termo iii (práctica 4)

8/20/2019 Termo III (Práctica 4)

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PRACTICA No8 +

“Equilibrio 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 2"ta,o. .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" 0" act**0a0 co2%ara,0o.os r"su.ta0os co, .os 0atos "%"r*2",ta."s8

ntroducción teórica:


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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" C %ara

2uc5as susta,c*as8

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 0" B "s *0!,t*ca a .a )u" s" 0a ",tr" .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*!,


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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' %%8'9=8


5/37


6/37

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 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: PB /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.


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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 %araca0a co2%o,",t"8


8/37

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:


9/37

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 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


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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*osos* ,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 cua0ra0os8Los !odelos de $ar%ules & Van Laar s*r", %ara 0"scr*4*r RT9& GE $ RT GE0" 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 o0*;"r",c*a4."s ", 0*c5o *,t"ra.o .o cua. %"r2*t" o4t","r ;-c*.2",t" .as otrasar*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 %or9K& s" o4t*",":


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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,*2oscua0ra0os %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:


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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,*2oscua0ra0os8 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.a0as0*r"cta2",t"8


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Procedi!iento e'peri!ental:

a=8 Pr"%arar u,a s"r*" 0" so.uc*o,"s 0" c.oro;or2o 2"ta,o. a,otar.a: "s .a t"2%"ratura 0" 4ur4u@a80=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"ta0ota%-,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


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(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 .at"2%"ratura a24*",t" %ara 2"0*r ". 3,0*c" 0" r";racc*$,


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*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,/ 89+.,/1 8&+.,12 8'

+.,33 8++.4244 8+.4+41 8+.440 8(+.4,1 8+.4,3+ 8+.444+ 9

++8+ ɳ .*) & 998 ɳ .*) (8

Do,0" s" a@usta ta24*!, a:

H9 ++8+ ,co,0 & 998 ,co,0 (8 8 "c",0o a.or"s 0" ,co,0 ", "c & %or0*;"r",c*a:

ncond '+ &+ e'p5 & e'p5

+- &+5

98'&( 2 +98'( 89 2.,4/2+4 2./0,31/98' 8& 2.44,1, 2.00/+/4

98+9+ 8' 2.0/202,3 2.4,343/+98+9' 8+ 2.0303 2.424+98+9 8 2./,2+ 2.,/3398+9 8 2.//,//0 2.,,/,,098+&9' 8( 2./30/04 2.,24,4/


16/37

98+&&+ 8 2./3+1 2.,2198+&& 8 2./3,,4, 2.,2//098+++9 9 + 2

T",*",0o .os 0atos "%"r*2",ta."s 0" 9 ,co,0 ɳ .*) T"% H9 s" %ros*1u" aca.cu.ar %ara ca0a "s%"c*" &= .os a.or"s "%"r*2",ta."s 0" P9sat > P&sat

co, "cuac*$, 0" A,to*," ɣ i 9 > ɣ i

& co, LRM8

(onde “Pisat”#se calcula:

Lo1


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8 +( 4//.2+049 '8 01/.31+/

Para $etanol especie 5

P&sat


18/37

E,to,c"s 0"s%"@a,0o a. co";*c*",t" 0" act**0a0 ɣ i :

ɣ i= y i P

T

x i P isat

Por lo tanto# para *loro)or!o especie +5

ɣ 1= y1 P

T

x1 P1sat "c",0o .os 0atos 0" P9sat


19/37

ɣ 2= y2 P

T

x2 P2sat "c",0o .os 0atos 0" P&sat

I, ɣ 2 %ara ca0a a.or 0" ɣ 1 ɣ 2 > 1ra;*ca,0o I,

ɣ 1 s 9 co2o ta24*!, I, ɣ 2 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, .osa.or"s 0" a 4 > c8

a= I, ɣ 1 8+9& &8&9 98'

a 4 c

Do,0" 9 %ara sacar ". a.or 0" c=+ 98'

4= I, ɣ 2 '8&((&& 8&+&& 98+'

a 4 c

Do,0" & %ara sacar ". a.or 0" c=+ 98+'


20/37

T",*",0o ". a.or 0" A9& > A&9 s" ca.cu.a I, ɣ 1 u0a

0" .a "cuac*$, 0" Vaa, Laar:

Inɣ 1= A12

[1+ A12 x1

A21 x2 ]2

"c9PTɣ 1 9 P9sat

>&PT ɣ

2 & P&sat


21/37

PT ɣ 1 9 P9sat ɣ

2 & P&sat

A%.*ca,0o .a "cuac*$, 0" A,to*," > 0"s%"@a,0o .as Psat .a "cuac*$, a,t"r*or )u"0aco2o:

PT ɣ 1 X9 10 A

1− B1

T +C 1 ɣ 2 ",0o .os 0atos 0" { } rsub {1}ɣ y { } rsub {2}ɣ 9 .as co,sta,t"s 0"

A,to*," %ara ca0a "s%"c*" >a %u"stos a,t"r*or2",t" ", .a "c + teo5ɣ teo5ɣ 8 9*5teo5

9 '8''999 9 01.2,30389 8 '8&+9 989&9' 0+./,+4+8& 8 &8'9 98+++9 41.4+28' 8( &8&+'+9&99 9899(' 4/.40018+ 8 98+& 98&9'( 40.0,3218 8 98&(+' 98''' 40.+3438 8+ 98'&&++ 98(9(9' 40.23428( 8' 98&9(9' &899'&& 40.+13/8 8& 98'' &8'( 40.431438 89 98&(''( +8&( 4/.34+43

9 9 8('' 0,.422/,

Co,oc*",0o .os a.or"s 0" t"2%"ratura t"$r*ca s" ca.cu.a .as P 9sat + 8 9*5

teo5

P+sat !!7%5

teo5

Psat !!7%5

teo5

8' /14./0+,4 01089 98'9+(9 002.+,32, 44/.3001


22/37

8& +8&+9&( 41.3330 ,10.1+8' +8+(( 40./22+4 ,0/.02/38+ +8(' 44,.+0,++ ,4.02408 +89+(& 4,.200,/ ,,/.30/08 +8(+& 4,0.+3 ,,0.,4,1

8( +89&( 4,/.22,/4 ,,0.31+048 +8+(+ 44+./,,30 ,4+.,23338 +8&+9+ 4/0.4444 ,/4.2224

9 '8+&' 010 41.244,

Co,oc*",0o .os 0atos 0" P9sat 9

t"o co, LRM:

y1=ɣ 1 x1 P1

sat

PT 8 "c


23/37

nliq 8

9*5

“e'p

”

'+ ncond &+ e'p5 P+sat

!!7%5

“e'p”

Psat

!!7%5

e'p

ɣ+

“e'p”

ɣ2

(exp)

98'&(

98'&(

(8+

8+(9 89+&

'98''

89 98'(

8'+(9

+9(8+'

'98+(

'8&(&

98&&'9

98'&

9 8& 98' 8++(''

('899'

+'+8

&&8+'9&

8&

(98'

&+ 8' 98+9

+8'

98'&

9'8'&

&89((

98&&

998'&

+ 8+ 98+9'

8((&

+'899

'98(9(

98+&+

(98&(

98++

+

+( 8 98+9

8'&&9 +8(9

+

'8&&+

&

98('

9

989++

998+9+

+ 8 98+9

8'(

+8(&

'+8'+9

98+'(

98+

998+&+

+ 8( 98+&9

'8(

++8(&

'+8'+9

98&9

&98(

98+'&

+( 8 98+&&

+8&9(&

+8(9

+'8&&+

&98+& &8+'

98+'9

+( 8 98+&&

8''&+'

+8(9+

'8&&+&

8&

+89&9

98+++

9

'8 9

9

98+++

9

9 8(9

++8+

8&

8abla de resultados

>+ > 8 9*5

teo5

P+sat

!!7%5

teo5

Psat

!!7%5

teo5

?+

teo5

9 8' +89'+ 89 8 98'9+(9 89'' ++8( 8'&('

8& 8 +8&+9&( +(8 '8((&9 8++'+8' 8( +8+(( +(89+ '8( 8&++&8+ 8 +8(' ++'89'99 '+&8(+ 8(9'+98 8 +89+(& +'(8' ''8( 8+&(8 8+ +8(+& +'8&9&( ''8&'+' 89(9'&8( 8' +89&( +'8'+ ''89+ 8'+((8 8& +8+(+ ++98'' '+98' 8'9+'


24/37

8 89 +8&+9+ +8+&+++ '+8+( 8('++9 '8+&' +&8++'& 9

@rá)icas

@rá)ica +: “*urva de calibración”

“ ɳ L"quido5 vs '+”

'+ ɳ liq 98'&(

89 98''8& 98'&8' 98'&8+ 98'&8 98+++

8 98+9+8( 98+&+8 98+'&8 98+'9

9 98+++9


25/37

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

1.26

1.28

1.3

1.32

1.34

1.36

1.38

1.4

1.42

1.44

1.46

'+

liqɳ

@rá)ica : “'+ vs ɳ L"quido5”

ɳ liq '+98'&( 98'' 8998'& 8&98'& 8'98'& 8+98+++ 898+9+ 898+&+ 8(98+'& 898+'9 898+++9 9


26/37

1.32 1.34 1.36 1.38 1.4 1.42 1.44 1.46

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

f(x) = 44.85x^2 - 116.09x + 75.07

x1

Polynomial (x1)

L"quido5ɳ

'+

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 e'p5

9*5

8'+(9+

89

8++(''(

8& 9

8'

8' +

8((&

8+ +


27/37

8'&&9 8 +(8'(

8 +

8(+

8( +

8&9(&

8 +(

8''&+'

8 +(

9 9 '8

0 0.2 0.4 0.6 0.8 1

30

35

40

45

50

55

60

65

70

x1

y1

'+ l"quido5# &+ e'p5 vapor5

8 e'p 9*5

@rá)ica 4: “8 teo5 9*5 vs '+ l"quido5# &+ teo5 vapor5”

>+ ?+

teo5

8 9*5

teo5


28/37

8'89 8'&(' 98'9+(98& 8++'+ +8&+9&(8' 8&++& +8+((8+ 8(9'+9 +8('

8 8+&( +89+(&8 89(9'& +8(+&8( 8'+(( +89&(8 8'9+' +8+(+8 8('++ +8&+9+

9 9 '8+&'

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

30

35

40

45

50

55

60

65

70

Y

x

'+ l"quido5# &+ teo5 vapor5

8 teo5 9*5

@rá)ica 0: “&+e'p5# &+ teó5 vs '+”


29/37

X1 ?+

teo5

&+ e'p5

0 20.1 8'&(' 2.,4/2+40.2 8++'+ 2.44,1,

0.3 8&++& 2.0/202,30.4 8(9'+9 2.03030.5 8+&( 2./,2+0.6 89(9'& 2.//,//00.7 8'+(( 2./30/040.8 8'9+' 2./3+10.9 8('++ 2./3,,4,1 9 +

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Y1T!

Y1"P

#

'+

&+e'p5# &+ teó5


30/37

@rá)ica /: “n ɣ 1

vs '+”

'+n

ɣ 1

89 98999+

8& 8+&'&8' 8((&+8+ 89'+8 8+('+'8 8'''98( 8&'&+'+&8 899+'8 8'+(+(

9 8''(((

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.1

0.1

0.3

0.5

0.7

0.9

1.1 f(x) = 0.84x^2 - 2.25x + 1.37

$ny1Polynomial ($ny1)

X1

nɣ

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'


31/37

a 4 c

@rá)ica : “n ɣ

2 vs '”

>n

ɣ 2

9 8'''(+98 89'8 8('(98( 8&'('8 8&(9+8 89'9(&8+ 8'+&9(+8' 89+9+8& 8&'9&

89 989(9+

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

f(x) = 3.28x^2 - 5.25x + 1.95

$n%2

Polynomial ($n%2)

X2

nAAɣɣɣɣɣɣɣɣɣɣɣ

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


32/37

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 > 0osr"s%"ct*a2",t"8 S" 2*0*$ .a t"2%"ratura 0" 4ur4u@a 0" ca0a u,a 0" .asso.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*$, 0" ca0a u,a 0" .as susta,c*as%r*2"ro ", "sta0o %uro > 0"s%u!s ", 4as" a .as so.uc*o,"s ;or2a0as co, "stosr"act*os8 Ha 5"c5as .as so.uc*o,"s s" 0"st*.a4a, 5asta )u" s" %r"s",tara, .os%r*2"ros s*1,os 0" 4ur4u@as s" to2a4a u,a 2u"stra > s" o.3a a 2"0*ar su3,0*c" 0" r";racc*$, 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**0a01a22a 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 %arasusta,c*as 0" co,st*tuc*$, )u32*ca s"2"@a,t" ", so.uc*$, co, otra 0" r";"r",c*as" 5a %o0*0o o4s"rar ". ";"cto 0" ca0a 1ru%o )u32*co co,st*tu>",t" 0" .asusta,c*a t*"," so4r" ". co2%orta2*",to 0" .a so.uc*$,8 U,a so.uc*$, co2o "stas" 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" ac"ro > s" o4t*",", .os a.or"s 0" .os %ar-2"tros 0" .as "cuac*o,"s 0" Mar1u."s oVa, .aar > 0"s%u!s 0"t"r2*,a,0o .os a.or"s r")u"r*0os ta."s co2o .a t"2%"ratura0" 4ur4u@a


33/37

*onclusiones

D" acu"r0o a u,a s"r*" 0" so.uc*o,"s %r"%ara0as 0" c.oro;or2o 2"ta,o. co2%ara2os .os r"su.ta0os co, .os

0atos "%"r*2",ta."s 0" acu"r0o co, .a *,"st*1ac*$, r"a.*#a0a a,t"r*or2",t"8Pu"sto )u" .as %ro%*"0a0"s 0" .a ;as" .3)u*0a so, *,s",s*4."s a ca24*os2o0"ra0os 0" %r"s*$, .a %r"s*$, otras8


34/37

Biblio%ra)"a:

• SMIT/ 68M88? VAN NESS /8C8 ABBOTT M8M88 0" I,1",*"r3a8T"rc"ra "0*c*$, ", *,1.!s8 6o5, [*."> So,s I,c8 Nu"a Hor8

• C/APRA STEVEN CANALE RAHMOND8 %ara "a.uar.as t","2os ar*as o%c*o,"s8 La 2-s co27, "s ". 2o0".o W\ 8 Para ". cua.:ϕ

; * ; *

L

^ Ø i >*PT*P*sat

ɣ i

Do,0"^ Ø i=1

&iP86

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


35/37

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*. %araso.uc*o,"s ", .as )u" s$.o ". 0*so.",t" t*"," u,a ;racc*$, 2o. c"rca,a a .au,*0a0: to0os .os so.utos "st-, %r"s",t"s ", ca,t*0a0"s r".at*a2",t" %")u"as8Para 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*$, %arc*a. 0". co,st*tu>",t" ", .a ;as" a%or ", ")u*.*4r*o co, ". .3)u*0o8 Co2o ", ". ")u*.*4r*o .os %ot",c*a."s )u32*cos 0" ca0aco,st*tu>",t" 0"4", s"r *1ua."s ", .as ;as"s a%or > .3)u*0o8 La ")u*a.",c*a 0" .aact**0a0 r"s%"cto a. %ot",c*a. )u32*co "%r"sa0a %or u,a r".ac*$, "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


36/37

E, "st" 2!to0o .a ;as" .3)u*0a s" co,s*0"ra r"a. %or .o )u" s" a@usta co, ɣ *

0" Raou.t ". cua. s*r" %ara "a.uar 0" ;or2as",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 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" .as2o.!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*$,


37/37

Los %u,tos %or ",c*2a 0" .a .3,"a or )u" .a %r"s*$, 0"a%or= corr"s%o,0", a. .3)u*0o co2o ;as" "sta4." > .os %u,tos %or 0"4a@o 0" .a.3,"a .a ;racc*$,2o.ar ", ". a%or =

)5 (escriba el si%ni)icado )"sico del dia%ra!a P'& para un siste!a binario no

ideal.

Mu"stra ". co2%orta2*",to 0" .a co2%os*c*$, .3)u*0a > 1as"osa ", ;u,c*$, 0" .a%r"s*$, a u,a 7,*ca t"2%"ratura 0"t"r2*,a0a8 Para co,stru*r.o co,",*",t"2",t"

"s ,"c"sar*o 5ac"r %or .o 2",os & c-.cu.os Roc3o P o Bur4u@a P a "sat"2%"ratura 0"t"r2*,a0a

%5 (escriba el si%ni)icado del dia%ra!a '& para un siste!a binario no ideal

La cura 0" ")u*.*4r*o "s s*2%."2",t" .a 1r-;*ca 0" .a ;racc*$, 2o.ar 0".co2%o,",t" o.-t*. ", ;as" a%or = ;r",t" a .a ;racc*$, 2o.ar 0". 2*s2oco2%o,",t" ", .a ;as" .3)u*0a

termo iii (práctica 4)

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