Heat Capacity, Enthalpy and Entropy of Citric Acid Monohydrate

BY D. M. EVANS, F. E. HOARE AND T. P. MELIA

Schools of Chemistry and Physics, The University, Leeds 2

Received 5th March, 1962

The heat capacity of citric acid monohydrate has been measured in the range 20" to 300°K. A value of 67.74f0.14 cal deg.-1 mole-1 has been calculated for the entropy of the monohydrate at 25°C and with existing published data leads to the free energy of formation of the aqueous citrate ion = -277.69f0.34 kcal mole-1.

Thermodynamic data for citric acid monohydrate and the aqueous citrate ion are of biochemical interest in connection with the energy changes of metabolic processes.

We have measured the heat capacities of the crystalline monohydrate in the range 20-300°K. From these data an accurate value for the entropy of formation at 25°C has been calculated and used in conjunction with the heat of formation 1 and data for the solution 2 and ionization 3 to obtain an accurate value for the free energy of formation of the aqueous citrate ion.

EXPERIMENTAL

The apparatus and method used will be described elsewhere. MAmruALS.-The citric acid monohydrate was kindly given by Prof. Sir Hans Krebs

and was found to contain 0.16 % adsorbed water. The weight of the sample used was 53.119 g.

RESULTS AND DISCUSSION

The observed values of the heat capacity are given in table 1. These results were smoothed graphically and the smoothed values of the heat capacity together with the derived entropy and enthalpy values are shown at 10-deg. intervals in table 2. The values of heat capacity below 22°K were obtained using the Debye function,

C = 0*366f~( 150/T), which fitted the heat capacity data at 22, 24 and 26°K. Measurements on benzoic acid, whose heat capacity has been accurately measured by Furukawa, McCoskey and King,4 indicate that above 50°K the heat capacity results are accurate to 0.3 % ; below 50°K the uncertainty increases to about 1 % at 20°K.

Since many biochemical reactions involve aqueous ions the free energy of forma- tion of the aqueous citrate ion (in the conventional standard state of unit activity) is of more practical value than that of the undissociated acid. Biochemical data lead to the value AGf" = -278-8 _+ 1.5 kcal mole-1 at 25"C.S By combining the entropy obtained in this work with existing published data, a more accurate value of AGj can be obtained.

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1512 HEAT CAPACITY OF CITRIC ACID MONOHYDRATE

The entropy of formation of the crystalline monohydrate obtained by combining our value for the entropy at 25°C with data for the entropies of the constituent elements in their standard states 6 is -292.49+0.20 cal deg.-1 mole-1. The free energy of formation of the monohydrate at 25°C found from this and the heat of formation 1 ( -439.2 & 0.2 kcal mole-1) is - 352.0 0.3 kcal mole-1.

TABLE I.-oBSERVED VALUES OF THE HEAT CAPACITY FOR CITRIC ACID MONOHYDRATE

temp., OK C(abs. J deg.-lg-l) run 1

67.07 73.87 81.41 90- 1 1

100.29 111.75 123.56 135-29 146.20 157.19 168.85 181.33 193.90

0.3 749 0.4131 0.4484 0.49 17 0.5283 0.5810 0.6278 0.67 10 0.71 03 0.7474 0.7882 0.8266 0.8792

temp., O K C(ak J &g.-lgl) m 4

280.72 1.210 287-33 1.234 293-93 1.260

temp., OK C(abs. J deg.'lgl) run 7

21.83 0.073 3 24.08 0.0908 26-41 0.1075 29.1 3 0.1264 32.12 0- 1468 35.00 0.1663 39-36 0.1957 44.77 0.2324 49.65 0-2653 54.68 0.2983 59.86 0.3314 67-06 0.3748 75-67 0.4224

temp., "K

198.48 204.80 214.60 226.50 237.98 248.53 258.68 269.12

C(abs. J deg.-lg-l)

0.9048 0.9279 0.9601 1 *004 1.044 1 -092 1.127 1-167

run2

temp., O K C(abs. J deg.-lgI)

65.98 0.3686 75.57 0.42 1 9 84.1 6 0.4673 91.93 0.5038

102.50 0.5414 115.51 0.5941 127.53 0.6363 138.80 0.6802 149.48 0.7171 160.80 0,7591

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emp., OK C(abs. J deg.-1 g-1) run 8

275.58 1.191 281.07 1.21 1 287.8 1 1.237 295.77 1.266 302.79 1 -29 1

temp., O K

196.12 200.24 205.84 213-59 223.45 233.1 1 242.52 251.68 260.58 268.44

temp., O K

21-88 24-34 26.52 28.48 30.76 33.34 36.02 40.22 45-76 51-15 57.1 1 63.25 69.56 76.16

C(abs. J deg.-lgl) run3

0.8888 0.905 1 0.928 1 0.9641 0.9961 1.030 1 -065 1.101 1.134 1.164

C(abs. J deg.-lrl)

0.0736 0.0925 0.1082 0.1233 0.1374 0.1551 0.1 730 0.20 1 7 0.2390 0-2754 0-3142 0.3517 0,3895 0.4250

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D. M. EVANS, F. E. HOARE AND T. P . MELIA 1513

At 25°C citric acid monohydrate dissolves in water to give a saturated solution which is 8.487 M with respect to unhydrated citric acid. Since the solution is satu- rated we may put AG = 0 for the reaction?

where H3Ci denotes citric acid. Isopiestic data 2 give a value of 0.778 for the activity of water in a saturated aqueous solution of citric acid, The free energy of formation

H3Ci . H20 (solid)+H3Ci(8*487 M) +H2O(in sat. soln.),

TABLE 2.GMOOTHED VALUES OF THE HEAT CAPACITY, ENTROPY AND ENTHALPY OF CITRIC ACID MONOHYDRATE

so-sg H g - H g T (abs. J deg.-lg-l) (abs. J deg.-lg-l) (abs. J g-1)

C temp., O K

0 10 20 30 40 50 60 70 80 90

100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 273.15 280 290 298.15 300

0 0-0085 0.0594 0.1324 0.2001 0.2676 0.3322 0.3919 0.4444 0.49 17 0.5329 0.571 1 0.6 107 0.6491 0.6846 0.7196 0.7552 0.79 17 0.8280 0.8651 0 9042 0.9437 0.98 16 1.017 1 *055 1.093 1.132 1.170 1.182 1 -207 1.245 1 -276 1.282

0 0.0034 0.021 8 0.060 1 0.1073 0.1593 0.2136 0.2694 0.3252 0.3803 0.4344 0.4870 0.5384 0-5888 0.6381 0.6865 0.7341 0.78 10 0.8273 0.8730 0.9 1 84 0.9635 1.008 1.053 1 -097 1.141 1.184 1.228 1.241 1.271 1.314 1.349 1.357

0 0.0267 0.3203 1.301 2.950 5.289 8.292

11-92 16-10 20.79 25.92 31.44 37.35 43.65 50.32 57-33 64-7 1 72.44 80.54 89.01 97.85

107.1 116.7 126.7 137.1 147.8 158.9 170.4 174.2 182.3 194.6 204.9 207.2

of 1 mole of citric acid in a saturated aqueous solution, obtained by subtracting the free energy of formation of water in a saturated solution (= - 56.69 + 2.303 RT loglo 0.778 = -56.84 kcal mole-1) from the value for the free energy of formation of citric acid monohydrate, is -295.1 6 0.30 kcal mole-1.

From isopiestic data,3 using the method proposed by Lewis and Randall,7 the molal activity coefficient of citric acid in a saturated aqueous solution has been calculated to be 3.582. This quantity has been used in the equation?

AG = -2-303RTloglo ym,

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1514 HEAT CAPACITY OF CITRIC ACID MONOHYDRATE

where y represents the molal activity coefficient and m is the molality of the un- dissociated citric acid in a saturated aqueous solution, to calculate the free energy change, AG for the conversion from the saturated aqueous solution to the standard state of unit activity. In the absence of data for the degree of dissociation of citric acid in a saturated aqueous solution, we have assumed the molality of the undissoci- ated citric acid to be equal to the molality of the saturated aqueous solution. The value thus obtained for the free energy change is -2.02 kcal mole-1. The free energy of formation of undissociated citric acid in solution at unit activity is, there- fore, -297.18 +0=30 kcal mole-1.

The dissociation constants for the three stages involved in the ionization of citric acid have been determined3 and used to evaluate the free energy change which occurs in the overall process,

H3Ci(aq) = 3H+(aq) + Ci3-(aq). The value obtained is 19.49 0-04 kcal mole-1. The free energy of formation of the aqueous citrate ion in a solution of unit activity at 25"C, therefore, is -277.69 f 0-34 kcal mole-1. This is in good agreement with, but more precise than, the value -278.8 f 1.5 kcal mole-1 found by Burton 5 from enzymic equilibrium data.

The authors wish to thank Prof. Dainton for helpful discussions and Prof. Sir Hans Krebs for the sift of the citric acid monohydrate. D. M. Evans thanks the Department of Scientific and Industrial Research for the award of a maintenance grant and T. P. Melia thanks his employers I.C.I. Ltd., Alkali Division, who seconded him to the University of Leeds during the period in which this work was carried out.

1 Chappel and Hoare, Trans. Fm&y SOC., 1958,54, 367. 2 Levien, J. Physic. Chem., 1955,59,640. 3 Bates and Pinching, J. Amer. Chem. Soc., 1949,72, 1274. 4 Furukawa, McCoskey and King, J. Res. Nut. Bur. Stand., 1951,47,256. 5 Burton, Biochem. J., 1955,59,44. 6 Selected values of Chemical Thermbdyamic Properties (Nat. Bur. Stand., circ. 500, Washington)

7 Lewis and Randall, Thermodynamics, (McGraw Hill Book Co., New York), 1952, pp. 273. (1952).

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