Association Constant of Acetic Acid
in 1.02 m NaCl Aqueous Medium
at Elevated Temperatures and Pressures
P. Becker 1 and B. A. Bilal 2
Geochemical G roup, N uclear Chem istry Division, Hahn-M eitner-Institut, Berlin. FRG
Z. Naturforsch. 4 2 a, 849-852 (1987); received May 6, 1987
The association constant of acetic acid in 1.02 m (NaCl) aqueous solution has been determined
potentiometrically at tem peratures up to 260 °C and pressures up to 1005 bar. A high-tem perature high-pressure concentration cell having two hydrogen electrodes has been used for the
measurement. The apparent association constant Ö h a c increases with increasing tem perature but
decreases with increasing pressure:
( 0 H A C ) 2 5 ° C . 108 b a r
(0HAC)2OO °C, 500 b a r
= 2.86 • 104,
= 4.65 • 104,
(0HAc)25 ° C ,
500bar
= 2.7 • 104,
= 6.57 • 104 m_1.
( 0 H A c ) 2 6 O °C, 1005 b a r
The knowledge o f the association constant of
acetic acid at elevated tem peratures and pressures is
necessary for the calculation of acetate/acetic acid
buffer systems under the corresponding conditions.
Only data from conductivity m easurem ents for
diluted acetic acid in w ater are found in the litera­
ture for high tem peratures and pressures [ 1 - 3 ] as
well as data for high ionic strength m edia at
atmospheric pressure and normal tem peratures
[4 -6 ] ,
We have determ ined the acetic acid association
constant at tem peratures up to 260 °C and argon gas
pressures up to 1005 b a r in a 1.02 m N aC l m e d iu m
by means o f potential m easurem ents on the cell
so lu i:
solu2:
[A c-],[H +]2 interm ediate
[H+],
Pt. h 2
NaCl
electrolyte
NaCl
(sample)
NaCl
(reference)
1. Experimental
T he apparatus and the general experim ental con­
ditions and procedures have been described previ­
ously [7 -9 ], S u pra pure grade N aC l (M E R C K ) has
been used along with p.a. grade HC1, C H 3C O O H
(HAC), and N a C H 3C O O (NaAc) for the p re p a ra ­
tion o f the solutions.
The reference co m partem ent was filled with
0.01019 m HC1 and 1.00981 m N aC l solution in all
cases.
Sample solutions of two different compositions
have been used to investigate the association
equilibrium of acetic acid, containing 0.01019 m
HAc and 1.00981 m N aC l in one case (see T able 2)
and an analytical ratio o f acetate to hydrogen ions
of 2: 1 in the other case (see Table 1) represented by
0.01019 m N aA c and 0.005095 m HC1 as well as
1.003715 m NaCl to establish the desired ionic
strength.
1.02
m NaCl was used as interm ediate electrolyte
as in the former experiments.
The air in the high pressure cell was replaced by
repeated pressurization with pure hydrogen to
40 bar, and argon gas (special Argon, Linde;
0.1 vpm oxygen) was used to establish the desired
higher pressures. M easurem ents were m a d e by con­
tinuously increasing the te m perature (0.5 °C m in -1)
after initial stabilization of the electrode potentials
(overnight).
2. R esults and D iscu ssion
1 Present address: Ingold Messtechnik G m bH . D-6374
Steinbach/Ts.
: Reprint requests to B. A. Bilal, Goechem ical G roup,
N uclear Chemistry
Division, H ahn-M eitner-Institut,
D-1000 Berlin.
The experimental results are listed in Tables 1 - 2 .
Making the same assumptions as before [8 ] and
considering complete dissociation of HC1 and N aA c
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850
P. Becker and B. A. Bilal • A ssociation C onstant o f A cetic Acid
Table 1. EMF of Cell (1) and the apparent Association Constants of HAc.
T
(°C )
pa
(bar)
AEh
(mV)
Ej
(mV)
(1 0 ~ 3
25
30
40
50
60
70
80
90
108
109
145.54
147.96
152.17
156.55
161.33
166.60
172.18
178.08
184.27
190.47
197.05
203.99
210.99
218.37
226.06
233.90
242.10
249.50
257.85
266.13
275.13
284.60
0.639
0.622
0.593
0.576
0.542
0.518
0.499
0.481
0.468
0.454
0.441
0.430
0.420
0.410
0.400
0.391
0.383
0.374
0.365
0.355
0.346
0.337
5.0604
5.0604
5.0594
5.0588
5.0586
5.0591
5.0599
5.0610
5.0623
5.0635
5.0649
5.0665
5.0680
5.0696
5.0713
5.0729
5.0744
5.0755
5.0768
5.0780
5.0794
5.0807
100
110
120
130
140
150
160
170
180
190
200
210
220
230
111
114
116
119
122
125
128
131
133
137
140
143
148
151
155
160
164
169
174
180
[HAc]
m)
10 3 0HAc
(m -1)
28.60
28.55
27.79
27.27
27.16
27.52
28.16
29.08
30.26
31.43
32.95
34.83
36.78
39.15
41.90
44.88
48.38
50.93
54.78
58.63
63.66
69.65
pa
(bar)
A E b-d
(mV)
[HAc]
199
145.32
147.29
151.42
155.79
160.52
165.60
171.00
176.52
182.54
188.56
194.83
201.50
208.60
215.81
223.13
230.93
238.75
5.0601
5.0595
5.0584
5.0578
5.0576
5.0579
5.0585
5.0593
5.0605
5.0616
5.0629
5.0644
5.0662
5.0678
5.0694
5.0711
5.0733
201
207
213
219
224
230
233
242
249
255
262
268
275
282
289
297
(10~3
1 0 3 0 H A CC
m)
(m )
28.36
27.82
27.02
26.53
26.39
26.60
27.08
27.65
28.66
29.64
30.84
32.40
34.37
36.47
38.71
41.49
44.37
a p (H , + Ar). Probable error ± 3 bar.
b Probable error ± 0.1 mV.
c Probable error ± 3%.
d E: values are the same as in the left data series.
Table 2. EMF of Cell (1) and A pparent Association Constants of HAc.
T
(°C )
Pa
(bar)
AEb
(mV)
EJ
(mV)
[HAc]
(10~3 m)
(m -1)
20
25
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
202
205
208
214
220
226
232
239
245
252
258
265
271
278
285
291
299
306
314
321
329
338
347
72.18
72.94
73.87
75.99
78.21
80.47
83.03
85.66
88.60
91.51
94.60
97.62
101.17
104.57
108.32
111.96
115.62
119.40
123.45
127.29
131.37
135.71
140.78
0.624
0.614
0.599
0.575
0.562
0.534
0.516
0.502
0.488
0.479
0.470
0.461
0.455
0.448
0.442
0.435
0.430
0.425
0.419
0.413
0.407
0.401
0.396
9.619
9.608
9.600
9.593
9.587
9.583
9.585
9.589
9.598
9.606
9.617
9.626
9.643
9.656
9.673
9.688
9.702
9.716
9.732
9.745
9.759
9.775
9.797
29.5
28.3
27.6
26.9
26.4
26.0
26.2
26.6
27.4
28.2
29.3
30.3
32.2
33.9
36.3
38.4
40.7
43.2
46.5
49.2
52.7
56.9
63.4
a p (H : + Ar). Probable error ± 3 bar.
10-3 0 H A cC
b Probable error ± 0.1 mV.
Pa
(bar)
499
507
523
541
558
576
594
613
632
651
669
688
707
727
747
768
790
811
835
860
886
911
940
971
1005
AE
(mV)
Ei
(mV)
[HAc]
(10~3 m)
(m -1)
72.33
73.26
75.23
77.40
79.68
82.18
84.71
87.32
90.06
92.78
95.73
98.93
102.09
105.32
108.78
112.42
115.76
119.02
122.90
126.57
130.75
135.06
139.94
145.06
149.99
0.614
0.598
0.575
0.585
0.534
0.516
0.501
0.487
0.477
0.468
0.460
0.453
0.446
0.441
0.433
0.428
0.423
0.416
0.411
0.404
0.399
0.394
0.391
0.387
0.384
9.594
9.587
9.575
9.570
9.566
9.568
9.570
9.574
9.579
9.585
9.594
9.606
9.618
9.629
9.643
9.659
9.670
9.678
9.694
9.707
9.724
9.74
9.76
9.78
9.80
27.0
26.3
25.4
24.9
24.6
24.7
24.9
25.2
25.7
26.2
27.0
28.2
29.4
30.6
32.3
34.3
35.7
37.0
39.5
41.6
44.8
48.5
53.6
59.7
65.7
10
c Probable error ± 6%.
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3 0HAc
P. Becker and B. A. Bilal • A ssociation C onstant o f A cetic Acid
851
-H-----------1-----------1----------- 1----------- 1----------- 1----------- 1-----------1-----------1----------►
100
200
300
400
50 0
600
70 0
800
Fig. 1. T he association constant
o f acetic acid as a function o f
pressure at different tem p eratures.
90 0
p(bar)
the following equations apply to the acetate/acetic
acid system:
(2)
-E ,
/
[ H +h
The concentration of undissociated acetic acid is
given by
[HAc] = Whci. 2 - [ H +]2 .
(3)
The correction o f [H + ] 2 by subtracting the am ount
o f the free hydrogen ions generated from the disso­
ciation of water could be neglected for the same
reasons as before in both experimental series
[8 - 11].
Mass balance then yields for the concentration of
free acetate ions
[Ac ] = w NaAc - [HAc]
= w NaAc -
W HC1,2 + [ H + ] 2 .
(4)
The acetic acid association constant
[HAc]
Q HAc —
(5)
[Ac-] [H +] 2
may therefore be calculated from the measured
potentials by the equation
where: / = Faraday's Constant, 96,485 C mol 1 and
R = Gas Constant, 8.315 J m ol -1 KT1.
The junction potentials Ej were calculated from the
Henderson equation as described before [8 ], using
stoichiometric
concentrations
(molalities)
and
limiting equivalent conductances / ° ( i ) as given by
Quist and Marshall [12]. /° ( A c _) values were extra­
polated from the literature data at 18 °C and 25 °C.
The error expected from such an extrapolation is
negligible because the contribution o f acetate ion to
Ej is small [8 , 9].
A Öhac value o f 3 • 104 m _1 is obtained from the
extrapolation of the graph at 25 °C in Fig. 1 to
1 bar. This value is abo u t 10% lower than that given
by Ellilä [6 ] for 1 m N aC l m e d iu m (3.3 • 104). P atter­
son and Mesmer [13] determ ined the dissociation
quotient of acetic acid in 1 molal N aC l m e d iu m up
to 300 °C but only at pressures along the saturation
curves at the corresponding temperatures. T heir
work yields the values 3.1 • 104, 3.3 • 104, 4.3 • 104
and 6.3- 1 0 4 m _1 for the apparent association con­
stants at 25, 100, 150 and 200 °C respectively. The
extrapolation of our plots to the corresponding
saturation pressures yields values which are 3 to 5%
lower than those o f Patterson and Mesmer. This
small deviation towards lower values may be related
Whci .2 - m HCl, 1 • exp [ - (A E + Ej) • f / R T ]
Q iHAc
"* H C U
■exP [“ ( A E + Ej) ' f / R T ]
( w N a A c - "»HC1.2 + w h c i.
1 ‘ exp [ - (A E + Ej) • f / R T ] )
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(6)
852
P. Becker and B. A. Bilal • A ssociation C onstant o f A cetic Acid
to the use of argon as pressurizing m ed ium in our
experiments. This m ay change slightly the dielectric
constant e o f the solvent, where a small increase of s
has to be expected. Such relative increase may be
due to the m oderation o f the e lowering electrostatic
interaction between the N a + and Cl- ions and the
water dipols resulting from the dissolved inert gas.
Figure 1 shows that £>hac increases with rising
te m perature but decreases with increasing pressure.
T hat is quite in agreem ent with the expected
behaviour considering an electrostatical model of
the association, since the dielectric constant e varies
in the opposite direction and electrolyte systems
tend to generate more charged species with increasing
pressure and so to increase the electrostriction as a
contribution to volume reduction.
However, this sim ple electrostatical model does
not apply alone for the protonation of the acetate
anion. This is underlined by the fact that the <2hac
values at 50 °C are lower than those at 25 °C and
the graph for 25 °C intersects that for 100 °C at
p = 500 bar. Also the values o f the association con­
stant of acetic acid as a function of tem perature
( 0 - 5 0 °C) at atm ospheric pressure and infinite
dilution show a m in im u m at 25 °C [14]. U n fo r­
tunately there are no values in the work o f Patterson
and Mesmer [13] between 25 and 100 °C. Also the
measurements o f Ellilä [6 ] did not exceed 40 °C.
However, a plot o f his values (calculated as associa­
tion constants) vs. te m p e ra tu re shows a decrease
with rising te m perature and a zero slope at 40 °C,
so that a m in im u m a ro und 50 °C is probable.
[1] S. D. H amann and W. Strauss, Trans. Faraday Soc.
5 1 ,1684 (1955).
[2] A. J. Ellis and D. W. Anderson, J. Chem. Soc. 1765
(1961).
[3] D. A. Lawn, H. R. Tirsk, and L. Wynne-Jones, Trans.
Faraday Soc. 66, 51 (1970).
[4] H. M. Dawson and A. Key, J. Chem. Soc. 1239
(1928).
[6] E. Larsson and B. Adell, Z. Phys. Chem. 156, 332
(1931).
[6] A. Ellilä, Ann. Scient. Fennicae A. II. Sumalainen
Tiedea Katemia, Helsinki 5 1 ,1 (1953).
[7] P. Becker and B. A. Bilal, Fresenius Z. Anal. Chem.
3 1 7 ,118 (1984).
[8] P. Becker and B. A. Bilal. J. Solution Chem. 12, 573
(1983).
[9] P. Becker and B. A. Bilal, J. Solution Chem. 14, 367
(1985).
[10] R. H. Busey and R. E. Mesmer, J. Chem. Eng. Data
23,175 (1978).
[11] R. E. Mesmer, F. H. Sweeton, B. F. Hitch, and C. F.
Baes Jr., Int. Corros. Conf. Ser. NACE-4, 1973 (1976).
[12] A. S. Quist and W. L. Marshall. J. Phys. Chem. 73,
978 (1969).
[13] C. S. Patterson and R. E. Mesmer, private com m uni­
cation.
[14] Handbook of Chemistry and Physics. CRO Press, 67th
Edition: D-163 (1986-1987).
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