JAMES,J. CHRISTEKSEY AND Rnm M,IZATT
1on0
List of Symbols atom fraction of constituent i; 2 = solute molal free energy of constituent, i in the reference state Xi = 1 AG1-a" = molal freo energy of mixing of the binary solvent G,--sXa = excess molal free energy of mixing of the binary solvent
Xi G,O
= =
a, 6 9 8
VOl. 60
= partial molal free energy of constituent in = excess partial molal free energy of constitu-
ent i in the binary solvent excess partial molal free energy of constituent i in solvent j Superscript ' = phase having constituent 1 in large excess Superscript " = phase having constituent 3 in large excess K2 = atom fraction partition ratio (distribupn coefficient) of solute between " and G ( i p
=
TEIliliJIODYKARIICS OF PROTON DISSOCIATION I N DILUTE AQUEOUS SOLUTIO1\'. 11. IIEATS OF PROTOX DISSOCIATION FROM I~Tl~OSTJ(:T,I~OTInES AND IiEL,4TED COMPOUNDS DETERMINED BY A THEKMO,1IETRIC TITRATION PROCEDURE' BYJAMES J. CHRISTENSEN AND REEDM. IZATT Department of Chemical Engineering and Department of Chemistry, Brigham Young University, Provo, Uiuh Recezved Nabember 1 , 1961
A thermometric titration procedure is described for measurement of heats of proton dissociation, and equations are developed for determination of heats of reaction from the data which account for the various heat effects throughout the titration. A thermistor used as the temperature sensing element allows measurement of a 0.02"change with 1%accuracy. The experimental equipment is housed in an air-box whose temperature is controlled a t 25 i 0.05'. Heats of proton dissociation w e given for the pK 4 (pyrimidine N-H), pK 7 and 9 (phosphate), and pK 9 (imidazole N-H) groups when.present in protonated adenine, adenosine, adenosine mono-, di-, and tri-phosphate, ribose phosphate, pyro hosphoric acid, and tripolyphosphoric acid. A H , values are given ~ t 9a function of p , and AHna values are obtained in eacg case by extrapolating a plot of AHn us. p to p = 0. ASn0 values are calculated from AH,@ and corresponding AFn0values. The magnitude of AHo appears to be a function of the proton donor atom and the type of bonding between it and the parent molecule (e.g., 0; primary, secondary, tertiary N; etc.), but not of either the pK or the nature of the parent molecule.
Introduction Despite the importance of proton ionization in the functioning of ribonucleotides, few dissociation constant or heat of ionization data are available for them or related compounds. For this reason, a study has been initiated in this Laboratory to determine under the same experimental conditions the thermodynamic quantities associated with the stepwise removal of protons from these substances, This paper presents heats of proton dissociation determined calorimetrically a t 2 5 O and as a function of ionic strength, F, from protonated adenine, adenosine (A), adenosine monophosphate (AMP), adenosine diphosphate (ADP), adenosine triphosphate (ATP), ribose phosphate (RP), pyrophosphoric acid, and tripolyphosphoric acid. Rawitscher and Sturtevant* report heats determined calorimetrically in 0.1 F NaCl for proton dissociation from the pyrimidine group of adenine and A. This appears to be the only other calorimet,ric study involving the substances studied here. Alberty, Smith, and Bock3report pKa values at 25 and 38' in 0.15 F NaC1 for the pyrimidine and phosphate ionizations of adenine, A, AMP, ADP, and ATP ; however, heats calculated from these pK values would be unreliable because of the small temperature range covered, and the uncertainty of thc p l i values. (1) Supported in part by NIII Grant A-3272, AEC Contract AT(043)-299, and a Research Corporation Grant. Presented in part a t the Pacific Northwest Regional A.C.S. Meeting, June, 1960, and a t t h e
Calorimetry Conference, Ottawa, August, 1961. Part I, J . Phya. Chem., 6 6 , 369 (1062). ( 2 ) hI. Ruwitscher and J. Stnrtrvant, J . A m . Chem Sac., 8 3 , 3739 (1960). (3) R. A . Alberty, R X I . Snntli, and R. RI. Bock, J . Rzol. Chem., 193, 425 (1951).
Use of a low heat capacity, rapid response thermistor as the temperature sensing device in the calorimetric measurements makes possible the determination of heats of reaction at relatively low reactant concentrations. I n order to take advantage of these thermistor characteristics and to obtain a permanent record of the temperature change a modification of the thermometric titration procedure used by Jordan and Alleman4 has been developed. Previous work in the field of thermometric titrations has been summarized recently.6 Several factors are inherent in the thermometric titration method which make subsequent calculations more difficult than those using standard calorimetric data. These factors are (a) the titrant is continuously added during the time of reaction a t a temperature different from that of the solution except perhaps a t one point during the titration, (b) the solution concentration is continuously changing during the titration with resultant change in the heats of solution and dilution, and (c) the walls of the calorimeter are not necessarily a t the same temperature as the solution during the titration. Previous investigators have noted these effects and have proposed various methods or equations which allow for them in their calculations. Jordan and Alleman4 proposed an extrapolation method for heat loss and heat of dilution corrections. Keily and Hume6used only the initial slope of the titration curve in order to correct for heat losses and to minimize errors due to the titrant being a t a different temperature than the solution. Keither of these workers has taken into account the (4)' J . Jordan and T. G. Allernan, Anal. ChPm., 29, 9 (1957). ( 5 ) 8. T. Zenchelsky, ibid., 32,389R (1960). (6) I f . J. Keily and D. N. Hurnr, ibid., 28, 1294 (1956).
HEATS01 PROTON
June, 1962
1031
h S S O C I A T I O N FROM RIBONUCJAEOTTDES
fact that the temperature difference between the titrant and the solution is continually changing during the course of the titration. Equations developed in this paper take into account the effects outlined above and give a more precise method for the calculation of heats of reaction from thermometric titration data.
Experimental %fateriaid.-hagent grade perchloric (Fisher), hobutyric (Eastman), butyric (Eastman), hydrochloric, and phosphoric acids; adenine (Schwarz Labs.), A (Sigma Chem. Co.), AMP (Sigma Chem. Co.), ADP (Sigma Chem. Co.), ATP (Sigma Chem. Co.), R P (Sigma Chem. Co.), Na2H2P20~(Mallinckrodt), NasHzP3010 (Food Machinery and Chem. Corp.), (CW3)JJOH (Eastman), and NaOH were Rtandardized by conventional methods for use in the determinations. Complexing between Naf and the pyro- and tri oly-phosphate groups was eliminated by substituting W%3l4K+ for Na+ with a cation-exchange resin in the cases of those substances containing the -6-P-0-P-0- linkage. Theirnonetrid Titration A p p a r ~ ~ ~ . - ~ e a s u r e m e nwere ts made in an air-bath which consisted of a cubic wooden box (two feet on a side) within another with 4 in. of insulation between the boxes. The bath temperature was maintained at 25 f 0.05’ by circulation of water from a 30-gal. tank through copper tubing placed on aluminum foil on the inside box surfaces. Air, constantly circulated in the box, was maintaimd at a constant temperature by passing i t through a mesh of copper tubing containing the circulated water. A thermoregulator 1oca;tedin the air-bath controlled the temperature of the circulating watm by actuating auxiliary heating and Iefrigeration units located in the water tank. The room in xrhich the air-bath was located was maintained at a temperature of 25 & 1 The calorimeter stirring motor, buret drive motors, and blower motor for circulation of conditioned air within the box were located on the outside of the bath. Titrant waa delivered with a constant flow titrimeter consisting of an ultra-buret (Scientific Industries, T-200), driven throu h precision-machined gears by two Series 500 30-r.p.m. Gfemon Avery, Inc., synchronous gt’ar motors, The buret delivered 0.00852 ml. The calorimeter titrant/sec. with a precision of S O . l % . was a 250-ml. dewar flask in which w a ~placed through a tightly fitting rubber stopper the micro-buret tip, a glass stirrer (driven by a 600 r.p.m. Wes Co. stirring motor), and a thermistor (Victory Engineering Corp., 31A-6 type) in a 2-mm. 0.d. glass tube. The thermistor resistance was approximately 1000 ohms at 25” and it had a temperature coefficient of -3.SOJo/O. The glass stirrer was positioned to sweep titrant immediately from the buret tip into tho solution. The thermistor was incorporated as one arm of a Wheatstone bridge whose circuits were shielded and guarded to eliminate parasitic currents. I n operation, the thermistor resistance change resulted in an unbalanced bridge potential which wm fed to a Minneapolis-Honeywell extended range strip chart recorder (Model 153X14-V-II-III-30-N6) having a span of 2.2 mv. with a total of five ranges giving an effective span of I 1 .O mv. Thermistor Calibration.-The thermistor resistance change as a function of temperature wm determined a t various applied bridge voltages by observing the thermistor response to small, accurately measured temperature changes: The temperature changes were measured by placing a 5 Beckmann thermometer and the thermistor in close proximity in a water-bath which was allowed to slowly cool through the temperature range for which the thermhtor was t o be calibrated. A linear relationship between temperature change (read from the Beckmann thermometer) and recorder deflection was found at each bridge voltage. The calibration covered a 1 interval. At the bridge voltage used in this study (1.4500 v.), a deflection of one scale unit on the recorder corresponded to 0.000739 or 0.15” per chart width. Thus, a temperature change of 0.02O could be measured with an accuracy of 1% and a change of 0.7” could be recorded over the five available spans of the recmder in & single titration. Procedure.-The calorimeter and auxiliary equipment, constant rate microburet titrimeter, and all solutions 48 hr. prior t o use were kept in the constant temperature air-bath
.
O
100 0 . 2f--
/
__-
RLDlOn
(I
1
_ _ - --c
’%\.“PI v+/’ -----“i-L---
I
in order to improve temperature control of the calorimeter and its contents and to ensure that all solutions and equipment used in the titration were a t the same temperature. The titrant in all determinations was approximately 100 times more concentrated than the solution being titrated. The initial volume of the solution being titrated was always 100 ml.; however the solute concentration varied from approximately 0.05 to 0.005 F . The temperature of the solution was continuously recorded in each determination throughout the four regions of the titration curve which is described below. Calculrttions.-The calculation of AH by the method outlined here is based on the typical thermometric titration curve obtained from the reaction of a strong acid with a strong base. The derived equations are sufficiently general, however, for the method to be extended to any system, exothermic or endothermic, so long m the concentrations of the species causing the heat changes are known. The method also can be extended t o systems containing two or more reacting species, but if these systems react in the same pH region, z e., their pK value8 are close together, it is necessary to know the quantity of each species present in order that heats may be correctly assigned. Equations can be derived for these more complex systems, providing pK values are known, in the same manner as is done below for the single species system. These equations are not presented here because of their length and complexity. The curve in Fig. l a has four distinct regions: (a) titrant off-temperature change is due to stirring, power dissipated by the thermistor, and heat transfer if air-bath and solution temperatures are different; (b) titrant on-temperature change is due to heat of neutralization reactions, heat of solution of titrant, addition of titrant at a lower temperature than solution, and items in (a); (c) titrant on-neutralization reaction is completed, temperature change is due to heat of solution of titrant, addition of titrant a t a lower temperature than solution and items in (a); (d) titrant offtemperature change due to items in (a). Region (b) may consist of heat effects resulting from neutralization of protons from more than one acidic group of the same substance. An example of a system involving such simultaneous equilibria is ADP. A typical titration of ADP with NaOH is shown in Fig. l b where the % species is plotted us. time. Distance along the ordinate or time axis is equivalent to moles NaOH added. I n Fig. l a is plotted the corresponding temperature rise as a function of time that the titrant base has been added. It is seen that the temperature rise a t any point along the curve in Fig. l a is a result of the simultaneous dissociation of protons from two ADP species (Fig. l b ) although the contribution is mainly from one species in each case. It now is possible to distribute the heat measured in region (b) among the species reacting in that region by solving appropriate simultaneous equations. For the simple case where region (b) contains only one reacting species, the following equationv are written (treating regions a and d a~ closed systems, L e . , regions in which no mass crosses the boundaries of the calorimeter and its contents, and treating regions b and c &s open systems, i . e . , regions in p-hich titrant enters the calorimeter).
JAMES J. CHRISTENSEN AND REEDM. IZATT
1032
d& - dW = d E regions a and d (1) dE (h U2/2g, Xg/Go)dm regions b and c ( 2 ) (For Pymbols used in this and succeeding equations, see section at end of article.) Expanding and integrating these equations in the usual manner with the assumptions that the neutralization reaction is essentially instantaneous, the heat capacity of the solution is independent of small temperature and concentration changes, and C, = C, one obtains Qa = (m&p. mvCp,)ATa Wa (3) &b = (mscpa m v c p v f mtbCpt)ATb mti,Cpt(Tz- I't) AH, AH,, Wb (4) Qc = (m8Cp. mvCpv mtbCpt mtoCpt)ATc mteCpt (TI 2't) AHno Wo (5) ( ~ S C P . mvcpv mtbcpt f mt8pt)ATd w d Qd (6) The heat of reaction, AH,, can be found from eq. 4 if &b, AHnb, and Tt are known. &b and 9: (eq. 4 and 5) can be evaluated in t e r m of known quantities &d and QB if the assumption is made that over the small temperature rise encountered in the titration the rate of heat loss from the calorimeter is directly roportional to the temperature difference between the sobtion and the surrounding air-bath. Tt then can be evaluated from eq. 5, and Qb and T t substituted in eq. 4 to give the following expression for AHr in terms of known and measured quantities d&
- dW
=
+ + +
+
+
+ +
+
+ +
+
+
-
+
+ + +
Vol. 66
and are obtained by subtracting -13.50 from the AHn0 measured for the reaction occurring in the calorimeter, eq. 9. The present results are wen to be in good agreement with previous work.
TABLE I THERMOCHEMICAL DATAFOR THE TITRATION OF NaOH WITH SEVERAL ACIDSAT 25' NaOH
-AH
formality x 102
Titrant
1.034 F HClOi
0.678 F (CH8)zCHCOOH
1 ,080 F CHs(CHz)2COOH
10'
(kca1.l mole)
2.30 5.78 11.6 17.4 23.1 2.30 4.62 5.78 11.6 17.4 4.62 5.78 11.6 17.4 23.1
13.62 13.46 13.43 13.42 13.35 13.99 14.32 14.25 14.18 13.98 14.40 14.22 14.28 14.14 13.98
p
0.4634 1.159 2.317 3.479 4.634 0.4634 0.9268 1.159 2.317 3.479 0,9268 1.159 2.317 3.479 4.634
x
TABLE I1 THERMOCHEMICAL DATAFOR THE TITRATION OF &PodWITH BASEAT 25' ACCORDING TO THE REACTION &POIOH- = HPO4Hg0
+
+
H.PO4 formality
x
Titrant I
where Y is the heat capacity of the calorimeter and its contents. Either heats of dilution AH,b and AH,, can be evaluated at the average ionic strength in each respective region or if heat of dilution us. p data are available a true average heat of dilution can be determined. All calculations were made on an IBM 650 computer. Equipment Calibration.-Y (eq. 7), the effective heat capacity of the calorimeter and its contents, was determined by studying a system whose AHr is accurately known. The system chosen was the neutralization of a strong acid with a strong base in aqueous solution H OH = HzO (8)
+
(omitting ion charges and waters of hydration for simplicity in this and succeeding eq.) in which caee AH0 has been d e termined by a microcalorimetric procedure a t fi = 0 to be -13.50 =k 0.05 kcal./mole.' Using this value for AH,, a value of 111.53 cal./deg. was obtained for Y . The experimental procedure was further checked by calculating the heats of neutralization at fi = 0 of n-butyric acid, isobutyric acid, and dihydrogen phosphate ion and comparing these with results of previous studies. These heats determined ae a function of reactant concentration and p are given in Tables I and I1 for the reaction HA OH = A HzO (9) Each AH value in Tables I and I1 ww obtained by averaging the AH values from 2 to 4 determinations at the indicated p value. The precision of the AH values in Tables I and I1 is estimated to be ~ k 0 . 5 7 ~ . The substitution of tetramethylammonium hydroxide for NaOH in the H3PO4 titration (Table 11) made no difference in the observed heats. AHnovalues obtained by extrapolation of AH, vs. p plots to p = 0 are given in Table I11 together with results of previous workers. The AHno values in Table I11 are for the reaction HA=A+H (10)
+
(7)
H.M.
+
Papsi., IT. J. Canady, and I
