THERMODYNAMICS OF PROTON DISSOCIATION IN DILUTE AQUEOUS SOLUTION
3001
Thermodynamics of Proton Dissociation in Dilute Aqueous Solution. IX. pK, A H ,and AS"Values for Proton Ionization from
0-,
m-, and
p-Aminobenzoic Acids and Their Methyl Esters at 25"'"
by James J. Christensen,lbDonald P. Wrathal1,'c Reed M. Izatt,lband David 0. Tolman Departments of Chemical Engineering and Chemistry, Brigham Young University, Provo, Utah (Received January 9, 1967)
Calorimetric AHo values are given for stepwise proton dissociation from the protonated m-, and p-aminobenzoic acids together with AHo values for proton ionization from the three corresponding methylaminobenzoates. The pK1 values for the m- and p-aminobenzoic acids and pK values for the methylaminobenzoates were determined both by the entropy titration procedure and by the pH titration method. The pK1 value for o-aminobenzoic acid was determined by entropy titration and the pK2 values for 0- and m-aminobenzoic acids were calculated from pH titration data. The ratios ( K e ) of the molar concentrations of zwitterion and neutral molecule for the three aminobenzoic acids were determined by both a pK method and a calorimetric method. An error analysis is made to provide insight into the relative merits of the two methods, and criteria are given which provide the best method for Kz determination for any specific case. Microconstant, microenthalpy change, and microentropy change values are calculated for proton ionization from protonated m- and p-aminobenzoic acids from their respective K Z and macrothermodynamic values. 0-,
Introduction The 0-, m-, and p-aminobenzoic acids are unique amino acids in that a substantial proportion of each compound exists as the neutral molecule in aqueous solution at 25". Thus, proton dissociation from the
coz-
protonated aminobenzoic acids occurs by four different pathways as shown in reaction 1. The macroconstant, K1 and K z , macroenthalpy change, AH1" and AH2", and macroentropy change, AS1" and AS2", values can be determined by direct experimental measurements, but the letter subscripted microthermodynamic values in (1) cannot be measured directly and approximation methods must be used to determine them. The relationships between the microconstants and the macroconstants for a dibasic molecule2are
(1) (a) Supported by National Institutes of Health Grant RG9430-05. Presented in part a t the 151st National Meeting of the American Chemical Society, Pittsburgh, Pa., March 1966. Part VIII: J. J. Christensen, J. H. Rytting, and R. M. Izatt, J . Phys. Chem., 71, 2700 (1967). (b) To whom inquiries should be sent. (c) NDEA Fellow 1964-1967. (2) E. J. Cohn and J. T. Edsall, "Proteins, Amino Acids and P e p tides," Reinhold Publishing Corp., New York, N. Y., 1943.
Volume 71,Number 9 August 1967
J. CHRISTENSEN, D. WRATHALL, R. IZATT, AND D. TOLMAN
3002
Experimental Section 1 - _ 1 _ Kz Kc
+ -KD1
KlKz = K A K = ~ KBKD
(4)
(5)
Thus, once any one of the letter subscripted constants is approximated, the others can be calculated from the experimentally determined macroconstant values. Previously, in the determination of microconstant values for the aminobenzoic acids,2--8K Z has been approximated by assuming K B to be equal to the dissociation constant of the corresponding methyl or ethyl ester compound (pK method), or by assuming other physical properties (ultraviolet absorption, dielectric, solubility) to be unchanged on replacing the carboxyl hydrogen atom with a methyl or ethyl radical. Another approach is to calculate a K Z value and related microconstants from macroenthalpy changes and macroentropy change values according to the relationships
+
(6)
+ (1 - CY)AXD"
(7)
AX1" = CYAXA" (1 - a ) A X B 0 and
AX," = a A X c "
where A X " is either AH" or AS' and CY
Kz = 1-CY
If either of the pairs AXA"and AXB"or Axe" and AXD" is approximated, CY and Kz can be calculated. Although two approximations are required in this method compared to only one in the pK method, K Z is generally much less sensitive to errors in the assigned AX," (i = A, B, C, or D) values than it is to errors in the assigned K , values (see Discussion). The use of approximated AH," and ASt" values t o derive K Z will be designated the AH" method and the AS" method, respectively. As far as can be ascertained, no A S " or calorimetric A H " values for proton dissociation have been reported for the substances in this study. The pK, AS", and calorimetric AH" values determined here are used to make independent, quantitative determinations of the Kz values for the aminobenzoic acids. I n addition, the microthermodynamic AH,"(i = A, B, C, or D) and AS," values are determined for the four dissociative pathways in m- and p-aminobenzoic acids. The susceptibility of K Z values to errors in the assigned K,, AH,', and AS," values is analyzed for the pK, AH", and AS" methods, respectively. The Journal of Physical Chemistry
Materials. Reagent grade HC1O4 (Baker and Adamson), reagent grade NaOH (Baker Analyzed), reagent grade o-aminobenzoic acid (Matheson Coleman and Bell), m- and p-aminobenzoic acids (Eastman White Label), and the methylaminobenzoates (Eastman White Label) were all used without further purification. Equivalent weight determinations of 0-, m-, and paminobenzoic acids were made and values of 99.7 f O.l%, 99.0 f 0.2%, and 99.9 f 0.1% of the corresponding theoretical values, respectively, were obtained. The NaOH solutions were standardized with potassium hydrogen phthalate (National Bureau of Standards) and the HClOd solutions were standardized with tris(hydroxymethy1)aminomethane (Fisher primary standard). The titer of the XaOH and HClOd solutions was also checked by titrating one against the other. All water used in solution preparations was doubly distilled and boiled before use. All solutions were prepared, stored, and used under a nitrogen atmosphere. Equilibyium Constant Determinations. The pH titrations of all aminobenzoic acid and methylaminobenzoate solutions were made with standard HC1O4solutions, and pH titrations of 0- and m-aminobenzoic acid solutions were made with standard NaOH solutions at 25' in a water bath controlled to i=OO.O5". Equilibrium constant and heat determinations were made using identical solution concentrations. The titration procedure was identical with that already describeds except that the glass and calomel electrodes were calibrated against a pH 4.008 potassium hydrogen phthalate (SBS Sample No. 185c) buffer solution. Equilibrium constant determinations for the first proton dissociation from the protonated aminobenzoic acids and methylaminobenzoates were also made calorimetrically using the entropy titration method. lo Heat Determinations. The AH1 values were determined for the aminobenzoic acids by adding sufficient standard S a O H solution in each case to form the predominantly ionized form (A-), and by titrating the resulting solution with a standard HC104 solution. (3) A. Bryson and R. W. Matthews, Australian J . Chem., 14, 237 (1961). (4) A. Bryson, J . Am. Chem. Soc., 82, 4858 (1960). (5) J. T. Edsall and M. H. Blanchard, ibid., 5 5 , 2337 (1933). (6) G. Devoto, Gazz. Chim. Ital., 63, 247 (1933); 64, 371 (1934). (7) I. M. Klotz and D. M. Gruen, J. Am. Chem. SOC.,67,843 (1945). (8) A. V. Willi and W. Meier, Helv. Chim. Acto, 39, 318 (1956). (9) D. P. Wrathall, R. M. Izatt, and J. J. Christensen, J . Am. Chem. SOC.,86, 4779 (1964). There is an error in this article. For details, see D. P. Wrathall, R. M. Izatt, and J. J. Christensen, ibid., 87, 5809 (1965). (10) J. J. Christensen, R. M. Izatt, L. D. Hansen, and J. A. Partridge, J . Phys. Chem., 70, 2003 (1966).
THERMODYNAMICS OF PROTON DISSOCIATION IN DILUTE AQUEOUSSOLUTION
Table I : pK", AH', and ASo Values for Proton Ionization from the Aminobenzoic Acids and Their Methyl Esters at 25" a AS', AH', PK
cal/deg mole
kcal/mole
Methyl-o-aminobenzoate (HA+ = A 2.32 f 0.03,b2 . 3 6 f 0.03,' 4 . 5 7 f 0.12' 2 . 33,d 2.24'
+ H+) 4 . 5 f 0.4'
+
o-Aminobenzoic acid ( H A + = HA H +) 2 . 0 9 f 0.02,' 2.17 i 0.02,' 3 . 7 9 f 0.10' 3 . 0 f 0.3' 2.05,d 2.11,' 2 14,h 2.05,i 2 . 14i
3003
Values of AH1for the aminobenzoic acids and AH values for the methylaminobenzoates were determined by appropriate titrations with standard HClOd solutions. The thermometric titration apparatus used in these calorimetric determinations has been described." Calculations. A . AH and AH". The method used to calculate AH and AH" values from the thermometric titration data has been described.l2#l3 B. pQ and pK. 1. From p H Titration Data. The method used to calculate pQ and pK values from pH measurements has been d e ~ c r i b e d . ~The DebyeHuckel expression
+
o-Aminobenzoic Acid (HA = AH+) 4.97 f 0 . 0 1 J b 4 . 8 5f 0.03,f 2 . 7 9 f 0.08" -13.4 f 0 . 3 " 4.95,' 4.77,k 4.80,h4.95,' 4.98,j 4.97,i 4,97"
+ H +)
Methyl-m-aminobenzoate (HA + = A 3 . 5 8 f 0.02,"3.61 f O.OIJb 6 . 5 0 & 0.06" 3 . 5jlk3.55,' 3 . 56e m-Aminobenzoic acid ( H A + = HA 3.07 i 0.05,' 3 . 0 7 f O.O1,b 2.56 f 0.03' 2.90,d3 . 0 8 , p 3 . 1 2 , p3.07,; 3.05,"3.09'
5 . 4 f 0.2'
+ H+) - 5 . 4 i 0.1'
+
m-Aminobenzoic Acid (HA = AH+) 4 . 7 9 f 0.01,b4.77,P4.74,0 4 . 1 7 f 0.03" - 7 . 9 f 0 . 1 " 4.73,; 4.60,"4.79,'4.78l
+ H+)
Lfethyl-p-aminobenzoate (HA+ = A 2 . 5 0 f O . O l l b 2 . 4 5 i 0.02,' 5.09 f 0.04' 2.46,' 2.40,; 2,38'
5 . 9 f 0.1'
+
p-Aminobenzoic Acid (HzA+ = HA H+) 2 . 4 3 i 0 . 0 2 , b 2 . 4 11 0 . 0 4 , " 4.97i0.12" 5.6f0.4' 2.33,d2.45,' 2.411g 2.49,*2.37,' 2 . 38;
+
p-Aminobenzoic Acid (HA = AH+) 4.85,'4.87,p4.85,e4.8gJi 0 . 7 0 f 0.02" - 1 9 . 8 f 0.1" 4.92,' 4.94' Uncertainties in pK, AH', and AS" values are given as standard deviations. This laboratory, pH titration. This laboratory, entropy titration.1° H. H. Stroh and G. Westphal, Ber., 96, 184 (1963). e A. C. Cumming, 2. Physik. Chem., 57, 574 (1907). P. Leggate and G. E. Dunn, Can. J. Chem., 43, 1158 (1965). P. 0. Lumme, Suomen Kemistilehti, 30B, 176 (1957). A. M. Liquori and A. Ripamonti, Gam. Chim. Ital., 85, 578 (1955). S. Kilpi and P. Harjanne, Suomen Kemistilehti, 21B, 14 (1948). ' K. Winkelblech, 2. Physik. Chem., 36, 564 (1901). D.Peltier and M. Conti, Compt. Rend., 244, 2811 (1957). B. Holmberg, 2. Physik. Chem., 62, 708 (1907). €I. Lunden, ibid., 54, 549 (1906). This laboratory, thermometric titration.12p1a C. G. Clear and G. E. K. Branch, J . Org. Chem., 2, 522 (1938). Reference 3. ' R. A. Robinson J. and A. I. Biggs, Australian J . Chem., 10, 128 (1957). Johnston, Z. Physik. Chem., 57, 557 (1907). A. Albert and R. Goldacre, Nature, 149, 245 (1942).
'
'
(9) ( A = 0.5092, B = 0.3286, ai = 5 A) was used to calculate activity coefficients for all charged species. Calculations were aided by an IBM 7040 computer. 2. From Thermometric Titration Data.lo The thermometric titration curve was read into the computer by supplying temperature rise data (11 points) taken at 1-min intervals. The pK value yielding the smallest deviation in the AH values calculated a t the 11 points of the thermometric titration curve was taken to be the pK value of the substance being titrated. Equation 9 was used t o calculate activity coefficients. C. K Z Values. 1. From pK Data. The dissociation constant K B is set equal to the dissociation constant for the corresponding methyl ester, KE. Then, from eq 3, K A = K1 - KE, and from eq 2, K Z = (K1 -
KE)/KE. 2, From AH" and AS" Data. K Z values for the aminobenzoic acids were calculated from calorimetric data using eq 6 and 8. I n these calculations, AXA" and AXB" (X = H or S)values are approximated in value is set equal to the the following way. The UB" value for the corresponding ester, AXE'. The AXA" value is assigned by taking the average of the corresponding AXo value^^^-^^ of ortho-, meta-, and para-substituted benzoic acids having electron-attracting substituents (-NOz, -CN, -Br, -C1, -I, and -COOH groups). AHA" values obtained in this way are 0.10 f 0.09, 0.02 f 0.22, and -2.4 f 1.3 kcal/mole and MA'values 2 cal/ are -16.8 f 0.3, -16.8 f 0.7, and -22
*
(11) J. J. Christensen, R. M. Izatt, and L. D. Hansen, Rev. Sci. Instr., 36, 779 (1965). (12) J. J. Christensen and R. M. Ieatt, J. Phys. Chem., 66, 1030 (1962). (13) R. M. Izatt, J. J. Christensen, R. T. Pack, and R. Bench, Inorg. Chem., 1 , 828 (1962). (14) G. Briegleb and A. Bieber, 2.Elektrochem., 55, 250 (1951). (15) D. H. Everett and W. F. K. Wynne-Jones, Trans. Faraday Soc., 35, 1380 (1939). (16) L. Eberson and I. Wadso, Acta Chem. Scand., 17, 1552 (1963).
Volume 7 1 , Xumber 9 August 1907
J. CHRISTENSEN, D. WRATHALL,R. IZATT, AND D. TOLMAN
3004
~
Table 11: Summary of K Z Values for o-, m-, and p-Aminobenzoic Acids a t 25"
a-Aminobenzoic Acid 0. loo m-Aminobenzoic Acid
0.20' 0.sg 2.2,o 2.5h 2.0, 2 . o j 2.3'
1.5,' 1.7h 1.2,i 1.23' 1.5'
1.5'
p-Aminobenzoic Acid 0.09" 0.02'
0.10," 0.17' 0.04,k 0.14' 0.1Oli 0.13'
0.06O
0.6-0. 8E
1.0'
34e
0.01'
0.09" 0.03d
0.1-0.2'
-
Calculated from K z - ( K I K E ) / K Ewhere , K E is the dissociation constant for the methyl ester. Calculated as described in text (see Results). Calculated using eq 6 and 8. Reference 7. Calculated from ultraviolet absorption data. e Reference 6. Reference 2. ' Calculated from calorimetric pK, AH", or AS" data, this laboratory. Calculated from dielectric increment data. Reference 8, valid a t 20' and ~1 = 0.1 F (KC1). Reference 3. R. A. Calculated from p H titration pK data, this laboratory. Calculated from Robinson and '4. I. Biggs, Australian J. Chem., 10, 128 (1957). E Reference k, K E determined using ethyl ester. Kz = KA/(K~ K A )where K A is the dissociation constant of p-trimethylbenzobetaine acid, J. Johnson, 2. Physik. Chem., 57, 557 (1907). Reference 7, determined using ethyl ester.
'
'
deg mole for p-, m-, and o-aminobenzoic acids, respectively.
Results I n Table I are given pK (calculated from both pH titration and thermometric titration data), AH", and AS" values together with corresponding literature values where available for the substances studied." I n Table I1 are summarized K z values for o-, m-, and p-aminobenzoic acids calculated from pK, AH", AS", absorption, and dielectric increment data, where the symbols in parentheses indicate the method of Kz determination. The calculation of K z ( K B ) is based on the assumption that KB may be set equal to the dissociation constant, K E , for the corresponding protonated methylaminobenzoate compound. Actually, the effect of a methyl ester group on the proton dissociation constant, of the neighboring -NH3+ group in the protonated methylaminobenzoate species will not be exactly the same as the corresponding effect of a carboxyl group in protonated aminobenzoic acids. The Hammett values for the meta-substituted carboxyl group (urn= 0.355), the meta-substituted methyl ester group ( a , = 0.315), and the pvalue ( p = 2.77) are well knownl8 for aqueous solution containing the metasubstituted anilinium cations at 25". Thus, the Hammett equation (log K - log K" = up) can be used to correct for the difference between KBand KE,and a corE 0.11 is calculated where rection term pKB' = ~ K u is the difference between u,(COOH) and u,(COOCH3). Values for Kz(KB') are calculated using this The Journal of Physical Chemistry
corrected pKB value. Using the K z values of 1.4 for m-aminobenzoic acid and 0.09 for p-aminobenzoic acid, the pK, AH", and AS" values for the four proton dissociation reactions given in (1) were calculated. The values are summarized in Table 111. I n the case of m-aminobenzoic acid, the K z value used is the average of the Kz(KB'), Kz(AH"), and Kz(AS") values in Table 11. For p-aminobenzoic acid, the K z ( K A )value in Table I1 was chosen as the most reliable for reasons explained in the Discussion.
Discussion The data in Table I show the pK values determined in the present study to be in good agreement with previous data where these are available. The pK values (Table I) calculated from pH titration and thermometric titration data are in excellent agreement. K Z values determined in the present study using the pK method lie in the same range as those determined by other workers using the same method for both m- and p-aminobenzoic acids. The K1; values for m-aminobenzoic acid determined using the AH" and AS" methods were substantially lower than those obtained using the pK method (Table 11) ; however, application of the Hammett correction to the K z ( K B )values results in (17) The p H titration data from which p K values were calculated and heat rise data from which pK, AH", and A S " values were calculated are included in the doctoral thesis of D. P. Wrathall, Brigham Young University, 1967. (18) H. H. Jaff6, Chem. Rev., 53, 191 (1953).
THERMODYNAMICS OF PROTON DISSOCIATION IN DILUTE AQUEOUS SOLUTION
~~~~~~~
~~~~~~~~
3005
~
Table I11 : Thermodynamic pK, AH",and ASo Values for Proton Dissociation from Protonated m-Aminobenzoic and p-Aminobenzoic Acids at 25" AS', cal/deg mole
AH',
kcal/mole
Reaction
+HbNCeHpCOOH = +HaNCeHpCOOH = +HaNCgHpCOO- = H2NCeHpCOOH HzNCeHpCOOH = +HaNCsH,COOH +H,NCeHpCOOH 'HaNCaH4COOHiNC6HaCOOH HzNCnHpCOOH
+HaNCsH&OOHiNCsHiCOOH HpNCsHpCOOHzNCsHaC00+HaNCsH&OO-
+HaNCaHpCOOHzNCeHpCOOH HzNCeHaCOOHzNCeHpCOO= +HaNCsHpCOO-
= = = =
m-Aminobenzoic Acid (Kz = 1.4) AHA' = 0.0 ~ K =A 3.30 ~ K =B 3.45 AHBO = 6.5 pKc = 4.50 AHc" = 6.5 ~ K = D 4.41 AHDO = 0.1 pKz = -0.15 A H ~ O= -6.5
+ H+ + H+ + H+ + H+
p-Aminobenzoic Acid (Kz = 0 09) AHA' = 0.1 ~ K =A 3.49 PKB = 2.45 A H B O = 5.1 pKc = 3.79 A H c o = 5.1 ~ K= D 4.83 A H D O = 0.4 pKz = 1.04 AHzo = -5.0 I
+ H+ + H+ + H+ + H+
Kz(KB') values which agree well with the Kz(AHO) and Kz(AfJ0)values. The ASBO values of m- and p-aminobenzoic acids (Table 111) are within experimental uncertainty equal to each other, but the corresponding 1
i
A H B O
ASA" = -15.6 ASB" = 5.9 ASc" = -0.2 ASD"= -20.8 ASz" = -21.5
values differ by 1.4kcal/mole as shown in (10). Thus, the difference in acidity between I and IV is predominantly an enthalpy effect.
and AGBO
1
N
.^C
I
12
(AGO
IO
t '8
8 0
t
6
-30
z6 4
Error Analysis of Four Methods of
Determination
Figure 1. The average per cent absolute error in Kz is the error corresponding to an error of 0.01 pK unit in the assigned pK values or to an error of 0.01364kcal/mole (or 0.041 cal/deg mole) in both of the assigned AX" values. In the case where both PKA and ~ K are B approximated or where AXA"and AXB"are approximated, only the maximum possible error in K z is shown. D = IAXA' - A x g o [ .
I1
I11
= -1.4 kcal/mole; A H o
IV
- 1.4 kcal/mole; TASO = 0)
A possible explanation for the difference in acidity between I and IV in terms of resonance effects has been advanced by Cohn and Edsall.'O The A&" values are very close to zero for both nzand p-aminobenzoic acids. Diebel and Swin6hartJ2Oa following the reasoning of Frank and EvansJ20bstated: "A zwitterion. . .binds many more water molecules (than does a neutral molecule) due to interaction of the water dipoles with the widely separated charges of the zwitterion. Thus, when such a zwitterion separates into two independent ions, the change in amount of water bound is much smaller than for neutral acids, resulting in a markedly smaller entropy of ionization for the zwitterion.'' This reasoning was used by Diebel and Swinehart208 to argue that m- and p-aminobenzenesulfonic acids ( A S o of ionization -0.6 and -0.4 cal/deg mole, respectively, a t 25") exist in water predominantly in the zwitterion form. The ASCO values form- and p-aminobenzoic acids (0.9 and -0.2 cal/deg (19) Reference 2, pp 124-129; see also L. Fisher-Hjalmors, Arkiv Fysik, 2 1 , 123 (1962). (20) (a) R. N. Diebel and D . F. Swinehart, J. Phys. Chem., 61, 333 (1957); (b) H.S. Frank and M. W. Evans, J. Chem. P h y s . , 13, 507 (1945).
Volume 7 1 , Number 9 Auguet 1987
3006
J. CHRISTENSEN, D. WRATHALL, R. IZATT, AND D. TOLMAN
mole, respectively) support this conclusion since the aminobenzoic acid zwitterion ( +H3NC6H4Co2-)is quite similar in structure to the aminobenzenesulfonic acid zwitterion ( +H3NC6H4so3-). An error analysis has been made of the pK and AHo (or A S o ) methods for Kz determination and the results are shown in Figure 1. I n the calorimetric method, the error in Kz is inversely proportional to the difference [AxA'- AXB']. Thus, for example, if this difference were 3 kcal/mole or 10 cal/deg mole, the error in Kz would be twice as large as those shown in Figure 1. From Figure 1, it is apparent that (a) the calorimetric method is less susceptible to error than any of the pK methods when IAXAO - AXB'\ is greater than 6 kcal/mole ( X = H ) or greater than 20 cal/deg mole ( X = 8) and when 0.2 < Kz < 5 ; (b) in using the pK method, KA should be approximated when Kz is small, KB when K z is large, and either KA or KB or both K A and KB should be approximated for intermediate K Z values. The calorimetric method and approximation of both K Aand KB in the pK method of microconstant determination have the additional benefit that the errors in the assigned values may partially or wholly cancel each other. The wide variation in the Kz(K,) values given in Table I1 for p-aminobenzoic acid can be understood from the results of the error analysis shown in Figure 1. Since Kz is small for this compound, the calculated Kz value is very sensitive t o any error in the assigned KB value. A better way to determine the Kz value for this compound is to estimate KA since K Zis very insensitive to any error in the assigned K A value. The Kz(KA) value for p-aminobenzoic acid in Table I1 should therefore be considered the most reliable of any given for that substance.
The Journal of Physical Chemistry
Any intramolecular hydrogen bonding between the
-COOH and -NH2 groups in o-aminobenzoic acid would have the effect of raising the calculated Kz(KB)value, whereas the Kz(AS") value (assuming that the ASo value for intramolecular hydrogen bonding is small compared to the corresponding AGO value21) should be little affected. If the Ah'" value for intramolecular hydrogen bonding is assumed to be zero in o-aminobenzoic acid, then it is found that a postulated AGO value of -0.3 kcal/mole for reaction 11 is necessary to bring the Kz(KB) value (0.9) into agreement with the Kz(ASo) value (0.06). This is comparable to average
AGO values of intramolecular hydrogen bonding22for
P 0-P-0--H I
0 I 3-P-0-H
R&x
of -0.3 kcal/mole when X = Br or C1 and -0.6 kcal/mole when X = OCH3. (21) H.H.Jaff.6, J . Am. C h m . Soc., 79, 2373 (1957). (22) H.H.Jaff.6, L. D. Freeman, and G. 0. Doak, ibid., 76, 1548 (1954).
