heat capacity of sitric acid0c96051e8eb63eea58000000

Thermochimica Acta, 58 (1982) 341-354
Elsevier Scientific Publishing Company, Amsterdam-Printed in The Netherlands
341
THERMODYNAMIC PROPERTIES OF CITRIC ACID AND THE
SYSTEM CITRIC ACID-WATER
C.G. DE KRUIF, J.C. VAN MILTENBURG, A.J.J. SPRENKELS, G. STEVENS,
W. DE GRAAF and H.G.M. DE WIT
Department of General Chemistry, Chemical Thermodynamics Group, State University of
Utrecht, De Uithof, 3508 TB Utrecht (The Netherlands)
(Received 14 April 1982)
ABSTRACT
The binary system citric acid-water has been investigated with static vapour pressure
measurements, adiabatic calorimetry, solution calorimetry, solubility measurements and
powder X-ray measurements. The data are correlated by thermodynamics and a large part of
the phase diagram is given. Molar heat capacities of citric acid are given from 90 to 330 K
and for citric acid monohydrate from 120 to 300 K. The enthalpy of compound formation
A,,H (298.15 K)=(- 11.8* 1) kJ mole-‘.
INTRODUCTION
Many organic substances occurring in nature form hydrates. This means
they can crystallize stoichiometrically with one or more moles of water,
dependent on conditions of pressure and temperature. This hydrate forma-tion
is reflected in the phase diagram of the binary system ‘organic subs-tance-
water’, from which the regions of phase stability can be read.
As hydrates of organic substances play an important role in physiology
and pharmacology, biological research groups show an increasing interest in
their thermodynamic properties. Recently, our group received requests from
three different research disciplines for the determination of properties such
as solubility, stability region, transition temperatures and transition enthal-pies
for hydrates of calcium oxalate, citric acid and theophylline.
Our group has for many years been occupied with the determination of
thermodynamic properties of organic substances by means of calorimetry
and vapour pressure measurements. Apart from this, we are working on
lattice energy determinations and calculations (by the atom-atom potential
method). As in hydrates-the water molecules appear to be almost exclusively
bonded by hydrogen bridges, a comparison of their lattice energy calculation
0040-6031/82/0000-0000/$02.75 0 1982 Elsevier Scientific Publishing Company

342
with that for the corresponding anhydrates may contribute to a better
understanding in the matter of hydrogen bridge bonding.
While working on the hydrates, we decided to study one binary system in
greater detail, which could then be used as a reference system both for
theoretical and experimental aspects. Because certain relations exist between
a number of experimentally determined quantities, obtained by different
methods, this fact enables us to make an estimation of the accuracy and
consistency of the methods applied.
In this paper, a thermodynamic description of the citric acid-water binary
system is given, with special attention to the phase behaviour of the
stoichiometric crystalline hydrate. In addition, we will give a description of
the experimental methods used and a discussion of the results obtained.
THERMODYNAMIC DESCRIPTION
In view of the (limited) mutual solubility, we may predict that the T-X
phase diagram of the solid-liquid phases shows eutectic behaviour. Due to
compound formation, the phase diagram will contain a second three-phase
line at the peritectic temperature. So at constant pressure, the solid-liquid
phase diagram will have the form of Fig. l(a). Experimentally, the diagram
can be obtained from the solubility of citric acid in water and from the
three-phase line temperatures.
In addition to the solid-liquid phase diagram, we measured (at least in
part) __..._....._______________. the solid-vapour and liquid-vapour equilibria. Because citric acid is
less volatile than water by at least a factor of lo9 at temperatures below 373
K, we assume water to be the only species present in the vapour phase. The
system citric acid water-water vapour is monovariant and the P-X diagrams
T2 c- (a)
(b)
. Cc)
: :
i
:
.
:
______.__.
i 1
i
TP
SIN (A.x.1) +
TI
SlN(A,xT)+
A 6)
A.leq (S)
A.14 (S) +
TE t---
A 6)
0 m_.-x ’
UJ-x
A
C
Fig. 1. (a) General features of the expected phase diagram. (b) and (c) Sketched P-x
diagrams for temperatures below and above the peritectic temperature, respectively.

343
will be as sketched in Fig. l(b) and (c). Apart from these phase diagrams, we
are particularly interested in the change in values of the thermodynamic
functions, when a point in the diagram is realized by mixing the pure
components in appropriate quantities and at appropriate temperatures.
Because we also measured some equilibria along the two-phase lines, we will
write out these ‘phase reactions’ in a general form together with some
auxilliary equations.
‘GENERAL EQUATIONS
Citric acid will be denoted by A, the hydrate by A.laq, and a saturated
solution of citric acid in water by sln(A, x, T) meaning that the solution
contains (1 - x) moles of water and x moles of citric acid at temperature T.
The diluted solution is defined by sln(nH,O, A, T), containing 1 mole of A
and n (> = 500) moles water. For temperatures below the peritectic tempera-ture,
we may write
A(s) + H,O(l) + A.laq(s) (a)
A.laq(s) + A(s) + H,O(v) (b)
xA.laq(s) + (1 - 2x) H,O(l) + sln(A, x, T) (c)
xA(s) + (1 -x) H,O(l) + sln(A, x, T) (d)
A.laq(s) + (n - 1) H,O(l) + sln(nH,O,A,T)
A(s) + n H,O(l) --, sln(nH,O, A, T)
At the peritectic or transition temperature
(1 -x)-l ((1 -x)A.laq(s)*(l -2x)A(s)+sln(A,x,T)}
Above the peritectic temperature
(1 -x)-l {sln(A,x,T) *xA(s)+ (1 -x)H,O(v)}
(e)
(f)
(8)
(h)
We will also make use of
H,O(l) * H,O(v) (i)
Except for eqns. (a) and (i), we have determined the enthalpy and/or
entropy changes of the respective phase reactions. By suitable combination
of these quantities, others can be calculated. We will illustrate this on the
enthalpy changes but it can be done for the entropy likewise.

344
ENTHALPY OF COMPOUND FORMATION
A.,,,,H, = H*(A.laq, s) - H*(A. s) - H*(H#, 1)
This can be found from the following quantities determined experimen-tally.
A,;,,H,--Aa,,,H,=H(slnA,x,T)-xH*(A,s)-(1 -x)H*(H,O,l)
-H(slnA,x,T) +xH*(A.laq,s) +(1 -2x) H*(H20,1)
xAcom H, = x H”(A.1 aq, s) - x H*(A, s) - x H*(H*O, 1) (1)
A,,,H, = H*(A.laq, s) - H*(A, S) - H*(H,O,l)
A”.,Hi - ‘“,,H, = H*(H,O, v) - H*(H20,1)
- H*(A, s) - H*(H,O, v) + H*(A.laq, s)
A,,,H, = H*(A.laq,s) - H*(A, s) - H*(H*O, 1) (2)
A_,Hr - A,,, He = H(sln, nH,O, A, T) - H*(A, S) - n H*(H20, 1)
-H(sln,nH,O,A,T) + H*(A.laq,s) +(n - 1) H*(H20,1)
&,,H, = H*(A.laq, s) - H*(A, s) - H*(H*O, 1) (3)
ENTHALPY OF SOLUTION
It can be shown that the integral enthalpy of solution at saturation
concentration of citric acid is given by
4atHd=(l-4[LH~+A,,,H.J (4
As,,Hd=(l -X)[AvapHi-AvapHh] (5)
and similarly for the hydrate
A,,,&=(1 -2x)A,,,H,+(l -x)AtrsHp (6)
f&H, = L,H, - XLH, (7)
ENTHALPY OF TRANSITION
The enthalpy change connected with the phase transition of eqn. (g) is
measured calorimetrically or evaluated from

345
AVapHb L AVaPHh = +H*(H,O, v) + H*(A, s) - H*(A, laq, s)
-H*(H@,v)-x(1 -x)-‘H*(A,s)+(l -x)-‘H(sln,A,x,T)
A,,,H, = (1 - 2x)(1 - x)-‘H*(A, s)
+ (1 -x)-‘H(sln,A,x,T) - H*(A, laq,s) (8)
Of course other combinations are possible, but we consider those given as
the most relevant ones.
EXPERIMENTAL EVALUATION
The enthalpy changes corresponding to eqns. (e)-(g) are determined by
calorimetry. Absolute entropies and entropy changes are evaluated from
specific heat capacity measurements. The enthalpy changes corresponding to
eqns. (b) and (h) are derived from the Clausius-Clapeyron law
-Rdln[p(H,O)/p’]/d(l/T) =AvapH (9)
In the treatment given above, it was assumed that all enthalpy values are
determined at the same temperature. In practice, this will not be true and so
we have to account for the temperature dependence of the enthalpy.
AH(T)=AH(T,)+/rACr(T)dT (10)
G
In most cases, it will be accurate enough to use
AH(T) = AH(T,) +AC,(T- To)
in which AC’, is the mean value in the temperature range T-T,.
(11)
SAMPLES
Commercially available (Baker Analyzed, 99.8%) citric acid monohydrate
(formula mass 210.12) was used. Citric acid was prepared from the hydrate
by prolonged heating and evacuation at 60°C. From the mass loss, the ratio
citric acid : water in the hydrate was found to be 1 .OO I+ 0.005.
VAPOUR PRESSURE MEASUREMENTS
These measurements were performed by a static method employing a
diaphragm manometer (MKS Baratron Inc.) calibrated on a dead weight

346
gauge (CEC). Temperature was measured with a platinum thermometer
calibrated on IPTS-68 and accurate to within 0.01 K. The experimental
set-up has been described in detail previously [l]. The vapour pressure
measurements as a function of temperature are fitted to the equation
Rln(p/p’)= -AG0(8)/t?+AH0(8)(1/f3- l/T)
+ACi(B){f3/T- 1 + ln(T/B)} (12)
in which p” is a standard pressure of 1 Pa, 9 is a reference temperature,
usually mid-range, while the coefficients to be evaluated, AGO, AH0 and
AC:, are the thermodynamic function changes on vaporization.
SOLUTION CALORIMETRY
An isoperibol calorimeter was used. About 0.2 g of sample was dissolved
in 100 ml water. The corresponding enthalpy effect was evaluated from the
measured temperature change and a separate specific heat determination.
Data were collected by a microcomputer and a correction for heat leak
(heat leak constant = -4.7 X 10e5 s-‘) was applied. The performance of the
apparatus was checked by measuring the heat of solution of potassium
chloride. From twenty measurements, a mean heat of solution of 17,34-t
0.035 kJ mole-’ was measured. This is in good accord with literature data of
corresponding concentrations.
TABLE 1
Solubility, x, of citric acid monohydrate in water
T(K) x (mole fraction)
290.1 0.1123
296.1 0.1233
299.2 0.1354
304.0 0.1488
304.9 0.1501
307.6 0.1559
309.0 0.1636
313.9 0.1750
317.5 0.1860
322.1 0.1923

347
SOLUBILITY
The solubility of citric acid (monohydrate) in water yas determined by
putting together appropriate and precisely weighed amounts of the acid and
water in a glass tube which was then sealed off. The glass tubes were rotated
in a thermostat whose temperature was raised by approximately 1 K per day.
The temperature at which the crystals are completely dissolved was taken as
a point of the liquidus. The results are given in Table 1.
POWDER X-RAY DIFFRACTION
These measurements were made in the temperature range 32-38°C with a
heating rate of 0.2 K ks-’ and a film speed of 3 pm s-t. The diffraction
pattern of the CuKa, radiation was recorded on a Guinier-Simon camera
(Enraf Nonius, The Netherlands). From the abrupt change in diffraction
pattern, the transition temperature was evaluated.
ADIABATIC CALORIMETRY
The calorimeter used has been described before [2]; no alterations have
been made.
RESULTS AND DISCUSSION
The molar heat capacity of citric acid monohydrate (sample mass
17.4095 g) was measured under a helium pressure of about 200 Pa. The
measurements were made between 110 and 330 K. The experimental results
are given in Table 2 and the calculated thermodynamic values in Table 3. A
large transition, which was slightly superheated, took place at 3 12.1 K (see
Fig. 2). The heat capacity of the sample above the transition is very large and
does show a large temperature dependence. The enthalpy of transition was
calculated in the usual way by taking the enthalpy increment from 298 to
321 K and subtracting the heat capacity contribution. This heat capacity was
linearly extrapolated to 312.1 K using the regions from 285 to 298 K and
from 321 to 333 K. The enthalpy of transition was 14.98 kJ mole-‘. After
these measurements, the sample was cooled to 278 K and a cooling curve
made. After several hours at 278 K, a gradual exothermic effect took place
which is quite different from the sudden crystallisation of a supercooled
liquid. After two days, a new series of measurements was made. A significant

348
TABLE 2
Experimental molar heat capacities, CP
cP
(J K-’
mole- ‘)
TK)
cP
(J K-’ TK)
cP
(J K-’ TK)
cP
(J K-’
mole-‘) mole- ‘) mole-‘)
(a) Citric acid monohydrate
118.23 126.79
123.81 131.25
129.24 135.63
134.53 139.90
139.69 144.09
144.74 147.92
149.68 151.76
154.53 155.73
159.28 159.24
163.96 163.07
168.55 166.64
173.06 170.12
177.51 173.73
181.88 176.90
186.20 180.14
190.46
194.67
198.82
202.92
206.96
210.97
214.93
218.83
222.70
226.53
230.32
234.07
237.78
241.45
Second series
288.74 258.18
292.59 262.88
296.39 267.70
300.14 273.05
(b) Citric acid
84.19 83.93
94.47 93.34
104.04 100.76
113.07 107.53
121.67 114.05
129.94 120.25
137.92 125.55
145.67 130.66
153.19 136.46
160.54 141.29
167.73 146.04
183.38 245.09 225.29 291.86 262.2 1
186.23 248.69 228.16 295.05 264.3 1
189.61 252.26 23 1.06 298.21 267.36
192.33 255.79 233.77 301.34 271.02
195.67 259.30 236.62 304.44 275.35
198.56 262.77 239.52 307.50 282.28
201.83 266.21 241.71 310.48 301.15
205.17 269.63 244.55 3 16.22 406.97
207.76 273.02 247.38 318.58 399.46
210.83 276.37 249.9 1 320.88 406.27
213.63 279.70 252.15 323.16 413.19
216.66 283.01 254.77 325.40 419.78
219.54 285.42 256.71 327.62 426.56
222.60 288.66 259.19 329.80 434.56
303.82 279.68 316.47 403.41 324.73 418.76
307.33 324.79 319.27 401.98 327.39 427.3 1
309.77 788.29 322.03 410.34 330.01 436.40
174.77 150.29 245.33 193.79 302.98 228.45
181.67 154.61 257.16 201.16 305.66 230.30
188.46 158.94 262.94 204.57 308.32 231.21
195.14 163.34 268.66 208.19 310.98 233.36
201.71 167.50 276.69 213.03 313.63 234.69
208.17 171.45 282.27 216.44 316.28 235.92
214.55 175.43 287.79 219.05 318.91 237.36
220.84 179.01 293.27 222.75 321.54 239.20
227.05 182.95 298.7 1 225.99 324.15 241.22
233.18 186.44 297.59 224.80 326.76 242.32
239.34 190.31 300.29 226.75 329.35 244.23
difference in the heat capacity prior to the transition and a lower enthalpy of
transition (including the larger pre-effect) of 14.47 kJ mole-’ were found,
indicating that the formation of the monohydrate from the high-temperature

349
TABLE 3
Calculated thermodynamic values of citric acid monohydrate
TK)
CP
(J K-’ mole-‘)
G - G(0) H - H(0)
(J mole-‘) (J mole-‘)
s - S(0)
(J K-’ mole-‘)
120 128.14 - 5728 7849 113.14
130 136.28 -6913 9171 123.72
140 144.28 - 8202 10574 134.11
150 152.18 - 9594 12056 144.34
160 159.98 -11098 13617 154.41
170 167.70 - 12682 15255 164.34
180 175.37 - 14375 16971 174.14
190 183.00 - 16 165 18763 183.83
200 190.69 - 18051 20631 193.41
210 198.20 -20032 22 575 202.89
220 205.82 -22 108 24585 212.29
230 213.47 -24278 26691 221.60
240 221.18 -26540 28 864 230.85
250 228.95 -28895 31115 240.04
260 236.81 -31341 33444 249.17
270 244.78 - 33 878 35851 258.26
280 252.88 - 36 506 38 340 267.30
290 261.12 - 39224 40900 276.32
300 269.52 -42032 43 562 285.32
20000 - i
I
f
i
2
I 4
‘I
j’i
iI
9;
10000 *: o' .
1' ;
,A ,.'.
,/ /.r"
_,'.b'.-
*_--
5000
305 310
T/K
315
-I
J
Fig. 2. The enthalpy curve by adiabatic calorimetry. 0 = first series; X = second series.

350
phase was not complete. In this second measurement, the superheating of the
transition was only about 0.1 K.
For citric acid, a sample of 8.0608 g was used. Helium gas was admitted to
a pressure of 200 Pa. Measurements were made between 80 and 330 K. As
no specific heat anomaly was found in the region where the monohydrate
has its transition, it is safe to assume that no hydrate was present. The
experimental results are also given in Table2, and the calculated thermody-namic
values and the smoothed heat capacity values from 90 K are given in
Table4. Specific heat measurements of the monohydrate have been reported
by Evans et al. [3] ranging from 10 to 298 K. Comparing our data from 90 to
298 K shows no significant difference. Our data measured with automated
apparatus are more smooth, but the overall difference in enthalpy increment
TABLE 4
Calculated thermodynamic values of citric acid
5
(J K-’ mole-‘)
G - G(90)
J mole-‘)
H - H(90) s - S(90)
(J mole-‘) (J K-’ mole-‘)
90 90.03 0 0 0.00
100 97.79 -50 939 9.89
110 105.36 - 198 1955 19.57
120 112.74 -441 3045 29.05
130 119.94 - 778 4209 38.36
140 126.98 - 1207 5444 47.5 1
150 133.87 - 1728 6748 56.50
160 140.62 -2337 8121 65.36
170 147.24 - 3034 9560 74.08
180 153.74 -3818 11065 82.68
190 160.13 -4688 12634 91.17
200 166.43 -5641 14267 99.54
210 172.64 - 6678 15963 107.81
220 178.78 - 7797 17720 115.99
230 184.85 - 8998 19538 124.07
240 190.87 - 10278 21417 132.06
250 196.85 -11639 23 355 139.98
260 202.80 - 13078 25 353 147.81
270 208.73 7 14595 27411 155.58
280 214.65 -16189 29 528 163.27
290 220.57 - 17860 31704 170.91
300 226.5 1 - 19607 33940 178.49
310 232.48 -21430 36 234 186.01
320 238.48 - 23 327 38 589 193.42
330 244.53 -25299 41004 200.92

351
in this region is only 18 J mole-’ or less than 0.05% of the total effect.
Table3 is calculated by using the Evans values for the absolute entropy and
the enthalpy at 120 K. No measurements of the heat capacity of the
monohydrate above 298 K or of citric acid have been reported before.
The experimentally measured vapour pressures over the hydrate and the
saturated solution are given in Table5. After pumping a few seconds at the
hydrate sample, it took several hours before the equilibrium pressure was
re-established. Therefore the scatter in these data is much higher than in
those of the saturated solution for which equilibrium was established in a
few minutes. When the saturated solution was cooled well below the transi-tion
temperature, vapour pressures were not initially constant and were well
above the equilibrium values. Only after several days equilibrium were they
re-established, indicating again the slow equilibration mechanism as ob-served
in adiabatic calorimetry. The result of fitting the experimental vapour
pressure data to eqn. (12) is given in Table 6.
From the intersection of the two vapour pressure lines, the transition
temperature is found to be 309.5 + 0.5 K. The X-ray powder diffraction
patterns give a transition temperature of 309.0 +- 0.5 K. This is compared
TABLE 5
Experimental water vapour pressures above citric acid monohydrate and above a saturated
solution
Citric acid monohydrate Saturated solution
‘T lOO*AlnP* T lOO*A In P *
WI WI
278.10 325.00 -2.01 309.77 4141.00 -0.40
282.88 521.00 2.40 314.78 5414.00 1.89
289.11 893.00 3.14 316.95 5773.00 - 1.92
293.12 1212.00 0.95 321.87 7311.00 -0.73
293.75 1213.00 -4.01 322.89 7756.00 0.64
297.67 1748.00 1.77 329.30 10 109.00 -0.18
298.42 1760.00 - 3.34 330.09 10645.00 1.73
301.99 2332.00 -2.17 338.01 14 368.00 0.53
303.23 2582.00 - 1.18 342.22 16 609.00 -0.59
306.15 3240.00 0.23 342.31 16 662.00 -0.58
306.17 3399.00 4.78 342.27 16 530.00 - 1.26
306.42 3373.00 2.35 351.77 23 346.00 0.39
308.96 3902.00 - 1.20 351.81 23 333.00 0.20
309.06 3906.00 - 1.77 351.84 23 386.00 0.31
* The residuals are calculated from eqn. (12) and the coefficients given in Table 6.

353
with a literature value of 309.7 K [4,5]. The transition temperature found
with the adiabatic calorimeter is 312.1 K. Although a temporary superheat-ing
of 1.5 K is observed, it is not clear where this discrepancy originates,
particularly as we have used extremely low heating rates comparable with
those of the X-ray powder diffraction experiments. For further calculation,
we will adopt a transition temperature of 309.5 K.
The heats of solution of the hydrate and of the anhydrate were each
determined eight times. In Table6 we give the experimental results and
literature values.
The values of pure water have been taken from ref. 6. Employing eqns. (2)
and (3), we find for the enthalpy of compound formation as defined by eqn.
(a) from vapour pressure measurements A,,H, (298.15 K) = - 12.8 I+ 1 kJ
mole-‘, A,,,H, (309.5 K) = - 12.3 I+ 1 kJ mole-’ andA,,,H, (298.15 K) =
- 10.8 * 0.6 kJ mole- ’ from solution calorimetry. The enthalpy of transition
defined by eqns. (g) and (8) is found to be At,, Hg (309.5 K) = 15.69 f. 1 kJ
mole- ’ and A,,,H, (312.1 K) = 14.98 a0.2 kJ mole-’ from vapour pressure
measurements and adiabatic calorimetry, respectively.
For equilibrium (b), from the values in Table 6 we calculate AV$$,”
(298.15 K) = 157.21 + 2.7 J K-’ mole-‘.
Using the absolute entropies of the monohydrate and water vapour, we
calculate the absolute entropy of citric acid as So (s, 298.15 K) = 252.1 kJ_’
mole- ‘. The relative value So (s, 298.15 K) -So (s, 90 K) = 177.1 J K-l
mole-‘. Therefore to convert the entropy values in Table 4 to absolute values
they must be increased by 75 J K-’ mole-‘. So, So (s, 90 K) = 75 J K-l
T/K
Fig. 3. The experimental phase diagram between x =0 (water) and x =0.5 (the hydrate).
0 = literature data; X = our measurements.

354
mole.- ‘. Of course several other thermodynamic quantities of the system
citric acid-water can be calculated with the results presented here and
making use of the consistent set of phase transition equations given above.
We think that those given are the most interesting and useful ones.
Finally, we give in Fig. 3 the binary T-x phase diagram based on both our
measurements and literature values.
REFERENCES
I C.G. de Kruif, T. Kuipers, J.C. van Miltenburg, R:C.F. Schaake and G. Stevens, J. Chem.
Thermodyn., 13 (1981) 1081.
2 R.C.F. Schaake, J.C.A. Offringa, G.J.K. van den Berg and J.C. van Miltenburg, Rec. Trav.
Chim. Pays-Bas, 98 (1979) 408.
3 D.M. Evans, F.E. Hoare and T.P. Melia, Trans. Faraday Sot., 58 (1962) 1511.
4 Kirk-Othmer, Encyclopedia of Chemical Technology, Wiley, New York, 1978.
5 J.L. Marshall, J. Proc. Aust. Chem. Inst., 5 (1938) 383.
6 R.A. Robie, B.S. Hemingway and J.R. Fisher, Thermodynamic Properties of Minerals. U.S.
Government Printing Office, Washington, 1978.
7 B.J. Levin, J. Phys. Chem., 59 (1955) 640.
8 International Critical Tables of Numerical Data. Vol. V, McGraw-Hill, New York, 1929.

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