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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   (

       "   "   "   "

       "   "   "   "

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       "   $   )  *   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