Universidad Mayor de San S an Andrés Facultad de Ingeniería
QMC 206 L
DETERMINACIÓN DEL COEFICIENTE COEFI CIENTE DE EXP EXPANCIÓN ANCIÓN DE LOS GASES OBJETIVOS El objetivo que se persigue con esta primera práctica de laboratorio de Fisicoquímica es el de determinar determinar el coefciente de expansión térmica “α” y el coefciente de tensión “ β” !e pretende determinar el coefciente “ α” variando el volumen del gas "aire# en $unción de la temperatura a presión constante %ara la determinación del coefciente “ β” se pretende variar la presión del gas en $unción de la temperatura a volumen constante
FUNDAMENTO TEORICO Coefciente de expansión de os !ases " # &'arles en ()*) observó que el 'idrógeno+ aire y dióxido de carbono se expandían en igual proporción+ al calentarlos de , a (*, °&+ manteniendo la presión constante !in embargo+ $ue -ay . /ussac el primero que+ en (*,0+ encontró que todos los gases aumentaban igual volumen por grado de elevación térmica+ térmica+ y que tal incremento era aproximadamente aproximadamente (10)2(3 (10)2(3 ",,,244(# ",,,244(# Este valor corresponde corresponde al coefciente de expansión térica ! "# 5anto 5anto &'arles como -ay . /ussac 'icieron 'icieron medidas para una misma masa de gas+ manteniendo la misma presión+ encontrando encontrando que el volumen del gas variaba linealmente con la temperatura de acuerdo a la ecuación6 V
∂V = V 0 + * t ∂t
"(#
donde6
t $ temperatura "° % $ 7olumen "l# %& $ 7olumen a , °& 8E5E9:;<=&;>< 8E/ &?EF;&;E<5E 8E E@% E@%=<&;>< =<&;>< 8E /?! -=!E! A<;7 &B?CAE &?<59E9=! E8!?< =9;E/ %ágina 1
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Universidad Mayor de San S an Andrés Facultad de Ingeniería
QMC 206 L
-rafcando el volumen en $unción a la temperatura6 V (l)
V0
- 273.15
t (°C)
o
/os experimentos experimentos de &'arles y -ay . /ussac demostraron que el aumento relativo de volumen+ por cada aumento de una grado de temperatura+ era el mismo para todos los gases = este valor de denomina c$efciente de di%atación térica a & C ! $"# !iendo6 α =
∂V V 0 ∂t 1
"0#
9eemplaDando 9ee mplaDando en la la ecuación "(# se obtiene6 V
= V 0 + V 0 * α * t
"2#
? también6 1 = V 0α + t "# α /a ecuación "# expresa el volumen del gas en $unción del volumen a , °& y de la constante α+ que es la misma para todos los gases y es casi completamente independiente independiente de la presión a la cual se realiDan las V
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Universidad Mayor de San S an Andrés Facultad de Ingeniería
QMC 206 L
límite a presión cero (10)2(3 Entonces+ la ecuación "# sugiere una trans$ormación de coordenadas defniendo una nueva escala de temperatura “T” en $unción a la temperatura original “t” expresada en grados centígrados !iendo6 T =
1
α
+ t
"3#
teperat'ra a(s$%'ta para /a ecuación "3# se denomina esca%a de teperat'ra %$s )ases idea%es+ donde α y (1α son constantes para todos los gases y dependen de la escala de temperatura usada originalmente =si+ en la escala centígrada se tiene6 T (° K ) = t (°C ) + 273 .15
"4#
Finalmente+ la ecuación "# se trans$orma en6 V = V 0α T
")#
V = K * T
/ey de &'arles
%or tanto6
Entonces+ la /ey de &'arles establece que el volumen de un gas bajo presión constante varía de $orma proporcional a la temperatura absoluta en grados elvin "°# %ara dos puntos determinados se tendrá6 V 0 T 0
=
V T
= K
"*#
/a constante viene determinada por la presión+ la naturaleDa del gas y unidades de volumen Entonces tendrá distintos valores a distintas presiones y obtendremos una serie de rectas para cada presión constante+ cada una de las cuales
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Universidad Mayor de San S an Andrés Facultad de Ingeniería
QMC 206 L
V (l)
1 atm. 5 atm.
10 atm.
t (°C)
o
Coefciente de tensión de os !ases " # Este experimento se basa en la /ey de -ay H /ussac y consiste en medir las variaciones de la presión con la temperatura manteniendo siempre el mismo volumen para una masa de gas+ encontrando en esta $orma que esta variación corresponde a una $unción lineal
∂ P * t ∂t P
P = P 0 +
donde6
t $ temperatura "° P $ %resión "mmBg# P& $ %resión a , °&
P (mmHg)
"(#
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Universidad Mayor de San S an Andrés Facultad de Ingeniería
QMC 206 L
8e este experimento se observó que el incremento relativo de la presión por cada aumento de ( grado de temperatura era el mismo para todos los los gase gasesG sG a es este te valo valorr co cons nsta tant nte e se lo co cono noce ce co con n el nomb nombrre de c$efciente de increent$ de presión a & C#
β =
∂ P P 0 ∂t V 1
"0#
9eemplaDando 9ee mplaDando "0# en "(# se tiene6 P = P 0 (1 + β * t )
"2#
!iendo el valor de β I (10)23 I (15 , 9ealiDando 9ealiDando operaciones se obtiene6 1 + t β
P = P 0 * β
P = K * t
"#
/ey de -ay H /ussac
Entonces la /ey de -ay . /ussac establece que la presión de un gas
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Universidad Mayor de San S an Andrés Facultad de Ingeniería
QMC 206 L
8onde el valor de se serrá distinto para ara distintos volJmenes y obte obtend ndrrem emos os una una se seri rie e de rec ecta tas+ s+ ca cada da una una para para ca cada da volu volume men n constante y cada una de ellas se denomina isóc$ra+ verifcándose que la pendiente es mayor cuanto menor es el volumen
P (atm)
10 l.
40 l.
110 l.
o
t (°C)
REACTIVOS * MATERIA+ES En esta práctica+ se usarán los siguientes materiales6 • • • • • •
( Equipo completo para gases ( 5ermómetro de mercurio de .(, a (,, °& ( Bornilla eléctrica ( 9ecipiente de aluminio ( 7aso de precipitados de ,, ml Flexómetro
5ambién 5ambién se usaran los siguientes reactivos6 reactivos6 • •
&loruro de !odio =gua
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Universidad Mayor de San S an Andrés Facultad de Ingeniería
QMC 206 L
Coefciente de expansión de os !ases " # •
•
• • • • • •
:ontar el equipo para gases En la bureta iDquierda existe una columna de aire de aproximadamente 0, cm /a altura B ajustada de la columna de aire en la bur bureta eta iDqu iDquie ierd rda a dete determ rmin inar ara a el volu volume men n de gas gas contenido &ale &a lent ntar ar la co colu lumn mna a de air aire poni ponien endo do en el tubo tubo anc'o+ agua a la temperatura de ebullición Esperar que la temperatura estabilice el sistema 8esliDar la bureta derec'a 'asta que las columnas de mercurio de ambas buretas estén a la misma altura :edir ' y t de la columna de aire &ambiar el agua del tubo anc'o por otra a menor temperatura "unos (, °& menos# 9epetir todo lo anterior 'asta legar a la temperatura máss baja má baja posi posibl ble e Esto Esto Jlti Jltimo mo se logr logra a co colo loca cand ndo o 'ielo picado
Coefciente de tensión de os !ases " # :ontar el equipo para gases Fijar la altura inicial B , de la columna gaseosa Esto determinará el volumen constante de trabajo • &alentar la columna de aire colocando agua a temperatura de ebullición dentro del tubo anc'o • Esperar que la temperatura estabilice el sistema • 8esliDar la bureta derec'a 'asta que el menisco de la • •
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Universidad Mayor de San S an Andrés Facultad de Ingeniería
QMC 206 L
TEMPERATURA TEMPERATURA - VOLUM EN ,+,,2
,+,,03
,+,,0
] l [ n e ,+,,(3 m u l o v
,+,,(
y = 1E-05x + 0,0015
,+,,,3
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Universidad Mayor de San S an Andrés Facultad de Ingeniería 61 55.5 52.5 45.5 41.5 34.5 30.5 26.5 22.5 18.5 15.5 13 4 1 -16
QMC 206 L 18.3 17.8 17.5 16.3 16 15.1 14.5 14.2 13.7 13.4 13 12.8 12.4 12.3 11.3
0.00229965 0.00223682 0.00219912 0.00204832 0.00201062 0.00189753 0.00182213 0.00178443 0.0017216 0.0016839 0.00163363 0.0016085 0.00155823 0.00154567 0.00142
&omo se puede observar+ el gráfco traDado está basado en los datos de la tabla 5emperatura . =ltura . 7olumen El volumen en litros $ue 'allado aplicando a cada altura "de aire# la siguiente $ormula6 V [ l ] =
H [ cm ] * Π * (0.4[ cm ]) 2 4 * 1000
El diámetro del tubo es de , cm "'oja de datos# y el $actor de división (,,, se incluye para trans$ormar los centímetros cJbicos en decímetros decímetros cJbicos+ es decir litros 8ic'a $ormula $ue aplicada directamente en E@&E/ /a estimación lineal por medio de mínimos cuadrados+ 'ec'a también directamente por E@&E/+ arroja los siguientes resultados6 R = 0.9836000
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Universidad Mayor de San S an Andrés Facultad de Ingeniería
QMC 206 L
α =
1 0.0015
(1.155 * 10 ) −5
α = 0.0077
Deterinar )r4fcaente )r4fcaente 5 ana%1ticaente e% cer$ a(s$%'t$# ANAL(TICAMENTE)* !e deduce con la ecuación de la recta isóbara+ reemplaDamos 7 I ,+ y despejamos t V
= 0.0015 + 1.155 * 10 −5 * t
0
= 0.0015 + 1.155 * 10−5 * t
t = −
0.0015 1.155 * 10 − 5
t = −129 .87 [ C ]
GR+FICAMENTE)* Extrapolamos la recta ajustada 'acia atrás y marcamos la intersección de la misma con el eje x "temperatura#
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Universidad Mayor de San S an Andrés Facultad de Ingeniería
QMC 206 L
EXTRAPOLACION DE LA ECUACION DE LA IO!ARA
,+,,2
,+,,03
,+,,0
,+,,(3
] l [ n e m u l o v
,+,,(
,+,,,3
, H 0,,
H (3,
H (,,
H 3,
,
3,
(,,
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Universidad Mayor de San S an Andrés Facultad de Ingeniería
QMC 206 L
Deterine %a c$nstante de pr$p$rci$na%idad# pr$p$rci$na%idad# %artimos de la relación6 K = α V 0
K = 0.0077 * 0.0015
678#899:8& ;9 !e puede decir+ que la constante es la constante “L” “L” de la ecuación linealiDada de la isóbara
Deterine e% /$%'en de% )as a <9& C 9ecurrimos 9ecurrimos a la ecuación de la recta ajustada y reemplaDamos reemplaDamos tI03, V
= 0.0015 + 1.155 * 10 −5 * t
V = 0.0015 + 1.155 * 10 −5 * 250
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Universidad Mayor de San S an Andrés Facultad de Ingeniería
QMC 206 L
El valor de al$a es prácticamente independiente de la presión a la que se realiDan las medidas "teóricamente# %ero dada la enorme di$erencia que se tiene con el valor bibliográfco+ me animaria a decir que este valor de al$a es solo valido para el experimento realiDado en /a %aD y en las condiciones del 8;= de realiDación
Coefciente de tensión de os !ases " # +%e/ar %as ,resi$nes Man$étricas a ,resi$nes A(s$%'tas#
N ° 1
Altura H [cmHg]
Presión Absoluta Absoluta [mmHg]
N °
Altura [cmHg]
Presión Absoluta Absoluta [mmHg]
19.3
688
10
3.8
533
18.3
6!8
.3
518
11
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Universidad Mayor de San S an Andrés Facultad de Ingeniería
QMC 206 L
.rafcar , /s# V c$n %$s dat$s $(tenid$s en e% %a($rat$ri$#MNO PREION - TEMPERATURA TEMPERATURA ),,
4,,
3,,
E,,
] % $ m m [
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Universidad Mayor de San S an Andrés Facultad de Ingeniería
QMC 206 L
A0'star %$s dat$s dat$s ediante M1ni$s M1ni$s C'adrad$s# %rimero construyamos la tabla 5emperatura . %resión &abe recordar que el anterior gráfco se basa en la misma tabla Teperat' ra 2 C3 2 C3
,resión 2)3
83 72 61 55.5 52.5 45.5 41.5 34.5 30.5 26.5 22.5 18.5 15.5 13 4 1 -16
688 678 659 650 635 597 583 554 543 533 518 508 499 493 483 470 441
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Universidad Mayor de San S an Andrés Facultad de Ingeniería
QMC 206 L
GR+FICAMENTE)* Extrapolamo la r!"ta a#$ta%a &a"'a atr mar"amo la '*t!r!""'+* %! la m'ma "o* !l !#! x (t!mp!rat$ra). PREION PREION - TEM TEM PERATUR PERATURA A 700
600
500
y = 2,901x + 464,97 400
] % $ m [m
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Universidad Mayor de San S an Andrés Facultad de Ingeniería
QMC 206 L β = β = β
=
∂ P P 0 ∂t V 1
1 464.97
( 2.901) V
,,,402K
Deterine %a c$nstante de pr$p$rci$na%idad# pr$p$rci$na%idad# !e determina directamente comparando la ecuación de la isócora linealiDada El valor de es el de la constante de regresión “L” 5omando en cuenta un disePo lineal6
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Universidad Mayor de San S an Andrés Facultad de Ingeniería
QMC 206 L
Babiendo realiDado esta experiencia y concluido el análisis de los datos rec ecog ogid idos os en el labo labora rato tori rio+ o+ se pudi pudier eron on lleg llegar ar a las las sigu siguie ient ntes es conclusiones6 =l comparar los valores nominales de los coefcientes con los resultados experimentales+ se encuentra una di$erencia grande Qustifcable+ si se quie quierre+ debi debido do a cir circuns cunsta tanc ncia iass exce cepc pcio iona nale less de un ma mane nejo jo no satis$actorio del equipo CuiDas seria bueno en próximas experiencias el armado de un papel milimetrado junto al equipo para poder goDar de una mayor precisión al momento de realiDar las lecturas 5ambién creo que se podria 'acer una estudio de errores entre di$erentes lecturas de di$erentes individuos "leer mas veces los instrumentos# =Jn cuando el resultado analítico de la experiencia no $ue del todo
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Universidad Mayor de San S an Andrés Facultad de Ingeniería •
&A9!? 8E F;!;&?CAS:;&= E@%E9;:E<5=/ 8aniels+ FarringtonG FarringtonG =lberty+ 9obert =G Tilliams+ QT QT
ANE-OS DETERMINACIN DE+ COEFICIENTE DE E-,ANSIN !G" Montar equio ara e! exeri"ento
#a!entar !a $o!u"na de aire
QMC 206 L
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Universidad Mayor de San S an Andrés Facultad de Ingeniería
DETERMINACIN DE+ COEFICIENTE DE TENSIN !H" Montar equio ara e! exeri"ento
i/ar !a a!tura ini$ia! *+ o, de !a $o!u"na de aire
QMC 206 L