THE CLASSICAL DISSOCIATION CONSTANT OF BENZOIC ACID I N VARIOUS SALT SOLUTIONS*, LEONARD C. RIESCHS AND MARTIN KILPATRICK Laboratory of Physical Chemistry, University of Pennsylvania, Philadelphia, Pa.
Received Octohw 10, 1834
In the previous paper (lo) the catalytic constant of the hydrogen ion in the 'hydrolysis of diethyl acetal was determined in aqueous solutions of nine solvent salts. With the determination of the temperature coefficient this reaction can now be employed to measure kinetically the hydrogen-ion concentration of suitable buffer solutions. This paper presents the determination of the dissociation constant of benzoic acid in the nine solvent salt solutions over a wide range of concentration. (kH30t)
EXPERIMENTAL PART
Suitable buffer solutions were made from benzoic acid and carbonatefree sodium hydroxide solution, and the purified salts were added. The experimental method was the same as that used in the previous paper. The hydrogen-ion concentration was calculated from the equation: kobsd./kH~O+ = c H a O +
where the value of hH30+is that for the corresponding concentration of the electrolyte. The classical dissociation constant (K,) was calculated from and the stoichiometric composition of the buffer solution. the CH~O+ Table 1 gives the results of the measurements with lithium chloride, and tables 2 and 3 summarize the results in the other salt solutions. The results are presented graphically in figure 1. The wide variation in the dissociation constant of the acid in the different salt solutiorp is particularly striking. For example, at 1 molar electrolyte concentration the difference between the lowest and the highest values is over 100 per cent, the value in lithium chloride being 12.84 and that in sodium p-toluenesulfonate 5.47. 1 An abstract of this paper was presented a t the Eighty-sixth Meeting of the American Chemical Society held a t Chicago, September, 1933. 2 Abstracted from the dissertation of Leonard C. Riesch presented to the Faculty of the Graduate School of the University of Pennsylvania in partial fulfillment of the requirements for the degree of Doctor of Philosophy, June, 1934. 3 George Leib Harrison Fellow in Chemistry, 1933-34.
891
892
LEONARD C. RIESCH AND MARTIN KILPdTRICK
In order to analyze the differences further, the value of the ratio fHfB/fHB was calculated from the equation:
Ka = Kc fHfB/fHB (1) where K , represents the thermodynamic dissociation constant. The value of K , used by Kilpatrick and Chase (4), 6.31 X has recently been confirmed by accurate measurements by Brockman and Kilpatrick (1).
I
0
I
I
I
I
2
1
I
3
E/ectro/yte Concen&vfion -Molarity FIQ. 1. ELECTROLYTE EFFECTON
THE
DISSOCIATION CONSTANTOF BENZOIC ACID
+,
0 , KC1; A, NaCl; LiC1; 0 , NaCIO4; 0, LiN03; X, NaN03; +, KNOa; V, CsH5SO3Ns; 0 , p-CeH4(CH3)S02”.
To -obtain the mean activity coefficient of the ions of benzoic acid, was calculated from the equation
d f H f B , fHB
10gfHB =
Pc
(2)
by using the experimental data in the literature. Table 4 gives the values of the ‘kalting-out” constant. In the case of the sulfonates the values were plotted from the data of Os01 and Kilpatrick (9), and the activity coefficients were read from the plots. The values of djTBare given in tables 5 and 6. A t 0.10 molar salt concentration the values ‘ /of l are the same within
893
DISSOCIATION CONSTANT O F BENZOIC ACID
2.5 per cent in the various salt solutions, while a t 1, 2, and at 3 molar the maximum differences are 20,25, and 40 per cent, respectively. The mean activity coefficient is greatest in sodium chloride solutions. The order for TABLE 1 The dissociation constant of benzoic acid in lithium chloride solutions at R6T. LiCl
HB
+ NeB
moles per liter
moles per lifer
0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.005 0.005 0.005
0.10 0.20 0.40 0.60 0.80 1 .oo 1.50 2.00 2.41 3 .OO
k
c&Ot
OBSERVED
x
io4
2.040 2.198 2.402 2.402 2.398 2.392 2.277 1.036 0.4772 0.3755
0.01794 0.02160 0.02828 0.03409 0.04030 0.04741 0.06770 0.04606 0.03025 0.04025
Ke X 106
10.83 11.73 12.90 12.90 12.87 12.84 12.18 IO.80 9.59 7.60
TABLE 2 The dissociation constant of benzoic acid in salt solutions at 36°C. SALT
+ NaB
1
Ko x
106
NaCl
KCI
CeH&903Na
10.59 11.46
IO. 15 11.21
10.09 10.99 11.12
9.88 10.22
IO,97 10.73
9.57
7nolos per liter
0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.80 1.oo 1.25 1.50 2.00 2.50 3.00
11.41 11.71 11.51 11.94 11.85 11.40
11.20 10.88
9.91 8.71 6.78 4.85
9.58 8.11 6.99 5.04
9.39 8.27 6.84 5.28
8.18 6.63 5.47
the chlorides and nitrates a t high concentrations is Na > K > Li, and for the sodium salts the order for the anions is C1 > Clod > NO3 > sulfonates. The other values for the dissociation constant of benzoic acid that are given in the literature are a t 18°C. and 20"C.,and it is probable that the change of the dissociation constant over this range of temperature is small.
894 .
LEONARD C. RIESCH AND MARTIN KILPATRICK
This is borne out by the results of the determination of the temperature coefficient of the dissociation constant between 35°C. and 25°C. by the two-thermostat method. The results are summarized in table 7. It is to be noted that, except for the values for 3 molar sodium chloride, the temperature coefficient in the various salt solutions is constant within approximately 3 per cent. From the average value 3.455, as compared TABLE 3 The dissociation constant of benzoic acid in salt solutions at 26°C. SALT
K c X 106
+ NaB LiNOa
1
NaNOa
KNOI
NaClO4
10.21 11.28 12.46 12.32 12.16 12.02
10.43 11.31 11.71 11.73 11.52 11.15
10.35 11.10 11.48 11.49 11.14 10.83 10.41
10.43 10.87 10.47 10.24 9.63 8.88
11.03 9.83
9.97 9.03 -8.01 6.81
moles per liter
0.10
0.20 0.40
0.60 0.80
1 .oo 1.20 1.50 2.00 2.50 3 .OO
7.16
7.45 6.15 3.73
Values o j the “salting-out” constant SOURCE
SALT
LiC1.. ................................. NaCl ................................... KC1.. .................................. LiNOs ..................................
0.192 0.177 0.138 0.078
N a N 0 3 . . ............................... KNOa.. ................................ NaClOl.. ..............................
0.080 0.040
0.062
Larsson (8) Larsson (7) Chase and Kilpatrick (2) Larsson (8), HaessIer (3) and Kolthoff and Bosch (6) Larsson (8) Larsson (8) Kolthoff and Bosch (6)
with 3.395 for h b / k 2 5 for strong acids, it is evident that the temperature coefficient of the dissociation constant is small over this range. A comparison of the values of the dissociation constant of benzoic acid in potassium chloride solutions as determined by the kinetic method with those determined by means of the quinhydrone electrode shows that the results are not in agreement a t concentrations above 2 molar. Repeated
895
DISSOCIATION CONSTANT O F BENZOIC ACID
determinations by the two methods in 3 molar potassium chloride solution consistently show this discrepancy. With 3 molar sodium chloride a TABLE 5 The mean activity coeflcient of the ions of benzoic acid at 86°C. ELPCTROLY T E CONCENTRATION SALT NaB
1
+
LiCl
NaCl
KCl
NaClO4
0.78 0.77
0.79 0.77
0.80 0.77 0.78
0.78 0.77
0.76
0.80
moles per liter
0.10 0.20 0.30 0.40 0.50 0.60 0.80 1.oo 1.50 2.00 2.41 2.50 3.00
0.80 0.80
0.82 0.85 0.91 1.08 1.28
0.80 0.83 0.87 1.oo
1.18
0.85 0.89 1.03 1.21
0.82 0.86 0.90 1.03 1.17
1.38 1.60 2.10
1.76
1.41 1.80
TABLE 6 The mean activity coeflcient of the ions of benzoic acid at ELECTROLYTE CONCENTRATION SALT NaB
+
LiNOs
NaNOa
KN0a
CaHrSOaNa
0.10 0.20 0.25
0.79 0.76
0.79 0.76
0.78 0.76
0.40
0.74
0.76
0..75
0.78 0.74 0.73 0.72 0.72
0.76 0.77 0.79
0.77 0.80 0.82
0.76 0.78 0.80 0.82
0.87 0.95
0.91
1.23
1.26
1.61
.Mac.
moles per liter
0.50 0.60 0.80
1 .oo
1.20 1.25 1.50 2.00 2.50 3.00
1 .oo 1.13
0.71 0.72
0.78 0.74 0.71 0.71 0.71 0.71
0.74 0.79
similar discrepancy exists. I n order to investigate this difference the assumptions of the kinetic met,hod were tested further. The assumptions
896
LEONARD C. RIESCH AND MARTIN KILPATRICK
involved in the determination of k ~ ~ are 0 + as follows: (1) The hydrogen ion is the sole catalyst. (2) The energy of activation is constant within the experimental error of measurement from 0" to 35°C. (3) The energy of activation is independent of the salt concentration. TABLE 7 The temperature coeficient in benzoate buffers SALT
SALT
NaB.. ..
. .. . , , . . . . , . . . . , , . . . . . . . . . . . . . . . . . .
KCI . . . .
. . . . . . . . . .. .. . . . . . . . . . . . . . . . . . . .
, .{
+ NaB
0.005 0.10 0.50 1.oo
1.50 2.00 3 .OO 2.00
NaC104.. . . . , . , , .. . . . . . . . . . , . , . . . . . . . . . . . . , LiCI.. . .. .. .. .. ... . , .. . .. . .. .. . . . . ,. . . . .. . . NaNOa.. . . .... . .. . . . . . . ... . .. . . .. . . . ... . CeHjS03Na.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p-C6H4(CHS)SO3Na. . . . . . . . . . . . . . . . . , . . . . . ..
3.00 3.00 3.00 3.00 1.OO 1.OO
.......................
.
-
Average . . . . . . . . . ,
{I ;:::
.
. , . , .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ,
DEVIATION FROM 3.456
moles per liter
(
NaCl . . . . . . .
kaslkna
3.469 3.384 3.505 3.474 3.457 3.395 3.519
0.011 0.071 0.050 0.019 0.002 0.060 0.064
3.417 3.168* 3.113* 3.148* 3.504 3.379 3.443 3.423 3.546
0.038
0.049 0.076 0.012 0.032 0.091
fO ,044
3.455
* Omitted from the average, TABLE 8 The effect of reaction products upon the velocity constant HB
I
I
KCI+NaB
moles per liter
mole8 per liter
0.005 0.005 0.005
3 .OO 3.00 3 .OO
0.01580 0.01523 0.01488
0.2590 0,2497 0.2440
K c X 106
5.22 5.03 4.91
To test these assumptions the dissociation constant of acetic acid in potassium chloride solutions was determined electrometrically. At the same time independent kinetic determinations were made on the same buffer solutions. Both methods gave results in agreement over the range from 0.10 t o 3.0 molar potassium chloride concentration (5). Similar
,
897
DISSOCIATION CONSTANT OF BENZOIC ACID
agreement was found for glycolic acid-glycolate buffers in potassium chloride solutions. Evidently the discrepancies a t 3 molar salt concentration in the case of benzoic acid are not due to the invalidity of the assumptions. In fact, the results indicate that the high primary salt effect is not conTABLE 9 Comparison with equation 6 ELECTROLYTE
PER
I
m
B
OBSERVED
I
‘ d f z CALCULATED
0.60
0.78 0.77 0.80 0.82
0.80 0.78 0.79 0.82
0.10 0.20 0.40 0.60
0.78 0.76 0.75 0.76
0.79 0.76 0.75 0.77
0.10 0.20 0.40 0.60
0.79 0.77 0.80 0.82
0.80 0.77 0.78 0.82
0.10 0.20 0.40 0.60
0.79 0.76 0.74 0.76
0.79 0.76 0.75 0.76
0.10 0.20 0.40
CsHaS03Na(B = -0.124)
KCl (B = -0.216) 0.10 0.20 0.30 0.50
0.10 0.20 0.40
0.60
0.80 0.77 0.78 0.80
0.80 0.77 0.77 0.80
0.10 0.20 0.25 0.50
0.78 0.74 0.73 0.72
0.78 0.74 0.73 0.72
0.78
0.79 0.77 0.76 0.79
0.10 0.20 0.40 0.60
0.78 0.74 0.71 0.71
0.75 0.74 0.71 0.71
0.77 0.76 0.80
1
0.10 0.20 0.40 0 60
0.79 0.76 0.76 0.77
0.79 0.76 0.75 0.77
nected with any catalytic effect of the hydrochloric acid molecules. Any explanation of the difference in the results must therefore be related to the benzoic acid buffer itself or to some specific reaction with the acetal, or to the products of the reaction. Varying the buffer ratio has little effect on the calculated dissociation constant. It is not possible to vary the acetal
898
LEONARD C. RIESCH AND MARTIN KILPATRICK
concentration very greatly, but the effect of the products of hydrolysis was tested in the following manner. An experiment was carried out in the usual way; the buffer solution was then drawn back into the mixing chamber, another portion of acetal was added, and the experiment repeated. Upon completion of this experiment the process was repeated. The results are given in successive order in table 8. Although there is about 6 per cent change in the kobsd. and in the resultant dissociation constant, the magnitude of this effect cannot account for the 20 per cent difference between the results by the two methods in 3 molar potassium chloride solution. In no case did the velocity constants show a trend. As pointed out by Chase and Kilpatrick (2) the mean activity coefficient of the ions of benzoic acid can be represented by an equation of the form
where K equals 0.33 X lo8 d C and 6 is the apparent average ionic diameter. The /3 is an empirical constant which should include salting-out and interaction effects. If we arbitrarily set b equal to 3.0 X lov8 cm. the above equation becomes:
By plotting log
0.5 dc djzB+ - against the concentration, B has been
1+dc
evaluated for each solvent salt. The observed and the calculated values up to 0.6 molar are given in table 9. Over this range the order of decreasing activity coefficients is Na > K > Li. For the sodium salts one finds Clod > C1 > NO3 > RSO1, but at higher concentrations the mean activity coefficients become greater in sodium chloride than in sodium perchlorate. SUMMARY
1. The classical dissociation constant of benzoic acid has been determined kinetically in solutions of lithium chloride, sodium chloride, potassium chloride, lithium nitrate, sodium nitrate, potassium nitrate, sodium perchlorate, sodium benzenesulfonate, and sodium p-toluenesulfonate. 2. From the values of the activity coefficient of molecular benzoic acid and the thermodynamic dissociation constant, the mean activity coefficients of the ions of benzoic acid in the several salt solutions have been calculated.
DISSOCIATION CONSTANT OF BENZOIC ACID
REFERENCES
(1) BROCEMAN AND KILPATRICK: J. Am. Chem. SOC. 66, 1483 (1934). J. Am. Chem. SOC. 63, 2589 (1931). (2) CHASEAND KILPATRICK: (3) HAESSLER: Thesis, Columbia University, 1929. AND CHASE:J. Am. Chem. SOC. 63, 1732 (1931). (4) KILPATRICK (5) KILPATRICE, CHASE,AND RIESCH:J. Ani. Chem. SOC.66, 2051 (1934). (6) KOLTHOFF AND BOSCH: J. Phys. Chem. 36, 1685 (1932). (7)LARSSON:Z.physik. Chem. 148A, 304 (1930). (8) LARSSON: Z.physik. Chem. 163A, 299 (1931). J. Am. Chem. SOC.66, 4430 (1933). (9) OSOLAND KILPATRICK: J. Phys. Chem. 39, 561 (1935). (10) RIESCHAND KILPATRICK:
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