta )u" to0o %asa ;*,a.2",t" a "sta0o 0" a%or8
La "st*2ac*$, 0" .as co,0*c*o,"s 0". E)u*.*4r*o L3)u*0o Va%or ", .os s*st"2as 0" so.uc*o,"s ,o *0"a."s "s u, t"2a 0" "s%"c*a. *,t"r!s %ara .a I,1",*"r3a Qu32*ca8 E*st", ar*os %roc"0*2*",tos "sta4."c*0os ", "s" s",t*0o8 La "st*2ac*$, 0" .as co,sta,t"s %ara ". Mo0".o 0" Mar1u."s a %art*r 0" 0atos "%"r*2",ta."s .o *.ustra, a0"cua0a2",t" S2*t5 a, N"ss > A44ott ", su t"to8 Ut*.*#a, .os a.or"s ca.cu.a0os 0" .a E,"r13a 0" G*44s ", Ec"so ", 2"#c.as ,o *0"a."s <"acta2",t" corr".ac*o,a, GE KRT9& "rsus 9= > r"a.*#a, u, a@ust" .*,"a. %ara o4t","r ", .os "tr"2os 0" .a 1r-;*ca a24as co,sta,t"s 0". 2o0".o8 Para 2"@orar ". a@ust" 0" 0atos "s co,",*",t" ,o to2ar ", cu",ta a.1u,os %u,tos "%"r*2",ta."s "s%"c*a.2",t" ", .os "tr"2os 0" .a 1r-;*ca co,s*1u*!,0os" 0" "sta ;or2a corr".ac*o,"s a0"cua0as8 As3 2*s2o "stos autor"s 0"@a, %ro%u"sto ". M!to0o 0" Bar"r )u" corr".ac*o,a .a 0ata "%"r*2",ta. P9>9 "rsus 9 %or 2"0*o 0" .a a%.*cac*$, 0". Mo0".o 0" Mar1u."s %ara a.or"s asu2*0os 0" .as co,sta,t"s 5asta .o1rar ". 2"@or a@ust" 0" 0atos8 Por otra %art" Sa,0."r ,os *,0*ca )u" a %art*r 0" .a 0ata "%"r*2",ta. au,)u" s" %u"0", "st*2ar .os co";*c*",t"s 0" act**0a0 ", .a 2a>or3a 0" .os casos "s 0*;3c*. 0"c*0*r s* "sos 0atos a@usta, 2"@or a. Mo0".o 0" Mar1u."s o a. 0" a, Laar8 A1r"1a )u" u,a ;or2a %ara to2ar "sta 0"c*s*$, "s 1ra;*car GE K9& "rsus 9 > 9&KGE "rsus 9 > 0"t"r2*,ar cu-. 0" .as 0os 1r-;*cas s" a%ro*2a 2-s a u,a .3,"a r"cta8 S* "s .a %r*2"ra .a 0ata a@usta 2"@or a. Mo0".o 0" Mar1u."s 0" 0os co,sta,t"s > s* "s .a s"1u,0a s" 0"4"r- ut*.*#ar ". Mo0".o 0" a, Laar8
La o4t",c*$, 0" las constantes de $ar%ules & Van Laar r")u*"r", .a "a.uac*$, ", co,0*c*o,"s 0" ;ro,t"ra 99 > 9 0" u, %o.*,o2*o 0" 1ra0o su%"r*or %ara *,cr"2",tar su "act*tu08 E. %r*,c*%a. %ro4."2a "s ,u2!r*co >a )u" ". c-.cu.o 0" .as co,sta,t"s 0" u, %o.*,o2*o 0" La1ra,1" %or "@"2%.o r"su.ta u, %oco t"0*oso s* ,o s" 0*s%o," 0" u, 0*s%os*t*o 0" c-.cu.o "."ctr$,*co8 M"0*a,t" ". 2!to0o %r"s",ta0o "s %os*4." ". c-.cu.o 0" 0*c5as co,sta,t"s ut*.*#a,0o 7,*ca2",t" u,a "cuac*$, 0" r"1r"s*$, .*,"a. .a 0" 23,*2os cua0ra0os8 Los !odelos de $ar%ules & Van Laar s*r", %ara 0"scr*4*r RT9& GE $ RT GE
0" u, s*st"2a 4*,ar*o 2"0*a,t" u,a "cuac*$, a,a.3t*ca 0";*,*0a ", ". *,t"ra.o 0" a 9 ", ;racc*$, 2o.ar8 D*c5os 2o0".os so, co2%."ta2",t" *,t"1ra4."s o 0*;"r",c*a4."s ", 0*c5o *,t"ra.o .o cua. %"r2*t" o4t","r ;-c*.2",t" .as otras ar*a4."s 0" "sta0o8 •
$ar%ules:
La ","r13a 0" G*44s r"s*0ua. s" 0";*," co2o .a su2a 0" .as 2u.t*%.*cac*o,"s 0" .as ;racc*o,"s 2o.ar"s co, ". .o1ar*t2o ,atura. 0" .os co";*c*",t"s 0" act**0a08
Mu.t*%.*ca,0o a a24os .a0os s" o4t*",":
A5ora 4*", ". 2o0".o 0" Mar1u."s s" %u"0" a%ro*2ar %or 2"0*o 0" .a "cuac*$,:
Do,0" A9& > A&9 so, co,stat"s )u" 5a> )u" ",co,trar8 Mu.t*%.*ca,0o to0o %or 9K& s" o4t*",":
E, "st" caso s" %u"0" a%ro*2ar "sto a u,a r"cta 0" .a ;or2a: > 42 Do,0" 2A&9 4A9& > 9K&8
S* s" 1r-;*ca > s" o4t*"," .a .3,"a r"cta )u" .a 0"scr*4a s" t*",", ;-c*.2",t" .as co,sta,t"s 0" Mar1u."s8 •
Van Laar
O4t",c*$, 0" .as co,sta,t"s 0" a, Laar ut*.*#a,0o .a "cuac*$, 0" 23,*2os cua0ra0os %ara u,a .3,"a r"cta8 La "cuac*$, 0" Va, Laar %ara s*st"2as 4*,ar*os "s .a s*1u*",t":
S* s" "."a to0o a .a 9 s" o4t*",":
Esto s" %u"0" "%a,0*r a.1"4ra*ca2",t" > s" o4t*",":
S" r"0uc" a:
P"ro &99
Esto s" %u"0" a%ro*2ar a u,a .3,"a r"cta 0" .a ;or2a: >24
E,to,c"s "sta r"cta s" %u"0" o4t","r 2"0*a,t" ". 2!to0o 0" 23,*2os cua0ra0os8 Pr*2"ro s" "a.7a A9& > s" *,tro0uc" ", 2 %ara .a o4t",c*$, 0" A&98 •
•
•
•
Es %os*4." ",co,trar .as co,sta,t"s 0" Mar1u."s ut*.*#a,0o .a "cuac*$, 0" 23,*2os cua0ra0os s* s" 2o0*;*ca %ro%*a2",t" .a "cuac*$, 2",c*o,a0a8 Las co,sta,t"s 0" Va, Laar %u"0", s"r ",co,tra0as ut*.*#a,0o .a "cuac*$, 0" 23,*2os cua0ra0os 0"s%u!s 0" .*,"a.*#ar ". s*st"2a8 La ",ta@a 0". 2!to0o 0" 23,*2os cua0ra0os ra0*ca ", su ra%*0"# 0" c-.cu.o s*, ,"c"s*0a0 0" t","r )u" ",co,trar %r*2"ro u, 2o0".o %o.*,o2*a. 0" a.to 1ra0o > a.uar ", .os "tr"2os 0". s*st"2a8 Las co,sta,t"s 0" Va, Laar > Mar1u."s %u"0", s"r ca.cu.a0as 0*r"cta2",t"8
Procedi!iento e'peri!ental: a=8 Pr"%arar u,a s"r*" 0" so.uc*o,"s 0" c.oro;or2o <9= > 2"ta,o. <&= ", .as )u" .a co,c",trac*$, 0". c.oro;or2o <9= ar3" 0"s0" 8 89888 98 ;rac8 2o.8 4=8 M"0*r a ca0a so.uc*$, ". 3,0*c" 0" r";racc*$, <= > ".a4orar u,a 1r-;*ca 0" s 9 a .a )u" s" ..a2a: Cura 0" ca.*4rac*$,8 c=8 Co.ocar .a %r*2"ra so.uc*$, ", ". r"c*%*",t" 0". ")u*%o %o,"r ". r"c*%*",t" so4r" .a %arr*..a 0" ca.",ta2*",to co, u,a a1*tac*$, .",ta ca.",tar ". .3)u*0o 5asta "4u..*c*$, "s%"rar u, 2o2",to %ara as"1urars" )u" .a t"2%"ratura s"a co,ta,t" > a,otar.a: "s .a t"2%"ratura 0" 4ur4u@a8 0=8 D" .a %rotu4"ra,c*a )u" t*"," ". ")u*%o ", ". %*" 0". r";r*1"ra,t" )u" "s u, 0"%$s*to 0" co,0",sa0o to2ar u,a 2u"stra %or 2"0*o 0" u,a %*%"ta 0".1a0a > u,a %"r*..a 0"%os*t-,0o.a ", u, tu4o 0" ",sa>o %r"*a2",t" "t*)u"ta0o ta%-,0o.a *,2"0*ata2",t"8 Para .as so.uc*o,"s )u" corr"s%o,0", a .as susta,c*as %uras ,o "s ,"c"sar*o to2ar 2u"stra 0" co,0",sa0o8 "=8 R"%"t*r %ara ca0a so.uc*$, .os %asos c > 08 ;=8 Es%"rar a )u" .as 2u"stras )u" co,t*",", ". co,0",sa0o "st!, a .a t"2%"ratura a24*",t" %ara 2"0*r ". 3,0*c" 0" r";racc*$, a ca0a u,a8 1=8 Co, a>u0a 0" .a cura 0" ca.*4rac*$, ".a4ora0a ", ". %aso 4 0"t"r2*,ar .a ;racc*$, 2o. 0". 2"ta,o. ", .os a%or"s ", ". 2o2",to ", )u" s" 0*o ". ")u*.*4r*o .3)u*0oa%or8
(ia%ra!a de )lujo del procedi!iento e'peri!ental Equilibrio Liquido-Vapor de una solución no ideal abaja te!peratura
a= Pr"%arar u,a s"r*" 0" so.uc*o,"s 0" c.oro;or2o > 2"ta,o.
4= Co.ocar .as so.uc*o,"s ", r"c*%*",t" 0". ")u*%o *,sta.a0o %o,"r r"c*%*",t" so4r" .a %arr*..a 0" ca.",ta2*",to co, u,a a1*tac*$,8 Ca.",tar ". .3)u*0o 5asta "4u..*c*$, "s%"rar a )u" t"2%"ratura s"a co,ta,t" > a,otar: "sa "s .a t"2 "ratura 0" 4ur4u a8 A a ar .a arr*..a8
c= D" %rotu4"ra,c*a )u" t*"," ". ")u*%o ", %*" 0". r";r*1"ra,t" )u" "s u, 0"%$s*to 0" co,0",sa0o to2ar 2u"stra %or 2"0*o 0" u,a %*%"ta 0".1a0a > u,a %"r*..a 0"%os*tar.a ", u, tu4o 0" ",sa>o %r"*a2",t" "t*)u"ta0o ta%-,0o.a *,2"0*ata2",t"8 Para .as so.uc*o,"s )u" corr"s%o,0", a .as susta,c*as %uras ,o "s ,"c"sar*o to2ar 2u"stra 0" co,0",sa0o8
0= Es%"rar )u" .as 2u"stras )u" co,t*",", ". co,0",sa0o "st!, a .a t"2%"ratura a24*",t" %ara 2"0*r ". 3,0*c" 0" r";racc*$, <= a ca0a u,a8
" R" "t*r ara ca0a so.uc*$, .os asos 4 c 0
;= Co, a>u0a 0" .os 0atos "%"r*2",ta."s ".a4orar c-.cu.os "%"r*2",ta."s > 0"sarro..ar c-.cu.os t"$r*cos %ara as3 0"s%u!s 5ac"r 1r-;*cas > %o0"r r"a.*#ar .as o4s"rac*o,"s > co,c.us*o,"s8
*álculos Gra;*ca,0o .os a.or"s 0" 9 s ɳ .*) s" ,ota )u" t*"," u, co2%orta2*",to 0" u,a "cuac*$, cua0r-t*ca > a%.*ca,0o a .a 1r-;*ca .a ;u,c*$, 0" "cuac*$, 0" r"1r"s*$, cua0r-t*ca ,os 0a 0*c5a "cuac*$, cua0r-t*ca co, .os a.or"s 0" a 4 > c8 ɳ liq +.,/ +.,0,/ +.,/1 +.,12 +.,33 +.4244 +.4+41 +.440 +.4,1 +.4,3+ +.444+
'+
89 8& 8' 8+ 8 8 8( 8 8 9
++8+ ɳ .*) & 998 ɳ .*) (8 Do,0" s" a@usta ta24*!, a: H9 ++8+ , co,0 & 998 ,co,0 (8 a
4
8 "c<9=
c
H sust*tu>",0o a.or"s 0" , co,0 ", "c <9= %ara ca0a a.or 0" 9 s" t*"," .os 0atos 0" >9 "%"r*2",ta."s > ta24*!, s" o4t*",", .os a.or"s 0" > & %or 0*;"r",c*a: ncond
98'&( 98'( 98' 98+9+ 98+9' 98+9 98+9 98+&9'
'+
89 8& 8' 8+ 8 8 8(
&+ e'p5
& e'p5 +- &+5
2 2.,4/2+4 2.44,1, 2.0/202,3 2.0303 2./,2+ 2.//,//0 2./30/04
+ 2./0,31/ 2.00/+/4 2.4,343/+ 2.424+ 2.,/33 2.,,/,,0 2.,24,4/
98+&&+ 98+&& 98+++9
8 8 9
2./3+1 2./3,,4, +
2.,21 2.,2//0 2
T",*",0o .os 0atos "%"r*2",ta."s 0" 9 ,co,0 ɳ .*) T"% H9 s" %ros*1u" a ca.cu.ar %ara ca0a "s%"c*" <9 > &= .os a.or"s "%"r*2",ta."s 0" P9sat > P&sat ɣ i
co, "cuac*$, 0" A,to*,"
>
9
ɣ i
co, LRM8
&
(onde “Pisat”#se calcula: Bi
Lo1
(
(onde +torr6+!!7%
)+ C
T ° C
i
Por .o ta,to: Para *loro)or!o especie +5 A1−
sat 9
P
B1 T ( ° C )+ C 1
8 "c<&=
Sus co,sta,t"s 0" A,to*," so,: A9
B9
8+ 99(8
C9 &&8&'&
Sust*tu>",0o ". a.or 0" t"2%"ratura "%"r*2",ta. ", .a "c<&= %ara ca0a a.or 0" 9 t","2os %or r"su.ta0o P9sat <"%= : '+
8 9*5 e'p5
89 8& 8' 8+ 8 8 8( 8
9 + + +( + + +(
P+sat !!7%5 e'p5 2/.1/343 /+.34,/, 0,1.++,20 02+.,3/+ 41,.12++1 4//.2+04 402.211 402.211 4//.2+04
8 9
+( '8
4//.2+04 01/.31+/
Para $etanol especie 5 A2−
sat &
P
B2 T ( ° C )+ C 2
8 "c<'=
Sus co,sta,t"s 0" A,to*," so,: A& B& 8( 9&8&(9
C& &'8(&
Sust*tu>",0o ". a.or 0" t"2%"ratura "%"r*2",ta. ", .a "c<'= %ara ca0a a.or 0" & t","2os %or r"su.ta0o P&sat <"%= : '6 + ' +5
9 8 8 8( 8 8 8+ 8' 8& 89
Do,0"
ɣ i
8 9*5 e'p5
9 + + +( + + +( +( '8
Psat !!7%5 e'p5 /21.4+ 0+0./4// 4,4.3311 ,31.1,2/ ,1+.+2/ ,/0./4 ,43.,42+3 ,43.,42+3 ,/0./4 ,/0./4 414.24301
s" ca.cu.a:
; * ; *L Ø i ^
>*PT*P*sat Ø i=1
Do,0" &iP86
ɣ i
^
ɣ i
'iPisat ;.. L<$ Le& de
E,to,c"s 0"s%"@a,0o a. co";*c*",t" 0" act**0a0 ɣ i
y i P
=
x i P i
ɣ i
:
T
sat
Por lo tanto# para *loro)or!o especie +5 ɣ 1
=
y 1 P
x 1 P1
T sat
0o,0" ". a.or 0" PT "s co,sta,t" > "s *1ua. a
"c<+=
22/1 Sust*tu>",0o .os 0atos 0" P 9sat <"%= PT >9 <"%= ", .a "c<+= %ara ca0a a.or 0" t","2os %or r"su.ta0o ɣ 1 ( exp) : 9
'+
&+
89 8& 8' 8+ 8 8 8( 8 8 9
8'+(9+ 8++(''( 8' 8((& 8'&&9 8'( 8(+ 8&9(& 8''&+' 9
Para $etanol especie 5
P+sat !!7%5 e'p5
(8+ 9(8+'' '899' 98'&9 +'899 +8(9+ +8(& +8(& +8(9+ +8(9+ 8(9
ɣ+ e'p5 2 ,.322+ .4,+101 .+311+ +.12/44 +.033,/+ +.4,/1/3 +./+120 +.21403 2.3/0/3/ 2.33//33
ɣ 2
=
y 2 P
x 2 P2
T sat
"c<=
0o,0" ". a.or 0" PT "s co,sta,t" > "s *1ua. a
22/1 Sust*tu>",0o .os 0atos 0" P &sat <"%= PT >& <"%= ", .a "c<= %ara ca0a a.or 0" t","2os %or r"su.ta0o ɣ 2 ( exp) : &
'
9 8 8 8( 8 8 8+ 8' 8& 89
Ca.cu.a,0o I, ɣ 1
ɣ 1
Psat !!7%5 e'p5
&
> I,
9 8&' 8&9+ 8+'+9 8+&+&(9 8'(( 8'''&' 8'&+'+ 8'(&(& 8'(( ɣ 2
8+(9 98+( +'+8& '8'& '98(9( '8&&+& '+8'+9 '+8'+9 '8&&+& '8&&+& ++8+
%ara ca0a a.or 0"
s 9 co2o ta24*!, I,
ɣ 2
ɣ e'p5 2.3/+4/, 2.1,1+0 2.313/3 2.323/+ +.21310 +.+14014+ +.42122/+ +.11/02/ .4/0,20 4.3++/00 2
ɣ 1
ɣ 2
> 1ra;*ca,0o I,
s & s" ,ota )u" a24as t*",", u,
co2%orta2*",to 0" u,a "cuac*$, cua0r-t*ca > a%.*ca,0o a .as 1r-;*cas .a ;u,c*$, 0" "cuac*$, 0" r"1r"s*$, cua0r-t*ca ,os 0a 0*c5as "cuac*o,"s cua0r-t*cas co, .os a.or"s 0" a 4 > c8 a= I,
ɣ 1
a
8+ 9& &8&9 98' 4
c
Do,0" 9 %ara sacar ". a.or 0" c =+ 98' 4= I,
ɣ 2
a
'8&((&& 8&+&& 98+' 4
c
Do,0" & %ara sacar ". a.or 0" c =+ 98+'
T",*",0o ". a.or 0" A9& > A&9 s" ca.cu.a I,
ɣ 1
I,
ɣ 2
u0a
0" .a "cuac*$, 0" Vaa, Laar: Inɣ 1=
A12
[
1+
A 12 x 1 A 21 x 2
Inɣ 2=
]
2
"c<=
A21
[
1+
A 21 x 2 A 12 x 1
]
2
"c<(=
Sust*tu>",0o .os 0atos 0" A 12 A 21 ", .a "c< > (= %ara ca0a a.or corr"s%o,0*",t" 0" 9 > & t","2os %or r"su.ta0o .os 0atos 0" I, I,
ɣ 2
(teo ) >
(teo ) : '+
'
89 8& 8' 8+ 8 8 8( 8 8 9
Ca.cu.a,0o ca0a a.or 0" ɣ i
ɣ 1
n
T",*",0o: >9PT
ɣ 1
9 P9sat
>&PT
ɣ 2
& P&sat
9 8 8 8( 8 8 8+ 8' 8& 89
ɣ 1
nɣ+ teo5 +.,/11 +.+414/ 2.313133 2.12331 2./,4+3 2.4+/213 2.,,312/ 2.+3/+ 2.2342/3+ 2.2040// 2
ɣ 2
0o,0" , "s ca0a a.or 0" I,
ɣ i
nɣ teo5 2 2.2+211 2.24,0,,/ 2.+244/4 2.+31,4 2.,,+140+ 2.0+3/ 2.0+,,/3 +.203203 +.40232,4 +.340,
PT
ɣ 1
ɣ 2
9 P9sat
& P&sat
A%.*ca,0o .a "cuac*$, 0" A,to*," > 0"s%"@a,0o .as P sat .a "cuac*$, a,t"r*or )u"0a co2o: T
P
ɣ 1
X9
A 1
10
−
B1
+
T C 1
ɣ 2
A2−
<99= 10
B2 T + C 2
88 "c<= Do,0" PT "s co,sta,t":
PT22/1
Sust*tu>",0o .os 0atos 0"
{ɣ} rsub {1} y {ɣ} rsub {2}
9 .as co,sta,t"s 0"
A,to*," %ara ca0a "s%"c*" >a %u"stos a,t"r*or2",t" ", .a "c<= s" o4t*",", .os a.or"s 0" t"2%"ratura t"$r*ca8 Para ",co,trar ". a.or 0" .as t"2%"raturas t"$r*cas s" ,"c"s*ta r"so."r .a "cuac*$, <= )u" "st- *1ua.a0a a 22/18 >+
ɣ+ teo5
>
89 8& 8' 8+ 8 8 8( 8 8 9
9 8 8 8( 8 8 8+ 8' 8& 89
'8''999 '8&+9 &8'9 &8&+'+9&99 98+& 98&(+' 98'&&++ 98&9(9' 98'' 98&(''( 9
ɣ teo5
9 989&9' 98+++9 9899(' 98&9'( 98''' 98(9(9' &899'&& &8'( +8&( 8(''
8 9*5 teo5 01.2,303 0+./,+4+ 41.4+2 4/.4001 40.0,321 40.+343 40.2342 40.+13/ 40.43143 4/.34+43 0,.422/,
Co,oc*",0o .os a.or"s 0" t"2%"ratura t"$r*ca s" ca.cu.a .as P 9sat P&sat
>+
8 9*5 teo5
89
8' 98'9+(9
P+sat !!7%5 teo5 /14./0+,4 002.+,32,
Psat !!7%5 teo5 010 44/.3001
8& 8' 8+ 8 8 8( 8 8 9
+8&+9&( +8+(( +8(' +89+(& +8(+& +89&( +8+(+ +8&+9+ '8+&'
Co,oc*",0o .os 0atos 0" P 9sat
41.3330 40./22+4 44,.+0,++ 4,.200,/ 4,0.+3 4,/.22,/4 44+./,,30 4/0.4444 010 ɣ 1 ( teo )
,10.1+ ,0/.02/3 ,4.0240 ,,/.30/0 ,,0.,4,1 ,,0.31+04 ,4+.,2333 ,/4.2224 41.244,
s" ca.cu.a .os a.or"s 0" >9
t"o co, LRM: y 1=
ɣ 1 x1 P1
P
sat
8 "c<=
T
Do,0" PT "s co,sta,t": PT22/1 P+sat !!7%5 teo5
'+
89 8& 8' 8+ 8 8 8( 8 8 9
+89'+ 89'' +(8 +(89+ ++'89'999 +'(8' +'8&9&( +'8'+ ++98'' +8+&+++
ɣ+teo5
'8''999 '8&+9 &8'& &8&+'+9&9 98+' 98&(+ 98'&&+ 98&9(9 98' 98&('+ 9
?+ teo5
8'&(' 8++'+ 8&++& 8(9'+9 8+&( 89(9'& 8'+(( 8'9+' 8('++ 9
8abla de datos e'peri!entales
nliq
98'&( 98'' 98'& 98' & 98'& 98++ + 98+9+ 98+&+ 98+'& 98+' 9 98+++ 9
8 9*5 “e'p ”
'+
ncond
89
9
8&
+
8'
+
8+
+(
8
+
8
+
8(
+(
8
+(
8
'8
9 9
98'&( 98'( 98' 98+9 + 98+9' 98+9 98+9 98+&9 ' 98+&& + 98+&& 98+++ 9
&+ e'p5
8'+(9 + 8++('' ( 8' 8((& 8'&&9 8'( 8( + 8&9(& 8''&+ ' 9
P+sat !!7%5 “e'p”
(8+ 9(8+' ' '899' 98'& 9 +'899 +8(9 + +8(& +8(& +8(9 + +8(9 + 8(9
Psat !!7%5 e'p
ɣ2 (exp)
ɣ+ “e'p”
8+(9
98+( +'+8 & '8'& '98(9( '8&&+ & '+8'+9 '+8'+9 '8&&+ & '8&&+ & ++8+
'8&(& 9 &8+'9& &89(( 9 98+&+ ( 98(' 9 98+'( 98&9 & 98+& 8& 8&
89+& ' 8&&'9 8& ( 8&& 9 98&( 989++ 9 98+ 9 98( &8+' +89&9
8abla de resultados >+
>
89 8& 8' 8+ 8 8 8( 8
8 9*5 teo5
9 8 8 8( 8 8 8+ 8' 8&
8' 98'9+(9 +8&+9&( +8+(( +8(' +89+(& +8(+& +89&( +8+(+
P+sat !!7%5 teo5
+89'+ 89'' +(8 +(89+ ++'89'99 +'(8' +'8&9&( +'8'+ ++98''
Psat !!7%5 teo5
?+ teo5
++8( '8((&9 '8( '+&8(+ ''8( ''8&'+' ''89+ '+98'
8'&(' 8++'+ 8&++& 8(9'+9 8+&( 89(9'& 8'+(( 8'9+'
8 9
89
+8&+9+ '8+&'
+8+&+++
@rá)icas @rá)ica +: “*urva de calibración” “ɳ L"quido5 vs '+” ɳ liq
'+
89 8& 8' 8+ 8 8 8( 8 8 9
98'&( 98'' 98'& 98'& 98'& 98+++ 98+9+ 98+&+ 98+'& 98+'9 98+++9
'+8+( +&8++'&
8('++ 9
1.46 1.44 1.42 1.4 1.38
ɳ liq
1.36 1.34 1.32 1.3 1.28 1.26 0
0.1
0.2
0.3
0.4
0.5
0.6
'+
@rá)ica : “'+ vs ɳ L"quido5” ɳ liq
98'&( 98'' 98'& 98'& 98'& 98+++ 98+9+ 98+&+ 98+'& 98+'9 98+++9
'+
89 8& 8' 8+ 8 8 8( 8 8 9
0.7
0.8
0.9
1
1 f(x) = 44.85x^2 - 116.09x + 75.07
0.9 0.8 0.7 0.6
'+
0.5 x1
0.4
Polynomial (x1)
0.3 0.2 0.1 0 1.32
1.34
1.36
1.38
1.4
1.42
1.44
1.46
ɳ L"quido5
A%.*ca,0o a "sta 1r-;*ca .a ;u,c*$, 0" "cuac*$, 0" r"1r"s*$, cua0r-t*ca ,os 0a .a "cuac*$, cua0r-t*ca co, .os a.or"s 0" a 4 > c8 H9 ++8+, co,0& 998 , co,0 (8 a
4
c
@rá)ica ,: “8 e'p 9*5 vs '+ l"quido5# &+ e'p5 vapor5” &+ e'p5
8'+(9 + 8++('' ( 8' 8((&
>+
8 e'p5 9*5
89
8&
9
8'
+
8+
+
8'&&9 8'( 8( + 8&9(& 8''&+ ' 9
8 8
+( +
8(
+
8
+(
8
+(
9
'8
70
65
60
55
8 e'p 9*5
50 x1 y1
45
40
35
30 0
0.2
0.4
0.6
0.8
'+ l"quido5# &+ e'p5 vapor5
@rá)ica 4: “8 teo5 9*5 vs '+ l"quido5# &+ teo5 vapor5” >+
?+ teo5
8 9*5 teo5
1
89 8& 8' 8+ 8 8 8( 8 8 9
8'&(' 8++'+ 8&++& 8(9'+9 8+&( 89(9'& 8'+(( 8'9+' 8('++ 9
8' 98'9+(9 +8&+9&( +8+(( +8(' +89+(& +8(+& +89&( +8+(+ +8&+9+ '8+&'
70
65
60
55
8 teo5 9*5
50 Y x
45
40
35
30 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
'+ l"quido5# &+ teo5 vapor5
@rá)ica 0: “&+e'p5# &+ teó5 vs '+”
0.8
0.9
1
X1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
?+ teo5
&+ e'p5
8'&(' 8++'+ 8&++& 8(9'+9 8+&( 89(9'& 8'+(( 8'9+' 8('++ 9
2 2.,4/2+4 2.44,1, 2.0/202,3 2.0303 2./,2+ 2.//,//0 2./30/04 2./3+1 2./3,,4, + 1
0.9 0.8 0.7 0.6
&+e'p5# &+ teó5
0.5 Y1T! Y1"P
0.4
#
0.3 0.2 0.1 0 0
0.1
0.2
0.3
0.4
0.5
'+
0.6
0.7
0.8
0.9
1
@rá)ica /: “n '+
n
89 8& 8' 8+ 8 8 8( 8 8 9
ɣ 1
vs '+”
ɣ 1
98999+ 8+&'& 8((&+ 89'+ 8+('+' 8'''9 8&'&+'+& 899+' 8'+(+( 8''((( f(x) = 0.84x^2 - 2.25x + 1.37
1.1
0.9
0.7
nɣ
$ny1
0.5
Polynomial ($ny1) 0.3
0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-0.1 X1
A%.*ca,0o a "sta 1r-;*ca .a ;u,c*$, 0" "cuac*$, 0" r"1r"s*$, cua0r-t*ca ,os 0a .a "cuac*$, cua0r-t*ca co, .os a.or"s 0" a 4 > c8 I,>9 8+ 9& &8&9 98'
a
4
c @rá)ica : “n
>
vs '”
ɣ 2
n
9 8 8 8( 8 8 8+ 8' 8& 89
ɣ 2
8'''(+9 89' 8('(9 8&'(' 8&(9+ 89'9(& 8'+&9(+ 89+9+ 8&'9& 989(9+
1.6 1.4
f(x) = 3.28x^2 - 5.25x + 1.95
1.2 1 0.8
ɣ nAA
$n%2
0.6
Polynomial ($n%2)
0.4 0.2 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-0.2 X2
A%.*ca,0o a "sta 1r-;*ca .a ;u,c*$, 0" "cuac*$, 0" r"1r"s*$, cua0r-t*ca ,os 0a .a "cuac*$, cua0r-t*ca co, .os a.or"s 0" a 4 > c8
I,>9 8+ 9& &8&9 98' a
4
c Observaciones
For2a0as so.uc*o,"s 0" c.oro;or2o > 2"ta,o. co2o co2%u"sto u,o > 0os r"s%"ct*a2",t"8 S" 2*0*$ .a t"2%"ratura 0" 4ur4u@a 0" ca0a u,a 0" .as so.uc*o,"s a. *1ua. )u" .a co2%os*c*$, 0" .os a%or"s a %r"s*$, at2os;!r*ca8 Ut*.*#a,0o u, r";ract$2"tro 0" 2*0*$ .a r";racc*$, 0" ca0a u,a 0" .as susta,c*as %r*2"ro ", "sta0o %uro > 0"s%u!s ", 4as" a .as so.uc*o,"s ;or2a0as co, "stos r"act*os8 Ha 5"c5as .as so.uc*o,"s s" 0"st*.a4a, 5asta )u" s" %r"s",tara, .os %r*2"ros s*1,os 0" 4ur4u@as s" to2a4a u,a 2u"stra > s" o.3a a 2"0*ar su 3,0*c" 0" r";racc*$, 5ac*!,0os" a5ora u,a co2%arac*$, ",tr" 3,0*c"s 0" r";racc*$, > ,ota,0o )u" .os 0atos 5a43a, ca24*a0o .*1"ra2",t"8 A %art*r 0" .os 0atos "%"r*2",ta."s s" 0"t"r2*,$ ". co";*c*",t" 0" act**0a0 1a22a 9 0" ca0a co2%o,",t" ", ca0a so.uc*$, Co2o co,s"cu",c*a 0". a,-.*s*s 0" 0atos 0" ELV "%"r*2",ta."s "*st",t"s %ara susta,c*as 0" co,st*tuc*$, )u32*ca s"2"@a,t" ", so.uc*$, co, otra 0" r";"r",c*a s" 5a %o0*0o o4s"rar ". ";"cto 0" ca0a 1ru%o )u32*co co,st*tu>",t" 0" .a susta,c*a t*"," so4r" ". co2%orta2*",to 0" .a so.uc*$,8 U,a so.uc*$, co2o "sta s" co,s*0"ra co2o u,a 2"#c.a 0" 1ru%os > ,o co2o 2"#c.a 0" susta,c*as8 S" 1ra;*c$ 1a22a 9 > 1a22a & %or ". 2!to0o 0" .a 0*.uc*$, *,;*,*ta ". cua. co,s*st" ", )u" .a 0*so.uc*$, t*"," u,a co,c",trac*$, ta, %")u"a )u" t*",0" a c"ro > s" o4t*",", .os a.or"s 0" .os %ar-2"tros 0" .as "cuac*o,"s 0" Mar1u."s o Va, .aar > 0"s%u!s 0"t"r2*,a,0o .os a.or"s r")u"r*0os ta."s co2o .a t"2%"ratura 0" 4ur4u@a
*onclusiones
D" acu"r0o a u,a s"r*" 0" so.uc*o,"s %r"%ara0as 0" c.oro;or2o <9= > 2"ta,o. <&=? s" %u0o 2"0*r a ca0a u,a su t"2%"ratura 0" 4ur4u@a > .a co2%os*c*$, 0" .os a%or"s to0o "sto a %r"s*$, at2os;!r*ca8 D"t"r2*,a2os ". co";*c*",t" 0" act**0a0 <
ɣ
*= 0" ca0a co2%o,",t" ", ca0a
so.uc*$, a %art*r 0" .os 0atos "%"r*2",ta."s8 I,"st*1a2os ". 2o0".o 0" so.uc*$, co2%ara2os .os r"su.ta0os co, .os 0atos "%"r*2",ta."s 0" acu"r0o co, .a *,"st*1ac*$, r"a.*#a0a a,t"r*or2",t"8 Pu"sto )u" .as %ro%*"0a0"s 0" .a ;as" .3)u*0a so, *,s",s*4."s a ca24*os 2o0"ra0os 0" %r"s*$, .a %r"s*$, * so, ca,t*0a0"s susc"%t*4."s 0" s"r 2"0*0as "%"r*2",ta.2",t"8 E. co";*c*",t" 0" act**0a0 0" ca0a co2%o,",t" 0" .a so.uc*$, %u"0" o4t","rs" 0". "%"r*2",to8 Los 0atos o4t",*0os 0" W* o4t",*0os s" a@usta, a "cuac*o,"s 2at"2-t*cas "2%3r*cas o s"2*"2%3r*cas co2o .as 0" Mar1u."s Va, Laar > otras8
Biblio%ra)"a: SMIT/ 68M88? VAN NESS /8C8 ABBOTT M8M88<&=8 I,tro0ucc*$, a .a T"r2o0*,-2*ca %ara I,1",*"r3a Qu32*ca8 (Y8 E0*c*$, ", *,1.!s8 McGraZ /*.. S"r*"s8 Nu"a Hor8
•
SANDLER STANLEH I8 <9=8 T"r2o0*,-2*ca Qu32*ca > 0" I,1",*"r3a8 T"rc"ra "0*c*$, ", *,1.!s8 6o5, [*."> So,s I,c8 Nu"a Hor8
•
C/APRA STEVEN CANALE RAHMOND8 <9(=8 M!to0os Nu2!r*cos %ara I,1",*"ros8 Pr*2"ra E0*c*$, ", "s%ao.8 McGraZ /*.. Co8 M!*co8
•
*uestionario a5 (escribir el si%ni)icado )isco de la ecuación de la Le& de
E. cr*t"r*o 0" ")u*.*4r*o "s -.*0o %ara cua.)u*"r s*st"2a8 Por .o ta,to s" 0"4" cu2%.*r )u" .a *1ua.0a0 0" .as ;u1ac*0a0"s %arc*a."s 0". ca0a u,o 0" .os co2%o,",t"s ", a24as ;as"s > %ara "a.uar.as t","2os ar*as o%c*o,"s8 La 2-s co27, "s ". 2o0".o W \ ϕ8 Para ". cua.: ; * ; *L Ø i ^
>*PT*P*sat Ø i=1
Do,0" &iP86
ɣ i
^
ɣ i
'iPisat
H "sta "cuac*$, r"c*4" ". ,o24r" 0" Ecuac*$, 0" Raou.t 2o0*;*ca0a .a cua. %r"0*c" 2"@or ". ELV > %u"0" %r"0"c*r .a "*st",c*a 0" u, a#"$tro%o a 0*;"r",c*a 0" .a "rs*$, or*1*,a.8 b5 ndique cuales son las condiciones que validan la aplicación de la ecuación de la Le& de
Para %r"s*o,"s 4a@as 2o0"ra0as s" co,s*0"ra .a ,o *0"a.*0a0 0" .a ;as" .3)u*0a ", .a "cuac*$, or*1*,a. 0" Raou.t8 Su%o,"r )u" .a ;as" 1as"osa s" co2%orta co2o u,a so.uc*$, *0"a. Ø i=1 ^
&iP86
ɣ i
'iPisat
P8 La %r"s*$, tota. 0". s*st"2a ", ")u*.*4r*o ?+ Co2%os*c*$, ", .a ;as" a%or co2%u"sto 9 >+ Co2%os*c*$, ", .a ;as" L*)u*0a co2%u"sto 9 Pisat Pr"s*$, 0" a%or co2%u"sto 9 ɣ i
Co";*c*",t" 0" act**0a08
E. s*st"2a %r-ct*co 0" act**0a0"s > co";*c*",t"s 0" act**0a0 "s 7t*. %ara so.uc*o,"s ", .as )u" s$.o ". 0*so.",t" t*"," u,a ;racc*$, 2o. c"rca,a a .a u,*0a0: to0os .os so.utos "st-, %r"s",t"s ", ca,t*0a0"s r".at*a2",t" %")u"as8 Para u, s*st"2a 0" "st" t*%o "2%."a2os ". s*st"2a rac*o,a. %ara ". 0*so.",t" > ". s*st"2a %r-ct*co %ara .os so.utos8 Co,;or2" .a co,c",trac*$, 0" .os so.utos s" "2%o4r"c" ". co2%orta2*",to 0" cua.)u*"r so.uc*$, r"a. s" ac"rca a. co2%orta2*",to 0" .a so.uc*$, 0*.u*0a *0"a.8 c5 (escribir el si%ni)icado de Ciste!a de Equilibrio no deal
La act**0a0 rac*o,a. 0" .os co,st*tu>",t"s o.-t*."s 0" u,a 2"#c.a .3)u*0a %u"0" ca.cu.ars" ;-c*.2",t" 2*0*",0o .a %r"s*$, %arc*a. 0". co,st*tu>",t" ", .a ;as" a%or ", ")u*.*4r*o co, ". .3)u*0o8 Co2o ", ". ")u*.*4r*o .os %ot",c*a."s )u32*cos 0" ca0a co,st*tu>",t" 0"4", s"r *1ua."s ", .as ;as"s a%or > .3)u*0o8 La ")u*a.",c*a 0" .a act**0a0 r"s%"cto a. %ot",c*a. )u32*co "%r"sa0a %or u,a r".ac*$, "s .a %ro%*"0a0 ;u,0a2",ta. 0" .a act**0a08 La t"or3a 0". ")u*.*4r*o %o0r3a 0"sarro..ars" ", su tota.*0a0 ", ;u,c*$, 0" .as act**0a0"s 0" .as susta,c*as ", "# 0" 5ac"r.o ", ;u,c*$, 0" sus %ot",c*a."s )u32*cos8 Fas" 1as *0"a. ;as" .*)u*0a ,o *0"a. E. co";*c*",t" 0" act**0a0 "s u,a 2"0*0a 0". 1ra0o 0" 0*"r1",c*a 0". co2%orta2*",to 0" .a susta,c*a co, r"s%"cto a. *0"a. < ɣ =8
E, "st" 2!to0o .a ;as" .3)u*0a s" co,s*0"ra r"a. %or .o )u" s" a@usta co, ɣ *
N$t"s" )u" %ara "stos casos .a co,sta,t" 0" ")u*.*4r*o %asa a s"r ;u,c*$, 0" T P > X E, "sta ;as" 0" .a 2at"r*a s" %ro%orc*o,a ". a.or 0". co";*c*",t" 0" act**0a0 o s" 2u"stra ". 2o0".o 0" so.uc*$, 0" ;or2a s",c*..a8 M!to0o )u" to2a co2o 4as" .a ."> 0" Raou.t ". cua. s*r" %ara "a.uar 0" ;or2a s",c*..a .os %ro4."2as 0" ")u*.*4r*o "s a%ro%*a0o %ara 5*0rocar4uros .*1"ros > 0" 2o.!cu.as s*2%."s co, ;u"r#as *,t"r2o."cu.ar"s s",c*..as8
d5 (escriba la diná!ica de aplicación & li!itaciones de la Le& de
La r".ac*$, ",tr" .a %r"s*$, 0" a%or 0" ca0a co2%o,",t" ", u,a so.uc*$, *0"a. 0"%",0*",t" 0" .a %r"s*$, 0" a%or 0" ca0a co2%o,",t" *,0**0ua. > 0" .a ;racc*$, 2o.ar 0" ca0a co2%o,",t" ", .a so.uc*$,8 U,a 0"s*ac*$, %os*t*a 0" .a LRM ocurr" cua,0o .os co2%o,",t"s 0" .a 2"#c.a %r";*"r", "star c"rca 0" 2o.!cu.as 0" su 2*s2o t*%o ", .u1ar 0" "star c"rca 0" .as 2o.!cu.as 0". otro co2%o,",t"8 La 0"s*ac*$, ,"1at*a su"." %r"s",tars" ", so.uc*o,"s ", )u" .as 2o.!cu.as 0" 0*st*,tas c.as"s t*",0", a atra"rs" ",tr" s3 0*;*cu.ta,0o .a t",0",c*a a. "sca%" 0" .as 2o.!cu.as ", ". %roc"so 0" a%or*#ac*$,8 e5 (escriba el si%ni)icado )"sico del dia%ra!a 8'& para un siste!a binario no ideal.
La .3,"a r"cta r"%r"s",ta .as %r"s*o,"s a .as )u" .as 0os ;as"s "st-, ", ")u*.*4r*o ", ;u,c*$, 0" .a co2%os*c*$, 0" .a 0*so.uc*$, <=
