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8/18/2019 Lab Keyder
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FUERZA IÓNICA Y COEFICIENTE DE ACTIVIDAD DE ELECTROLITOS
KEYDER ANDRÉS SUAREZ RAMOS
MILTON SAEL APARICIO VILLANUEVA
MARÍA CAMILA TAMAYO SALAZAR
MARÍA CAMILA LÓPEZ DELGADOMÓNICA MARÍA GALEANO MARTÍNEZ
DAIRO PÉREZ SOTELOINGENIERO QUÍMICO
UNIVERSIDAD DE CORDOBAFACULTAD DE CIENCIAS BÁSICAS
DEPARTAMENTO DE QUÍMICA
QUÍMICA
2016
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INTRODUCCIÓN
P D!"#! # E $%&'!( )1*2+,- ./"/3 !3 !( 4/"(!5 ! (7 83.!/&&83!7 8938&7- 7"/!( "7! ! :;! (7 83!7 !3 7(;&893 7! !3&;!3./3 /!7 ! ;3 !!/ 8938&,- :;! (858. 7; 5?858!3. )!7 5@7 4/""(!- 4/
!!54(- :;! ;3 893 478.8?- &378!/ &!3./( ! /!>!/!3&8- 7! !3&;!3./! /!4/ 83!7 3!=.8?7- :;! 4/ 83!7 ! 7; 5875 78=3, E( 5?858!3. 7! ?! (858. !37 74!&.7 ( .597>!/ 8938& !7 !>/5 &;3 !( 893 &!3./( 7! 5;!?!- !53!/ :;! 7; &!3./ 7! !3&;!3./ !./@7 !( 893- # !( 5?858!3. ! 7.! !7 /!./4/ ( .597>!/ )!>!&. ! /!(&893, .5"83- !7. (.85- ( .!3!/ &/= 4;!7. (!( 83 &!3./(- .!3!/@ 5?!/7! !3 7!3.8 &3.//8 ( !( 83- !"8 ( &54!(&./8&- ;/3.! ( 58=/&893 )!>!&. !(!&./>/.8&, L7 ./&&83!7 83.!/8938&7 # !(!>!&. !( 7(?!3.! 73- !3 !7!3&8- ( &;7 ! ( !7?8&893 :;! 7;>/!3 (7 !(!&./(8.7!( &54/.58!3. 8!(
E7 854/.3.!- 4/ ./ 4/.!- &!/ /!>!/!3&8 ( &3.8 &3&8 &5 >;!/ 8938&-
I- :;! !7 ;3 5!8 !&; !( !>!&. ! (7 83.!/&&83!7- 83 83 ! 83 7(?!3.!-!3 ;3 7(;&893 !(!&./(H.8& L >;!/ 8938& 7! !>83! &5 ;3 5!8 ! ( 7;5./8 !
( &3&!3./&893 5(/ ) 5((, ! & .84 ! 893 ) c i ,- 5;(.84(8& 4/ !( &;/
! ( ?(!3&8 ) z i , [email protected]&5!3.! 7! !
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OBJETIVOS
OBJETIVO GENERAL
D!.!/583/ !( &!>8&8!3.! ! &.8?8 ! (7 8>!/!3.!7 7(;&83!7 ! &!.. !4(. 4/!4/7 ;73 ( .!/H ! D!"#! $%&'!( &3 ( (!# (858.3.! # (!
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MARCO TEÓRICO
U3 !(!&./(8. !7 ;3 7;7.3&8 :;! 4/;&! 83!7 !3 87(;&893 D!"8 (7 >;!/.!783.!/&&83!7 ! (/= (&3&! !8&8!3.!7! &.8?8 8>8!/!3 "7.3.! ! ( ;38 83&(;7 !3 87(;&83!7 8(;87 E7.7 >;!/7
83.!/8938&7 4/;&!3 ;3 /!358!3. ! (7 83!7 !3 ( 87(;&893 ! >/5 :;!(/!!/ ! ;3 83 478.8? "/@ 5@7 83!7 3!=.8?7 # ?8&!?!/7 E7. 87./8";&893 35=3! ! &/=7 4/;&! ( 4/8&893 ! ;3 4.!3&8( !(&./8& 4;!7 ( &/= 3!.!3 &;(:;8!/ 4;3. ! ( 87(;&893 3 7!/@ 3;( E7. 4/;&! ;3 !7."8(8&893 ! (87(;&893 !"8 :;! (7 83!7 7! /!3 ! ./7 ! &/= 4;!7.- ( :;! &! :;!.!3=3 5!37 .!3!3&8 !7&4/ ! ( 87(;&893 # ( &.8?8 7!/@ 83>!/8/ (&3&!3./&893 U3 5!8 ! ( 83.!378 !( &54 !(&./8& &/! 4/ (7 83!7!8&&893 7! &3&! &5 !&;&893 !
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log f i=−0.51Z i
2√ I 1+√ I
+0.2 I
RESUMEN EJECUTIVO
L >;!/ 8938& # &!>8&8!3.! ! &.8?8 ! !(!&./(8.7 3! ( .!/H ! D!"#! $%&'!( 7!/@ ;3 ! (7 !(!5!3.7 "@78&7 ! ( >878&:;H58& ! (7 7(;&83!7!(!&./(H.8&7 3! 7! !.!/583 !( ?(/ ! >;!/ 8938& !3 8>!/!3.!7 7(;&83!7 7H&5 !( &!>8&8!3.! ! &.8?8 4/ 5!8 ! (7 8>!/!3.!7 &3&!3./&83!7 ! &!..! 4(.- (=/3 7H ?!/8>8&/ !7. .!/H # :;! 4/""(!5!3.! !7 ( ! 5@7 54(8 ;7!3 !( ./.58!3. ! 87(;&83!7 ! !74!&8!7 &/=7
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I!ÓTESIS
U3 .84 ! >;!/ 8938& >;35!3.( 4/ &54/!3!/ ( !&;&893 ! D!"#!$%&'!( 73(7 83.!/&&83!7 !(!&./[email protected]&7 !3./! (7 83!7- !5@7 ! .!3!/ ;3 !>!&. 854/.3.! !3(7 &3;&.8?8!7 ! (7 7(;&83!7 ! !(!&./(8.7 >;!/.!7- 83>(;#!3 !3 (7 4/48!!7.!/583@58&7 ! (7 83!7- &5 4/ !!54( !( &!>8&8!3.! ! &.8?8
E( ./.58!3. ! D!"#! $%&'!( 7;43! :;! ( 87(;&893 !(!&./(H.8& !7 5;# 8(;8E7. /!7./8&&893 4!/58.! &!/ ?/87 7854(8>8&&83!7 [email protected]&7 # 4/H78&7 A 8(;&893 (.- ( !7?8&893 4/83&84( &3 /!74!&. ( &54/.58!3. ! (87(;&893 8(;8 8!( 7! !"! ./&&83!7 # /!4;(783!7 ! (/= (&3&! !3./! (783!7 D!"#! $%&'!( 7;4;78!/3 :;! .7 (7 !7?8&83!7 &3 /!74!&. (&54/.58!3. ! ( 87(;&893 8(;8 8!( 7! !"!3 >;!/7 8938&7
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E"UI!O # MATERIALES
• B(3 3(H.8&• T!/595!./• B;/!. ! 0 5L• P84!.7 ! # 10 5L• E74@.;(• B(3!7 >/ ! 2 5L• C/35!./• A=8./ ! ?8/8• F/7& (?/ • V8/8 ! /!(•
E/(!35!#!/7 ! 100 5L• E7.;>• A=8./ !(!&./938&• V8/8 ! /!(• G.!/• S4/.! ;38?!/7(
REACTIVOS
• A=; !7.8(• S(;&893 KSCN 01N• Á&8 3H./8& )$NO+ , 6M• I38&/ )A(;5"/! >//8& 01M,• A&!.. ! 4(.• N8./. ! 78 )NNO+,
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P / ! 4 / 5 7
N 1 0 0 5 L 6 ! 7 ( ; & 8 3 ! 7 6 ! 3 8 . / . 6 ! 7 6 8 0 0 K M - 0 1 M - 0 2 M # 0 K M
P ! 7 5 7
N K ? ! & ! 7 2 = 6 ! & ! . . 6 ! 4 ( .
A 6 8 & 8 3 5 7 N C 6 & 3 . 8 6 6 4 ! 7 6 K ! / ( ! 3 5 ! # ! / 6 ! 1 0 0 5 ( ( 8 5 4 8 7 # 7 ! & 7 # 7 !
( ( ! 3 / 3 ! 7 . 7 E 7 . ( . ! / & ! / 4 / . ! & 3 & 6 ; 3 6 ! ( 7 7 ( ; & 8 3 ! 7 4 / ! 4 / 6 7 6 ! 3 8 . / . 6 ! S 6 8 # ; 3 & 3 = ; 6 ! 7 . 8 ( 6
DIAGRAMA DE $LUJO
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C ( ! 3 . 5 7
L 7 ! / ( ! 3 5 ! # ! / ! 3 ; 3 " J ! 5 / 8 E 7 . 0 G 6 0 C
A = 8 . 5 7
L 7 7 ( ; & 8 3 ! 7 ? 8 = / 7 5 ! 3 . ! 4 / 2 5 8 3 ; . 7
U " 8 & 5 7 L 7 ! / ( ! 3 5 ! # ! / ! 3 ! ( = 8 . / . ! 5 4 ! / . ; / 5 " 8 ! 3 . ! # ( 7 ! 5 7
( ( H 4 / P 5 8 3
R ! . 8 / 5 7
L 7 ! / ( ! 3 5 ! # ! / ! ( = 8 . / # ! 5 7 ! 3 / ! 4 7 4 / 1 0 5 8 3
T / 3 7 > ! / 8 5 7 U 3 5 ; ! 7 . / ! 1 0 5 L ! & 7 ( ; & 8 9 3 ; 3 5 . / F # 8 & 8 3 5 7 1
5 L ! = ; - 5 L ! $ N O + 6 M # = . 7 ! ( 8 3 8 & /
T 8 . ; ( 5 7
C 7 ( ; & 8 3 & 3 K S C N 0 1 N
MONTAJE
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Mezcla + sln de NaNO3 y agua +++++Acetato +++
Agitamos por 45 min
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$" ml de muestra + 5 ml sln de %NO3 + $5 ml agua& y gotas de indicador
Muestra
'itulamos
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CALCULOS # RESULTADOS
A=SCN A= SCN
L7 .7 ".!387 !3 ( .8.;(&893 ! ( 7(;&893 )2 5(, &3 KSCN 01 N- 7! 5;!7./3 &3.83;&893
1 A=; !7.8(2 N8./. ! 78 00M+ N8./. ! 78 01M N8./. ! 78 02M N8./. ! 78 0M
T%b&% '
M(est)%s Vo&* +e ,SCN -L. Vo&* So&(ci/0 -L.
1 001* 00
2 00206 006
+ 00210 0060
002+1 001
002+ 00
N1 3/5(8 ! ( 7(;&893 ! KSCN )01,V ?(;5!3 ! KSCN =7.7 !3 ( .8.;(&893
ηAg 35!/ ! 5(!7 ! 4(.
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M(est)% '
N = Eq−g
V ( L)
E: = KSCN N V
E: = KSCN )01,)001*,
E:= ! KSCN E: = ! A= 0001*
E: = KSCN 0001*
ηAg= Eq – g de Ag
ηAg=0.00195mol
M(est)% 2
N = Eq−gV ( L)
E: = KSCN N V
E: = KSCN )01,)00206,
E:= ! KSCN E: = ! A= 000206
E: = KSCN 000206ηAg= Eq – g de Ag
ηAg=0.00206mol
M(est)% 3
N = Eq−gV ( L)
E: = KSCN N V
E: = KSCN )01,)00210,
E:= ! KSCN E: = ! A= 000210
E: = KSCN 000210
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ηAg= Eq – g de Ag
ηAg=0.00210mol
M(est)% 4
N = Eq−gV ( L)
E: = KSCN N V
E: = KSCN )01,)002+1,
E:= ! KSCN E: = ! A= 0002+1E: = KSCN 0002+1
ηAg= Eq – g de Ag
ηAg=0.00231mol
M(est)% 5
N = Eq−g
V ( L)
E: = KSCN N V
E: = KSCN )01,)002+,
E:= ! KSCN E: = ! A= 0002+
E: = KSCN 0002+
ηAg= Eq – g de Ag
ηAg=0.00235mol
L7 .7 ! ( &3.8 ! 83!7 A= :;! # !3 & 5;!7./
T%b&% 2
M(est)%s Mo& A67 Vo&* So&(ci/0 -L. 8A679 1 f(e):% i/0ic%
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1 0001* 00 00+
2 000206 006 001
+ 000210 0060 006
0002+1 001 000
0002+ 00 00
S! 4;!! 3./ :;! &;3 !;!/ 8938& ! !7. ;5!3.- 4/4/&83(5!3.! !7. 4!57 !&8/ :;! 78 7! !7.@ &;54(8!3 ( (!# D!"#!$%&'!( 7"/! (7 83.!/&&83!7 !(!&./[email protected]&7 !(7 83!7 !3 7(;&893
P/ ./ ( &3 !7.! 3@(8787 4!57 !&8/ :;! (7 &!>8&8!3.!7 ! &.8?8 ! (7(;&893 .5"83 ;5!3./3 4/4/&83(5!3.! ( &3&!3./&893
C(&;(57 ( >;!/ 8938& ! & 7(;&893 4/.8/ ! (7 &3&!3./&83!7 !3 5(!7 4/ (8./ ! 7(;&893 L &3&!3./&893 ! 83!7 A= !7 8=;( ( >;!/ 8938& !"8 :;! 7!./. ! ;3 &54;!7. 11 (;!= Z2 1
+¿ Ag
¿
¿¿
I =1
2 ∑ C i Z i
2
I =1
2(C 1Z 1
2+C 2Z 22) P!/ Z 1
2
1 Z 22
L;!= I =1
2(C 1+C 2) # C 1 C2 C
E3.3&!7 I =1
2(2C ) L;!= I =C
+¿ Ag
¿
¿¿
+¿ Ag
¿
¿¿
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+¿ Ag
¿
¿¿
+¿ Ag¿¿¿¿
I 1=0.0438
+¿ Ag
¿
¿¿¿
I 2=0.0451
+¿ Ag¿¿¿¿
I 3=0.0456
+¿ Ag
¿
¿¿¿
I 4=0.0480
+¿ Ag¿¿¿¿
I 5=0.0484
C(&;( ! (7 =/57 ! (7 !74!&8!7 83?(;&/7
S! 4/!4/9 ;3 7(;&893 5/! ! 20 5L ! NNO+ 0 M # (;!= &8!3 (78(;&83!7 &//!7438!3.!7 7! ((!=/3 (7 &3&!3./&83!7 ! 00 M- 010 M # 0-20 M
M 0- 5(L
PM -** =5(
V 20 5L 0-2 L
M = η
V ( L); η=
g NaNO3
PM
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M = g NaNO3
PM ∗V ( L)despea!dog NaNO3= M ∗ PM ∗V ( L)
gNaNO3=(0.5 g
L)∗(84.99
g
mol)∗(0.250 L)
gNaNO3=10,62g
$&8!3 &//!&&893 ! 4;/!
10,62g NaNO3 " 100
99,5=10,67 g de NaNO3
P/ ( ;(est)% ' 3 # 4/!7!3&8 ! NNO+ # :;! !7 7( !7 ( 7(;&893 ! &!.. !
4(. 87;!(. !3 =; !7.8(MUESTRA 2
C1 0- MV1 C2 0-0 MV2 100 5L
C (1)V (1)=C (2)V (2)
V (1)=C (2 )V (2 )C ( 1)
V (1)=(0,05 M )(100mL)
(0,5 M )
V (1)=10mL
S! .53 10 5L ! ( 7(;&893 ! 0- M # 7! =/!=3 ;3 "(93 >/ ! 5L # ;!=
7! &54(!. &3 =; !7.8( 7. !( >/
C(&;( (7 =/57 4/!7!3.!7 ! NNO+ !3 ( 7(;&893
gNaNO3= M ∗ PM ∗V ( L)
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gNaNO3=(0.05 g
L)∗(84.99
g
mol)∗(0.100 L)
gNaNO3=0,425 g
MUESTRA 3
C1 0- MV1 C2 0-10 MV2 100 5L
C (1)V (1)=C (2)V (2)
V (1)=C (2 ) V (2 )
C (1)
V (1)=(0,10 M )(100mL)
(0,5 M )
V (1)=20mL
S! .53 20 5L ! ( 7(;&893 ! 0- M # 7! =/!=3 ;3 "(93 >/ ! 5L # ;!=7! &54(!. &3 =; !7.8( 7. !( >/
C(&;( (7 =/57 4/!7!3.!7 ! NNO+ !3 ( 7(;&893
gNaNO3= M ∗ PM ∗V ( L)
gNaNO3=(0.10 g
L)∗(84.99
g
mol)∗(0.100 L)
gNaNO3=0,850 g
MUESTRA 4
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C1 0- MV1 C2 0-20 MV2 100 5L
C (1)V (1)=C (2)V (2)
V (1)=C (2 ) V (2 )
C (1)
V (1)=(0,20 M )(100mL)
(0,5 M )
V (1)=40mL
S! .53 0 5L ! ( 7(;&893 ! 0- M # 7! =/!=3 ;3 "(93 >/ ! 5L # ;!=7! &54(!. &3 =; !7.8( 7. !( >/
C(&;( (7 =/57 4/!7!3.!7 ! NNO+ !3 ( 7(;&893
gNaNO3= M ∗ PM ∗V ( L)
gNaNO3=(0.20 g
L)∗(84.99
g
mol)∗(0.100 L)
gNaNO3=1,700g
M(est)% 5
S! .5 ! ( 7(;&893 5/! !( ?(;5!3 ! 100 5L # :;! ( &3&!3./&893 !7 (
!7! 0- M
C(&;( (7 =/57 4/!7!3.!7 ! NNO+ !3 ( 7(;&893 ;3 ?! 7! .5 (7 100 5L
gNaNO3= M ∗ PM ∗V ( L)
gNaNO3=(0.5 g
L)∗(84.99
g
mol)∗(0.100 L)
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gNaNO3=4,250 g
C%&c(&o < 6)%fic% +e logC #s AI
1
2
1+BI
1
2A 1 =*5=> < B 1 '*25
T%b&% 3
M(est)%s8 A679 1 f(e):%
i/0ic%Lo6 8 9
AI 1
2
1+BI 1
2
1 00+ 1+ 00
2 001 1+6 00
+ 006 1+1 00 000 1+1* 00
00 1+1 00
C3 (7 .7 ! ( t%b&% 3 4/&!!57 =/>8&/ logC #s AI
1
2
1+BI 1
2
G)?fico '
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( # 4 4 " "
" " " " " "
" " " "
" 3 ) * 2
( # 5 (
" " " "
" " " "
" " " "
" $ ) * 2
( # + (
" " " "
" " " "
" " " "
" 3 ) * 2
*$#3+
*$#3,
*$#35
*$#34
*$#33
*$#32
*$#3$
*$#3
*$#2-
./01 "#"$0 * $#3+
"#-(
G)?fico@ Lo6 8 9 vs AI'2'7BI'2
Lo6 8 9
C5 7! 4;!! "7!/?/ !3 !( 3.!/8/ 6)?fico '- !7 7!5!3.! ;3 (H3! /!&.- # 7!5;!7./ .5"83 ( !&;&893 !( =/>8& &;# 83.!/&!4. 7! ;"8& &3&!3./&893 &!/)C 0, !3 1-+6*1 ( &;( &//!743! !3 ( !&;&893 ! D!"#! $%&'!( ( L= K!3.3&!7
L=10 K 1-+6*1 4(8&3 3.8(=/8.5 .!3!57 :;!
,1 0-02 !( &;( !7 !( 4/;&. ! &.8?8 ! ( 7(;&893
A/ &(&;(57 !( &!>8&8!3.! 5!8 ! &.8?8 WX !( A=A& 4/ & 7(;&893 &3(7 ?(/!7 ! (7 &!>8&8!3.!7 .!9/8&7 ! &.8?8 !.!/5837 4/.8/ ! ( .!/H !D!"#! $%&'!(- ;73 .3. ( (!# (858.3.! &5 ( !
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T!38!3 (7 3.!/8/!7 .7 &(&;(57 !( &!>8&8!3.! 5!8 ! &.8?8 WX !( A=A&p%)% &% so&(ci/0 '@
ln γ $=−|12| 0.509√ 0,04381+1,25√ 0.0438
=−0,0844
γ $=0,9190
!%)% &% so&(ci/0 2@
ln γ $=−|12| 0.509√ 0,04511+1,25√ 0.0451
=−0,0854
γ $=0,9181
!%)% &% so&(ci/0 3@
ln γ $=−|12| 0.509√ 0,04561+1,25√ 0.0456
=−0,0858
γ $=0,9177
!%)% &% so&(ci/0 4@
ln γ $=−|12
| 0.509
√ 0,0480
1+1,25√ 0.0480=−0,0875
γ $=0,9162
!%)% &% so&(ci/0 4@
ln γ $=−|12| 0.509√ 0,04841+1,25√ 0.0484
=−0,0878
γ $=0,9159
Y &54/3 &3 (7 ?(/!7 ! (7 &!>8&8!3.!7 .!9/8&7 ! &.8?8 !.!/5837 4/.8/ ! ( .!/H ! D!"#!$%&'!(- ;73 .3. ( (!# (858.3.!- .!3!57 :;!
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log γ $=−|12|
−¿+¿Z ¿
Z ¿¿
A √ I −0,509√ 0.0438=−0,1065
γ $=0,7824
A7H &(&;(57 (7 !5@7 ?(/!7 4/ (7 ./7 7(;&83!7 ".!38!3 (7 78=;8!3.!7?(/!7 ! &!>8&8!3.!7 5!87 ! &.8?8
T%b&% 4
M(est)%s8 A679 1 f(e):%
i/0ic%γ $ γ $ &e< &i;it%0te
1 00+ 0*1*0 02
2 001 0*11 0*6+ 006 0*1 0
000 0*162 0+
00 0*1* 02
C5 7! 4;!! "7!/?/- !3 ( t%b&% 4- ( &!/ ( &54/&893 ! (7 &!>8&8!3.!7 !&.8?8 5!87 !.!/5837 !8&8!3.!7 ! &.8?8 !!(!&./(8.7 !"!3 !7./ !.!/5837 4/ ( >;!/ 8938& ! ( 7(;&893 # !( .84 !?(!3&8
$((57 K& 4/ & ;3 ! (7 7(;&83!7
+¿−¿ Ac
¿
¿ Ag
¿¿¿
%c=¿
p%c=log %c
p%c=log (0,0438 )=−1,3585
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R!(83 (7 58757 &@(&;(7 4/ (7 !5@7 .7 ".!3!57
T%b&% 5
M(est)% p,c I '7I
1 1-+ 0-1+0
2 1+ 0-11
+ 1+10 0-1*
1+1 0-1*
1+11 0-10+
C3 (7 .7 ! ( t%b&% 5 4/&! =/>8&/ 4K& ?7√ I
1+√ I
"#$+ "#$+ "#$+ "#$( "#$( "#$( "#$( "#$( "#$( "#$(
*$#3+
*$#3,
*$#35
*$#34
*$#33
*$#32
*$#3$
*$#3
*$#2-
./01 5#--0 * 2#4
$
Grafico: pKc vs /(1+ )√ √
G)%fico 2
A( =/>8&/ 4K& V7 I 1I 4!57 3./ :;! ".!3!57 ;3 =/@>8& 4/!&8 (6)?fic% '- !7. 7! !"! :;! 3 7! .8!3! !3 &;!3. !3 ( !&;&893 (7 ?(/!7 &37.3.!7! A # B- :;! ( :;! &!3 !7 &//!=8/ ;3 4& ( !&;&893 ! D!"#! $%&'!( # !7.7.8!3!3 ?(/!7 !74!&H>8&7 4/ & 7(?!3.! # 8>!/!3.!7 .!54!/.;/7
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CONCLUSIÓN
D! ( 3.!/8/ 4/@&.8& 7! 4;!! &3&(;8/ :;! ( &/= ..( ! (7 83!7 478.8?7 !7 8=;( ( &/= ..( ! 83!7 !(!&./(8.7 >;!/.!7 :;! !;!/.!7 (5!37 !3 7(;&83!7 8(;87 7! ((3 ..(5!3.! 8387 # (7 !>!&.7 "7!/?7 7!!"!3 "?85!3.! ( 87./8";&893 !78=;( ! (7 83!7 &5 /!7;(. ! ;3 ./&&893
L &3&!3./&893 ! (7 83!7 7! 83./;&! 4/ 5!8 ! ;3 &3.8 &3&8 4/ >;!/
8938& ! ( 7(;&893 :;! &3./8";#! ;3 5!8 !( 5!8 !(&./8& !3 7(;&893 # ;!=!3 7; .!/H ;3 44!( 3@(= ( ! &3&!3./&893 !3 ( .!/H ! A//!38;7 T!9/8&5!3.!!( &!>8&8!3.! ! &.8?8 ! ;3 83 !7 >;3&893 ! ( >/.(! 8938& ! ( 7(;&893 # &5!7.! !7 !8&8!3.! ! &.8?8 5!8 !(!(!&./(8.- ;3:;! 4/ (7 7(;&83!7 5;# 8(;87 !7 4!:;!J7 &8!/.7 ?(/!7 ! 83&(;7!3 &77 !74/!&8"(!7 !7 4/!&87 &378!// ( !&;&893 (H58.! ! D!"#! $%&'!( 4/(7 &!>8&8!3.!7 ! &.8?8 ! (7 !(!&./(8.7 >;!/.!7
S! 4;!! !7."(!&!/ :;! ;3 !>!&. !( ;5!3. ! ( >;!/ 8938& 854(8& ;3 5#/ 83.!/&&893 !3./! (7 83!7 !3 ;3 7(;&893 . :;! 7! 4;!! ;.8(8/ 4/ 3@(8787 ! .843(H.8& !74!&H>8&5!3.! !3 ( ;.8(8&893 ! &!(7 !(!&./:;H58&7 U.8(87 4/ (
!.!/583&893 ! ;3 3(8. !3 ;3 5;!7./ 4/"(!5
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BIBLIOGRA$A
MARON Y PRUTTON F;35!3.7 ! >878&:;H58& E8./8( L85;7 SA M