Difusividad Másica en Gases

8/18/2019 Difusividad Másica en Gases

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Universidad Nacional del CallaoDifusividad Másica en

Gases

ÍNDICE

INTRODUCCIÓN……………………………………………………

I. MARCO TEÓRICO…………………………………………………II. EQUIPOS Y MATERIALES…………………………………………III. PROCEDIMIENTO EXPERIMENTAL………………………………IV. OBSERVACIONES EXPERIMENTALES…………………………V. RESULTADOS OBTENIDOS Y CALCULOS ……………………VI. ANÁLISIS DE RESULTADOS………………………………………VII. CONCLUSIONES……………………………………………………VIII. REFERENCIA BIBLIOGRÁFICA…………………………………

L !"# $"#%" &' I()'(%'#* Q+*,%- II 1


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Gases

INTRODUCCIÓN

L &% +/%0%& & " -"' %-%'($' &' &% +/% ( '/ +( #" %'& &&' '(&' &' $', '# $+# #'/% ( 6 &' ( $+# '7 &' "/ -", "('($'/'8 #'/%"('/ # - -+ # &% +/%0%& & -+ (&" (" /' -+'($ '8 '#%,'($ '/ '/$ ( ! / & / '( $'"#* -%(:$%- &' "/ ) /'/.

;%#-< ' &'# B%#& 6 S "$7 +$% %7 (&" ' "$'(-% &' L'(( #'0 + # %( +'(-% &' / +'#7 / %($'#," '-+ #'/ '(-"($# #"( +(

&'-+ & -"' %-%'($' &' &% +/% ( -"##'/ "(&%'($' #'> / )," :-+ / (" " #'/ (" #' -$%0 / $', '# $+# / 6 #'/%"('/ ,"&'# & /.

E( ' #'/'($' %( "#,' /' < # +/" &' "/ & $"/ $", &"/ '8 '#%,'($ ,'($''( ' LOPU # - -+ # &% +/%0%& & &' -'$"( '( '/$'/$ -%"( #%".

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Gases

C"(/%&'#',"/ &"/ /%/$', / S1 6 S2 ,%/, $', '# $+# 6 - 7 %($'#- ,!% # #$*-+ /. S% < 6 +( - ,!%" '( '('#)* "$'(-% &' +

"# '>', " 1 2 +( +>" &' '('#)* /' #"&+-%# #$%# &' S1 S2( $+# '7 /%', #' #' %'#' ! >" -"(/+," &' '('#)* 6 , 8%, '($#" * .

A+(5+' "/ &% '#'($'/ /%/$', / '/$ ( '( '5+% %!#%" $"& 0* < 6 )+ 5$# 0:/ &' ,',!# ( /',% '#,' ! '. A/* 5+' /% -" "# ($' /' -" "- '( '/%/$', &' A -"( ' $%', " /'#* &' %)+ -" "# # ' /%/$', B.

D% +/% ( ," '-+ # /' &'/-#%!' $* %- ,'($' , $', $%- ,'($' +$% %7 (&&' &% +/% ( &' F%- .

DIFU IÓN MO!ECU!AR EN GA ET# (/ "#$' &' , $'#% '( ' *5+%&" '/$ (- &" " $# 0:/ &' # -%"(

+%&" '( +( +>" ,%( # /' #"&+-' "# -", #$%,'($"/ &6 -'($'/ &D"/ -", #$%,%'($"/ /' # &"/ "# #$%-% ( 5+' -"($%'(' "/ ) /'/ +#B /' +'&' #'0'# 5+' ' ,"0%,%'($" ' $"#%" &' $"& / / ," :-+

L !"# $"#%" &' I()'(%'#* Q+*,%- II 4


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Figura 2: Ilustración de la difusión molecular en gases (Fuente: wikispaces.com)


Gases

#"&+-' &' , ('# 5+' &'/ +:/ &' +( '#*"&" / ," :-+ / /' '(-+'($# ( &%/$ (-% &' /+/ "/%-%"('/ "#%)%( '/.

S% /' ' %,%( #$%-% ( )+( / ," :-+ / &' +( ,"0%,%'($" < -"-+ & "# B /+ ( ,'#" &' '(&' &' ( ,'#" &' ," :-+ / '( ' +($-"(/%&'# &". A ,%/," $%', " / ," :-+ / &' B /' &% +(&'( < -% #

($'#%"#,'($' "-+ &"/ "# +# A. A($'/ &' '/$' +($" '( ' $%', " +(0 #% -% ( )# &+ '( -"(-'($# -% ( &' A /' #"&+-' " #)" &&'/%)( &" 8 5+' /' +(' "/ -", #$%,%'($"/ "#%)%( '/. E/$ 0 #'8 #'/ , $', $%- ,'($' ?&CA &8 &"(&' CA '/ -"(-'($# -% ( &' A./%)(" (') $%0" /' &'!' 5+' -"(-'($# -% ( &' A &%/,%(+6' ,'&%&

+,'($ &%/$ (-% &' / 8. D' ,%/," ,"&" 0 #% -% ( '( -"&' ) / B '/ ?&CB &8. L 0' "-%& & &' &% +/% ( &' A NA &)# &%'($' &' -"(-'($# -% ( 6 0' "-%& & #",'&%" -"( 5+' / ,"

A /' ,+'0' '( &%#'--% ( 8.

!E" DE FIC#

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Gases

L '8 '#%'(-% ("/ &',+'/$# 5+' -+ (&" !#%,"/ +( # /-" &' '# +,' " &-+ 5+%'# "$#" *5+%&" 0" $% "&',"/ " '# " # %& ,'($' '(-'## &". D'-%,"/ 5+' / ," :-+ / &' *5+%&" &'/ +:/ &' '0 "#

&% +(&'( "# ' %#' &%/$#%!+6:(&"/' '( $"&" ' '/ -%" -%#-+(& ($"-+##' /% -" "- ,"/ +( $'## ( &' 7 - # '( +( 0 /" &' )+ / ," :-+/ - #"/ /' &% +(&'( "# $"&" ' )+ . E/$"/ 6 "$#"/ '>', "/ ("/ ,+'/$#5+' # 5+' $'() +) # ' '( ,'(" &' &% +/% ( &%/$#%!+-%," :-+ / (" &'!' /'#


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Gases

V #% / '-+ -%"('/ /',%', *#%- / /%,% #'/ ($'#%"# /' < ( &'&+-% $'"#* -%(:$%- -"," ! /'. F+ '# S-+/$' &' +( -+#0 "/ & $"/ '8 '#%,'($ '/ /'5+%! '/

D"(&' DAB $%'(' / +(%& &'/ ,2 / T '/ $', '# $+# !/" +$ '( J 6#'/% ( P '/$ & & '( $, / '# /. L"/ $:#,%("/ X0 /"( /+, &' "/

0" ,'('/ $ ,%-"/ &' &% +/% ( &' $"&"/ "/ ' ','($"/ &' - & ," :-+ $ ! 1 . S' #' "#$ 5+' '-+ -% ( &' F+ '# '$ FSG #'&%-' &&'($#" &' +( , #)'( &' '##"# %( '#%"# K -"( #'/ '-$" 0 "#'/

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Fuente: Gu as de laboratorio de operaciones unitarias II ! "amiro #etancourt Gra$ales


Gases

'8 '#%,'($ '/ 6 /' +'&' +/ # $ ($" # ) /'/ " #'/ -"," # ) /'/ ("" #'/.

C< , ( 6 E(/ ") $# ! > (&" &' "#, %(&' '(&%'($' #' -%"( #"( &' / #" %'& &'/ &' "/ ) /'/ -"( / +'#7 / 5+' -$ ( '($#' / ," :-+

U/ (&" ' "$'(-% &' L'(( #& ="('/ # #' -%"( # / +'#7 / &' 6 #' + /% ( '($#' $","/ ;%#/-< %' &'# B%#& 6 S "$7 &'/ ##"/%)+%'($' '-+ -% ( # #'&'-%# &% +/%0%& & # #'/ &' )

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Gases

D"(&' DAB '/ &% +/%0%& & '( -,2 / T $', '# $+# !/" +$ '( J M ' '/" ,"J) J," P #'/% ( !/" +$ '( $,σ AB ' &% ,'$#" &' -" %/% ( '(

A,/$#"()/ U( # ,'$#" &' L'(( #& ="('/ 6Ω D %($')# &' -" %/% (.

M)TODO DE *IN#E!MANN

P # ( %7 # ,'>"# "/ #'/+ $ &"/ '8 '#%,'($ '/

P # ' '-$" &' & $ # (",'(- $+# +( '8 '#%'(-% &' ,'&%-%"(', $% '/ < -',"/ 7 ( 7 "()%$+& %(%-% &' - ,%(" &' &%

"()%$+& &' - ,%(" &' &% +/% ( '( -+ 5+%'# %(/$ ($'. A/* / -"/ /

O '( "#, '5+%0 '($' '( $:#,%("/ &' # --%"('/ ," #'/ '( /' ) /'"/

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Gases

A -"(/$#+%# +( )# %-" &' $ 7 ? 7 -"," "#&'( & -"($# 7 ? 7!/-%/ /' &'!' "!$'('# +( *(' #'-$ &' -+6 '(&%'($' /' " - -+ #

&% +/%0%& & !+/- & .

II. E+UI'O " MATERIA!E

II.,. MATERIA!E• C#"(",'$#"

• N C 2M 11K ) L2 , &' /" +-% ( &' - "#+#" &' /"&%"

• A-'$"(

II.-. E+UI'O

E '5+% " +$% %7 &" # &'$'#,%( # &% +/%0%& &) /'"/ /' ! / '( ,'&%-% ( &' '0 "# -% ( &' +( /+/$ (-0" $% '( ' /'(" &' +( -"##%'($' &' %#'. E '5+% " -"(/$ &'

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Gases

• U( -", #$%,%'($" &' -#* %-" $# (/ #'($' 5+' /' +$% %7 -","! @" &' $', '# $+# -"(/$ ($'

• E - % # 5+' -"($%'(' /+/$ (-% 0" $%• U( $'#, ,'$#"• O$#" -", #$%,%'($" 5+' -"($%'(' +( !",! &' %#'• U( -"($#" &"# &' $', '# $+# 6 "/ %($'##+ $"#'/ # !",!

%#' 6 ' - '($ &"#• U( ,%-#"/-" %" # ,'&%-% ( &' $+# &' *5+%&" '(

III. 'ROCEDIMIENTO E 'ERIMENTA!

,/ 'A O .? C '($ # ' )+ < /$ +( $', '# $+# &' C , ($'('# -"(/$ ($' -"( 6+& &' - '($ &"#

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Gases

Fi0ura N/1

Fuen2e3 Ela4oraci5n 6ro6ia

-/ 'A O.7 S' %(6'-$ -'$"( $ (&" +( '8$#'," &' $+!" - % #< /$ 5+' ' (%0' &' *5+%&" 5+'&' "# &'! >" &' 2 -'($*,'$#"/ '8$#'," /+ '#%"#.

1/ 'A O.? %($#"&+-%# ' - % # '( ' ! @" &' )+ 5+' /' '(-+'($#$', '# $+# -"(/$ ($' &' 4 C 6 /')+# #/' 5+' ' - % # /'

'(-+'($#' '( "/%-% ( ("#, #'($' ,%-#"/-" %".

Fi0ura N/8

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Gases


8/'A O.? -"('-$ # +( '8$#'," &' - % # , ()+'# &' /+,%(%/$#&' %#' 6 $", # '-$+# &' $+# &' *5+%&" &'($#" &' -

Fi0ura N/9


9/'A O.7 E(-'(&'# ' %($'##+ $"# &' !",! &' %#' 6 &'> #-%#-+ # +( /+ 0' !#%/ &' %#' "# ' '8$#'," &' - % # 6 ,'&&'/-'(/" &' -'$"( '( ' - % # %($'#0 "/ &' $%', " &' 3,%(+$"/.

I:. O& ER:ACIONE E 'ERIMENTA!E

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Gases

• ; 6 5+' %> #/' 5+' $', '# $+# &' )+ /' , ($'() -"(/$ ($' 4 C #"8%, & ,'($' .1 C '(-'(&%'(&" " ) (&" - '($ &"# &' )+ -+ (&" /' ('-'/ #%".

• L !#%/ &' %#' 5+' -%#-+ /"!#' ' - % # '/ " 5+' #"&+-' -'$"( 5+' /' '/$ 0 "#%7 (&" /' ## /$# & .

• D'!',"/ $'('# '( -+'($ ' +($" &' '!+ %-% ( &' -'$"( #/ !'# 5+: $', '# $+# $# ! > # -"( ' %( &' 5+' (" 0" $%# %& ,'($' -'$"(

:. DATO E 'ERIMENTA!E T 4 C S+/$ (-% 0" $%Ace2ona

Da2os 6ro6orcionados en una corrida co;6le2a 3

Ta4la N/,? F+'($' D $"/'83'#%,'($ 4'/ "!$'(%&"/ '( LOPUI

Da2os o42enidosen una corrida cor2a3

Ta4la N/-? F+'($' D $"/'83'#%,'($ 4'/ "!$'(%&"/ '( LOPUI

:. RE U!TADO O&TENIDO "CA!CU!O EFECTUADO

L !"# $"#%" &' I()'(%'#* Q+*,%- II 14

θ (h) 1 2.2

2 4.23 H.24

9.9H. 12.HK. 14.39 1H.H11 19.K14 24.2

θ (h)

. 1.1 2

1. 2.22 2.4


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Gases

A> E 'ERIMENTA!MENTE

'ara la corrida co;6le2a3

1 3H 2.2 . 22 1H3H3H3.H3H2 K2 4.2 . 44 1H3H3H3.H3H3 1 H.2 . H2 1K4193 .4 44 144 . 1

1 9.9 . 99 1 1 1 1. 1H. 234 12.H . 12H 1 K142. KK. 2K 14.3 . 143 1 111.9 324 1H.H . 1HH 19 1 K.22911 39H 19.K . 19K 2 1 1 2.2 414 4 24.2 . 242 2 2H44.H2

Ta4la N/ 1 ? F+'($' E !"# -% ( #" %

• R' %7 (&" +( )# %-(Z − Z 0 ) 0/.θ

(Z − Z 0 )

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θ (h) θ(s) Z − Z 0 (mm)

¿Z − Z 0 ¿ m)

θZ − Z 0 (sm)


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Gases

0 0.01 0.01 0.02 0.02 0.03 0.030

500000

1000000

1500000

2000000

2500000

f(x) = 20857294.89x + 1595945.69R² = 0.97

Grafico N/,• ; (&" -"( /%)+%'($' '-+ -% (

θ(Z − Z 0 )

= (Z − Z 0 )α

+2 Z 0

α ……………….(1 )

E/$ '-+ -% ( -"##'/ "(&' *(' &' +( #'-$ -"( '(&%'($'1

α

y= mx+b

S' #' %7 +( #')#'/% ( %(' )# %- 1 6 /' "!$+0" /%)+%'($' '-+ -% (

y= 19481500 x+1620375.7

m= 1α = 19481500 sm2

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α = 5.13307 × 10 − 8 m2 /s


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Gases

• ; (&" D AB '8 '#%,'($

D AB= α × ρ

A2 × C × M WA

× P

BM P A1 − P A 2 ……………(¿)

¿∗¿ D AB= α ×

ρ A × R × T

2 × P T × M WA× ln ( P B 2 P B 1 )……………¿

D5nde3

ρ A : densidad delaace !na

M WA : "es!m!lec#la$ de laace !na

P A1 : P$esi!n "a$cialdelaace !naenlain e$%ace = & P'A

P A2 : P$esi!n "a$cialdelaace !naenel sen! dela c!$$ien e(ase!sa

U$% %7 (&" "/ & $"/ &' P'##6 # '(-"($# # &'(/%& & &'

; -%'(&" +/" &' '-+ -% ( &"(&' &'(/%& & '/ +(-% ( &' $', '#

ρ A= C 1

C 2(1 +(1 − T

C 3)

C 4

)

P # -'$"(

C1 1.2332 C2 .2 H C3 .2 C4 .2913R'', 7 (&" '( '-+ -% ( &' &'(/%& & /' "!$%'('

ρ A= 769.22836 )( /m3

P # "/ &', / & $"/

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Gases

'ara la corrida inco;6le2a3

. 3H 2.2 . 1 121 K2 4.2 . 2 1

1. 1 H.2 . 22 24 4 4 .42 144 . 24 3

Ta4la N/ 8 ? F+'($' E !"# -% ( #" %

• R' %7 (&" +( )# %-(Z − Z 0 ) 0/.θ

(Z − Z 0 )

0 0 0 0 0 0 00

500000

1000000

1500000

2000000

2500000

3000000

3500000

f(x) = 1965464702.89x - 1866429.66

R² = 0.94

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θ (h) θ(s) Z − Z 0

(mm)

¿Z − Z 0 ¿ m)

θZ − Z 0 (

sm)


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Gases

S' #' %7 +( #')#'/% ( %(' )# %- 1 6 /' "!$+0" /%)+%'($

y= 1965400000 x− 1866429

m=1

α = 1965400000 s

m2

U$% %7 (&" "/ & $"/ 6 '(-"($# &"/ # -+ (&" /' $'(* +( -"##%&

D AB= 5.088022 × 10− 10 m

2 / s×769.22836 )( /m

3

× 0.082 a m×m

3

)m!l ×& * × 313.15 & *

2 × 1 a m×58.08 *( / *m!l × ln ( 10.44111 )

&> Te5rica;en2e

Median2e la ecuaci5n de $irsc=felder7&ird7 6o2? ;odificada6or *il@e7!ee

L !"# $"#%" &' I()'(%'#* Q+*,%- II 20

α = 5. 088022 × 10 − 10 m2 /s

D AB= 1. 057099 x10 −7m

2 /s


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Gases

Da2os3

T 313.1 J

'ara la Ace2ona3 C-$ O M ace !na = 58.08

)()m!l

T eb= 56.3 &C = 329.45 *

' b= 3∗14.8 +6∗3.7 +7.4 = 74 x 10 −3

$b= 1.18 ∗' b1 /3= 1.18 ∗0.074 1 /3 = 0.4954 (,

Ɛb

* = 1.21 ∗T eb= 1.21 ∗329.45 = 398.6345

U2ili?ando los da2os del e0undo co;6onen2 Bue no sedifunde3 'ara el Aire3

M ai$e= 29 )()m!l

Ɛa

* = 97

$a= 0.3711

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DAB 1?48

$AB¿2 x ) . T


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Gases

C -+ (&"

$ab=$a +$b

2 =

0.3711 +0.49542

= 0.43325 nm

Ɛab

* =√ Ɛa * ∗Ɛ b

* = √ 97∗398.6345 = 196.6406

*T Ɛ

ab

= 313.15

196.6406= 1.59249

% ( *T Ɛ ab )=

0.5769

E( )# %- T#'6!

Ree;6la?ando en la ecuaci5n inicial3

DAB 1?48

0.43325 ¿2 x0.5769101.325 x10

3 x¿

(1.084 − 0.249 x√ 158.08 + 129 ) x313.153

2 x(√ 158.08 + 129 )¿

E '##"# -"( #' -% ( " '(-"($# &" '8 '#%,'($ ,'($' 1 .H

Median2e la ecuaci5n se;i7e;6irica de Fuller

Da2os3

L !"# $"#%" &' I()'(%'#* Q+*,%- II 22

D AB= 1. 17981 x 10 −5m

2 /s

D AB= 10 − 7

. T 1.75

PT .[ (∑ - A)1 /3 +(∑ - B)1 /3 ]2 .(1 / M A+1 / M B)

1/

2


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Gases

A /' #' %'#' -'$"(

B /' #' %'#' %#'

T 323.1 J

MA . ) ,"

MB 2 .9 1 J) ,"

P # ' - -+ " &' 0" +,'( ," '-+ # $", ,"/ "/ & $"/ &' , (+ &'I()'(%'#" Q+*,%-"? P'##6 &' /: $%, '&%-% (

Ta4la N /8

Ace2ona3 C3; HO

∑ - A= 3∗- c+6∗- . +1∗- /

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