A Potentiometric Method for Determination of the Thermodynamics of

15

Downloaded by UNIV OF ARIZONA on March 11, 2017 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/ba-1976-0155.ch015

A Potentiometric Method for Determination of the Thermodynamics of Ionization Reactions in Partially Aqueous Solvents CHARANAI C. PANICHAJAKUL and EARL M. WOOLLEY Department of Chemistry, Brigham Young University, Provo, Utah 84602

A potentiometric method for determination of ionization con stants for weak acids and bases in mixed solvents and for deter mination of solubility product constants in mixed solvents is described. The method utilizes glass electrodes, is rapid and convenient, and gives results in agreement with corresponding values from the literature. After describing the experimental details of the method, we present results of its application to three types of ionization equilibria. These results include a study of the thermodynamics of ionization of acetic acid, ben zoic acid, phenol, water, and silver chloride in aqueous mix tures of acetone, tetrahydrofuran, and ethanol. The solvent compositions in these studies were varied from 0 to ca. 70 mass % nonaqueous component, and measurements were made at several temperatures between 10° and 40°C.

I

onization reactions have been investigated (I) b y a variety of methods that lead to reasonably accurate values of equilibrium constants over rather w i d e ranges of temperatures, pressures, a n d dissolved salt concentrations. However, the status of measurements leading to ionization constants i n aqueous organic m i x e d solvents has not been developed nearly so w e l l , i n spite of the excellent w o r k of H a r n e d , G r u n w a l d , Bates, a n d others (1-10). E x p e r i m e n t a l methods have been difficult and those methods that utilize the hydrogen electrode can be a p p l i e d only to systems i n w h i c h there are no c o m p l i c a t i n g r e d u c t i o n reactions. W e have recently devised a rapid and convenient method for determination of the ionization constant for water i n m i x e d aqueous organic solvents (11-16). T h e method utilizes glass electrodes a n d gives results i n satisfactory agreement w i t h earlier work. 263

Furter; Thermodynamic Behavior of Electrolytes in Mixed Solvents Advances in Chemistry; American Chemical Society: Washington, DC, 1976.

264

THERMODYNAMIC BEHAVIOR OF ELECTROLYTES

As a result of our continuing interest i n ionization equilibria i n m i x e d solvent systems (I J - 2 0 ) , w e have n o w devised a convenient a n d r a p i d m e t h o d for determining ionization constants for weak acids (16) and solubility product constants for certain slightly soluble salts i n aqueous organic m i x e d solvents.

T w o features

of the m e t h o d are significantly different f r o m earlier methods (1-10). provision is m a d e to determine glass electrode responses.

First,

Second, the experi-

m e n t a l procedure of d i l u t i n g aqueous electrolyte solutions w i t h a nonaqueous solvent component eliminates the need for most of the solution preparation a n d h a n d l i n g associated w i t h the earlier methods.

In this paper w e describe the

details of our m e t h o d a n d report on its a p p l i c a t i o n to the d e t e r m i n a t i o n of the


ionization constants for acetic acid, benzoic acid, phenol, water, and silver chloride i n mixtures of water w i t h ethanol, tetrahydrofuran, a n d acetone.

T h e mixtures

containing ethanol a n d acetone were studied at 1 0 ° , 1 5 ° , 2 0 ° , 2 5 ° , 3 0 ° , 3 5 ° , and 4 0 ° C , a n d the mixtures c o n t a i n i n g t e t r a h y d r o f u r a n were studied at 1 5 ° , 2 5 ° , and 3 5 ° C .

Method

and

Calculations

In our investigations w e describe the ionization reactions i n solvent S as follows: H 0 ( S ) = H+(S) + O H - ( S ) ;

AG °, Atf °, AS °

2

K

W

= a a H/flw = C C

w

H

H

0

H A ( S ) = H+(S) + A - ( S ) ; K

a

= dudA/diiA

MX(c)

s

x

(t/±) /l

a

a

H

2

A

a

4

AG °, AH °, AS ° S

S

= C C (y±) /l

M

M

2

x

(3) ()

H

S

(1) (2)

2

= C C (t/±) /C A!/HA

= a a /a x M

W

AG °, Atf °, AS °

= M+(S) + X - ( S ) ; K

O H

w

(5) (6)

In Equations 2, 4, a n d 6, a represents t h e r m o d y n a m i c activities based on molar x

concentrations C of the species i n d i c a t e d , y± Y

represents m e a n i o n i c activity

coefficients, I/HA is the activity coefficient of H A ( S ) molecules, a n d the activity of water is chosen to be one i n a l l solvents.

Consequently values of K, A G ° , a n d

A S ° are based on these choices r e g a r d i n g standard states. This study is based on measurement of the potentials of the cells represented by glass electrode | soln A : H C l ( d ) , K N 0 ( C ) , i n solvent S| A g C l , A g 3

2

(A)

glass electrode | soln B: K O H ( C ) , K C 1 ( C ) , i n solvent S | A g C l , A g 3

4


(B)

15.

PANICHAJAKUL AND WOOLLEY

Potentiometric

265

Method

glass electrode | soln C : H A ( C ) , K O H ( C ) , K C 1 ( C ) , i n solvent S | A g C l , A g ( C ) 5

6

7

glass electrode | soln D : A g N 0 ( C ) , H N 0 ( C ) , i n solvent S | A g C l , A g 3

8

3

(D)

9

In cells A - D , C\-Cg represent total f o r m a l a na lytic al concentrations. A general expression for the potentials of these cells is g i v e n b y E = fci + k log (a a \) 2

H

(7)

C


a n d specific equations for cells A - D are g i v e n i n terms of the definitions i n Equations 2, 4, a n d 6 of K , K , a n d K as w

E

A

s

= h + k log ( C i ) + k 2

2

E E

a

log (y±)

2

= * i + *2 log ( K C / C )

B

W

4

= ki + fc l o g [ ( C ) c C ] + * 2

c

£

(8)

2

A

H

7

= fc +

D

(9)

3

log ( t / ± ) c

2

(10)

2

fc log(K C /C )

1

2

s

9

(11)

8

As shown previously (11-16), c o m b i n a t i o n of Equations 8 a n d 9 gives E q u a t i o n 12 w h e n the solvent composition is the same i n cells A a n d B . pK

= (E

w

A

- E )/k B

2

- l o g [(C ) C (y±)A /C ] L

2

2

s

(12)

4

E q u a t i o n 12 is used first to determine electrode responses k , a n d then to deter2

mine p K

w

values, as described previously (11-16).

E q u a t i o n 13 is used to esti-

mate y± values. .

.

,

1.825 X 1 0

x

log (y±) = h

(d/D T ) / / /2

6

3

3

1

2

1

— — 1 + 2.298 X l O M d / D T ) / ! ^

y

1

2

(13)

1

V

1

Density a n d dielectric data were obtained f r o m the literature (23) or f r o m exp e r i m e n t a l measurements. C o m b i n a t i o n of Equations 8 and 10 leads to E q u a t i o n 14, w h i c h can be used in conjunction w i t h the "buffer ratio" defined b y Equation 15 i n obtaining values of K

a

as shown previously (16, 24, 25). log ( C ) c = ( E c " E A ) / * 2 + l o g ( C ! / C ) + l o g [(y±) y(y±h } 2

H

CA/CHA

=

7

(14)

2

A

(Ce + C H — C O H ) / ( C S — CQ — C H + C

0

H ) ~ C

6

/ ( C

5

- C

6

(15)

)

T h e value of k to be used i n E q u a t i o n 14 m a y be taken as that value cal2

culated f r o m E q u a t i o n 12, or one c o u l d calculate a value of k f r o m E q u a t i o n 2

14 f r o m a k n o w n value of K i n pure water a n d f r o m measured values of E a

E c i n pure water i n conjunction w i t h Equations 2, 4, 13, a n d 15.


A

and

266

THERMODYNAMIC BEHAVIOR OF ELECTROLYTES

Values of K h f o r the hydrolysis reaction A"(S) + H 0 ( S ) = HA(S) + O H - ( S )

(16)

2

can be obtained f r o m k n o w n values of K

w

K h = a Aa /a a H

OH

A

a n d K b y using E q u a t i o n 17. a

= K /K w

w

= Kb

a

(17)

C o m b i n a t i o n of Equations 8 a n d 11 leads to E q u a t i o n 18 w h e n the solvent composition is the same i n cells A a n d D . P

K

S

= ( £ - E )/k A

D

- log [ ( C i ^ s f o i J A V C o f l M x ]

2

(18)

Values of K c a n be obtained f r o m measured E\ a n d E D values i n a n y solvent


s

S w h e n the a n a l y t i c a l concentrations C\, C$, a n d C9 are k n o w n , w h e n AMX is known, and where y± is calculated f r o m Equation 13. In this work, a^x is taken to be unity. T h e value of k used i n E q u a t i o n 18 m a y either be taken as that value c a l 2

culated f r o m E q u a t i o n 12 or one could calculate a value of k f r o m E q u a t i o n 18 2

f r o m a k n o w n value of K i n p u r e water a n d f r o m measured values of E s

and

A

E D i n pure water i n conjunction w i t h E q u a t i o n 13. T h e assumptions m a d e i n the use of these methods to obtain the above i o n ization constants i n m i x e d solvents have been s u m m a r i z e d (16).

T h e fact that

the pK values calculated using the above assumptions are i n good agreement w i t h those values reported i n the literature is a n i n d i c a t i o n that a n y errors resulting f r o m these assumptions are p r o b a b l y relatively small. T h e calculation of A H ° a n d A S ° values f r o m the p K - t e m p e r a t u r e data i n each solvent mixture was performed b y the n o n e m p i r i c a l m e t h o d of C l a r k e a n d G l e w (26) as s i m p l i f i e d b y B o l t o n (27).

I n this m e t h o d the t h e r m o d y n a m i c

parameters are considered to be continuous, w e l l - b e h a v e d functions of temperature, a n d their values are expressed as perturbations of their values at some reference temperature 6 b y a T a y l o r ' s series expansion.

T h e basic equation

is: filnK

=

- A ^

+

A ^

l

l

+

4

C

^

2+

f

(

^ !

)

/

a

+

...

(

1

9

)

where the t h e r m o d y n a m i c parameters are the regression coefficients a n d the terms t are the temperature dependent variables. x

A l l e q u i l i b r i u m constants

were converted to the m o l a l i t y scale p r i o r to the above analysis (21, 22, 24). Values of K, A G ° , a n d A S ° were then converted back to the m o l a r i t y scale a n d are expressed o n that basis i n the " R e s u l t s " section.

Experimental Potential measurements were m a d e o n cells A , B , C , a n d D w i t h a M o d e l E 4 3 6 M e t r o h m Potentiograph recording potentiometric titrator.

T h e sensitivity

was set to 5 0 - m V f u l l scale so that potentials were readable to 0.1 m V . T h e glass


15.

PANICHAJAKUL AND WOOLLEY

Potentiometric

267

Method

electrodes used were the Fisher 13-639-1 and the C o l e m a n 3-472 w i d e p H range electrodes.

Silver-silver chloride electrodes were prepared f r o m B e c k m a n 39261

Silver B i l l e t electrodes b y electrolysis i n c h l o r i d e solution (5). E x p e r i m e n t a l measurements were m a d e b y i m m e r s i n g a p a i r of the electrodes i n a 15-ml portion of p u r e l y aqueous solution A , B, C , or D a n d a l l o w i n g the potentials to stabilize.

W h e n the potential became stable, a p o r t i o n of the

nonaqueous cosolvent was a d d e d to the solution i n the cell a n d the potential was again recorded. been added.

This procedure was continued u n t i l 50 m l of the cosolvent h a d

T h e temperature of the cells was kept constant to w i t h i n ± 0 . 0 5 ° C

of the reported temperatures throughout the experiments.

T h e potential m e a -


surement-cosolvent a d d i t i o n experiments were p e r f o r m e d at least t w i c e w i t h each c o m b i n a t i o n of glass electrodes a n d s i l v e r - s i l v e r c h l o r i d e electrodes o n at least t w o i n d e p e n d e n t l y prepared solutions. Total ionic strengths of solutions i n the cells were varied f r o m about 0 . 0 0 5 M to ca. 0 . 0 2 M .

T h e concentrations of solutions i n cell C were m a d e so that the

buffer ratio i n E q u a t i o n 15 always h a d a value between 0.4 a n d 0.6.

T h e non-

aqueous cosolvents used i n this study were Reagent G r a d e or better, a n d they were tested to be sure that they were free f r o m significant quantities of potentially i n t e r f e r i n g substances such as halide ions, acids, a n d bases.

Densities of tetra-

h y d r o f u r a n - w a t e r mixtures were d e t e r m i n e d p y c n o m e t r i c a l l y at 1 5 ° C a n d at 35°C.

Results and

Discussion

Values of k / T calculated f r o m Equations 12,14, and 18 ranged f r o m 0.1960 2

to 0.1980 m V / ° K for different electrode combinations i n d i f f e r e n t solutions at different temperatures, c o m p a r e d to 2.303 R/F

= 0.1984 m V / ° K .

D a t a for a t y p i c a l series of measurements o n cells A , B , C , a n d D are g i v e n in Table I.

In Table I are also given the auxiliary data a n d the results ( p K , p K h , a

p K , a n d p K values) for this series of measurements. w

s

E a c h pK value obtained i n this w o r k is the average result of at least t w o i n dependent series of measurements using d i f f e r e n t combinations of electrodes a n d different solutions i n the cells.

A l l these replicate measurements l e d to pK

values w h i c h have average deviations of

A Potentiometric Method for Determination of the Thermodynamics of

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