Surface tensions and densities of concentrated aqueous solutions of citric acid

    Surface tensions and densities of concentrated aqueous solutions of citric acid ˙ Monika Zarska, Marzena Dzida, Alexander Apelblat PII: DOI: Reference:

S0167-7322(16)31344-7 doi: 10.1016/j.molliq.2016.07.019 MOLLIQ 6033

To appear in:

Journal of Molecular Liquids

Received date: Revised date: Accepted date:

27 May 2016 3 July 2016 5 July 2016

˙ Please cite this article as: Monika Zarska, Marzena Dzida, Alexander Apelblat, Surface tensions and densities of concentrated aqueous solutions of citric acid, Journal of Molecular Liquids (2016), doi: 10.1016/j.molliq.2016.07.019

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT Surface tensions and densities of concentrated aqueous solutions of citric

PT

acid.

NU

SC

RI

Monika Żarskaa, Marzena Dzidaa and Alexander Apelblatb*

Abstract

MA

The surface tensions in unsaturated and supersaturated aqueous solutions of citric acid were measured in the temperature range from 283.15 K to 323.15 K. They were determined by the pendant drop method. Their values are compared with those

D

that exist in the literature. Together with measured surface tensions, the corresponding

TE

densities were also determined by using an oscillating tube densimeter. Basing on measured densities and surface tensions, the parachor values and apparent molar

AC CE P

volumes of aqueous citric acid solutions were calculated and discussed.

Keywords: Aqueous solutions of citric acid; Surface tensions; Densities; Parachor; The apparent molar volumes.

a

Institute of Chemistry, University of Silesia, Szkolna 9, 40-006, Katowice, Poland.

b

Department of Chemical Engineering, Ben Gurion University of the Negev, Beer Sheva,

Israel. *To whom correspondence should be addressed

ACCEPTED MANUSCRIPT Highlights .

The surface tensions of aqueous solutions of citric were measured in a wide

.

PT

concentration and temperature range.

From known measured surface tensions, a most reliable sets of them are

SC

.

RI

established.

Using determined densities the apparent molar volumes were determined and

MA

The parachor values in the citric acid + water system were evaluated and

TE

D

correlated.

AC CE P

.

NU

compared with the literature values.

ACCEPTED MANUSCRIPT 1. Introduction Citric acid, which is produced by fermentation methods, is one of the most important fruit acids used in large quantities in beverage, food, pharmaceutical, textile,

PT

metal, chemical and other industries. Citric acid plays a tremendous role in humans and animals, when in a series of enzymatic reactions energy is generated through the

RI

oxidation of fats, proteins and carbohydrates. Considering such exceptional position of

SC

citric acid and its aqueous solutions in biochemistry, medicine, chemistry and biochemical engineering, its physicochemical properties have been extensively

NU

investigated [1].

From all determined physical quantities, which are associated with the acid citric

MA

production (also with behaviour of cloud droplets), only surface tensions vary considerably when coming from different investigations. The measurements of surface tensions of aqueous citric acid solutions in the early period 1895 - 1913 [2-4] have only

D

historical value. Detailed, but engineering determinations of (T;m), over an extensive

TE

concentration and temperature range were performed during 1972 - 1977 period by the Averbukh group [5,6]. However, their two sets of surface tensions are inconsistent. In a

AC CE P

number of metrological and physicochemical studies surface tensions of citric acid solutions were also reported [7-9]. All available in the literature values of (T;m) are tabulated in [1]. They were determined by various experimental techniques and their accuracy is not always the same, and probably part of them have a doubtful value. It is evident from results coming from different investigations that accurate determinations of surface tensions in concentrated solutions of citric acid is not easy experimental problem. In order to validate the surface tensions of aqueous solutions of citric acid, which are needed in the mass-transfer engineering calculations, the systematic measurements of

(T;m) were performed and they are reported here.. Measurements were carried out from 283.15 K to 323.15 K and they cover the concentration range, 0 < w < 0.7, where w denotes the mass fraction of citric acid. At low temperatures, this range of mass fractions exceeds the solubility limits of citric acid in water, and therefore the surface tensions of some supersaturated solutions were also determined and presented.

ACCEPTED MANUSCRIPT Densities, which were simultaneously determined with surface tensions, permitted to evaluate the apparent molar volumes V2, (T;m) and the parachor P(T;m) values for citric acid in aqueous solutions. Taking into account the importance of citric acid

RI

PT

solutions, their densities were reported many times in the literature [10-17].

2. Experimental

SC

An anhydrous citric acid (CAS 77-92-9) was purchased from Acros Organics (0.996 mass fraction, ACS reagent) and was used for measurements without further

NU

purification. The water content of pure citric acid was less than 300 ppm, which was determined by Karl Fischer method (Schott, TitroLine 7500 KF trace). The aqueous

MA

solutions of citric acid were prepared by mass in whole solubility range by dissolving citric acid in bidistilled water with a conductivity 1.4 S cm-1. The solubility of citric acid in water was taken from literature [1]. The mixtures of higher concentration of citric acid

D

were heated to 323.15 K to increase the solubility and improve the dissolving of acid. All

measurement.

TE

samples were degassed for 10 min in an ultrasonic bath immediately prior to each

AC CE P

The surface tension measurements of citric acid aqueous solutions were performed using a drop shape analyser (Kruss DSA100) in the temperature range from 283.15 K to 323.15 K. The measurement of the surface tension takes place in a closed thermostated cell. In the applied procedure a pendant drop of the investigated liquid is

formed at the end of a needle placed in thermostated measuring cell and is filmed using a digital camera. The diameter of the needle and also density of investigated liquid are necessary for the calculations. During the temperature stabilization, which takes about 20 minutes, solution is located in a syringe and needle, so the evaporation is very small, because the diameter of the needle is only 1.8 mm. During the measurement, which takes about 30 seconds, evaporation is also limited, because a few drops of the solution is dropped to the bottom of the measuring chamber before the measurement to establish desired vapour pressure. Thus, the gas space around the pendant drop is saturated with vapors of the solution. It should be mentioned that in freshly prepared and warmed supersaturated aqueous solutions of citric acid no crystals were observed during he surface tension and density determinations. However, in few solutions of the highest concentration, and at the lowest

ACCEPTED MANUSCRIPT temperature, the crystals were observed in large magnification (80 times) of the pendant drop. There is an easy

possibility to distinguish between pendant drops of unsaturated and

supersaturated solutions. This is illustrated in picture 1 and 2, where are presented the

PT

unsaturated and supersaturated cases. Considering that the determination of surface tension in the citric acid + water system is very difficult, it was decided to report also surface tensions

RI

(indicated in tables) of supersaturated solutions. In order to validate consistency of measured

SC

surface tensions by applied equipment, in a gap of few months, (T;m) of two different sets of solutions were examined.

analysis using Laplace-Young equation 1 1  ) R1 R2

MA

p   (

NU

The surface tension of the liquid was determined from the pendant drop shape

(1)

where the pressure difference p over an interface between two fluids is expressed in

D

terms of the surface tension  and the principal radii of curvature, R1 and R2.

TE

The density of liquids have been measured using the Anton Paar DMA 5000 oscillating tube densimeter.

AC CE P

The accuracy of the surface tension equipment is ± 0.1 mNm-1 and thermal control of the cell is ± 0.1 K. Thermal control and stability of densimeter is ± 0.001 K and the

accuracy of density measurements is ± 0.05 kgm-3 . However, considering the nature of surface tension and density determinations in the investigated system, the actual values are in the case of surface tension about ± 0.4 mNm-1 and in the case of density about ± 0.2 kgm-3 .

3. Results and discussions The experimental values of surface tensions of aqueous solutions of citric acid in the temperature range from 283.15 K to 323.15 K are presented in Table 1. Part of these solutions lie outside of solubility region at given temperature and they are oversaturated. As already mentioned above, the available in the literature surface tensions vary considerably. It is observed not only scattering of experimental results, but a quite different behaviour of (T;m) curves with regard to concentration and temperature. This is illustrated in Fig. 1, where surface tensions in a rather narrow temperature range are

ACCEPTED MANUSCRIPT compared. As can be seen, the Linebarger [3] surface tensions at 288.15 K and those of Varga et al [8] and Mahiuddin et al [9] at 298.15 K over a whole concentration range are practically the same. At 293.15 K, the Averbukh group [5] early determinations differ

PT

considerably from those measured later [6]. There is no doubt, that our two sets of surface tensions values confirm the Averbukh et al results in [6]. This fact is of

RI

importance, because surface tensions were determined by different experimental

SC

techniques. However, it should be taken into account, that the precise determination of surface tensions in citric acid solutions is not easy, even by applying the modern

NU

equipment. As is evident in Fig. 1, a rather large scattering of results is observed in repeated determinations, the differences are larger than can be expected (see for example

MA

at w = 0.2).

The surface tensions decrease with increase of citric acid concentration, but a sharp increase is observed when it exceeds the solubility limits (Fig 1) and the surface

D

tensions decrease with increase of temperature (Table 1). This conduct of surface

TE

tensions in citric acid solutions is reported in all investigation, with an exception of Patel et al [18]. They claimed the opposite behaviour, in very dilute solutions, less than 0.01

AC CE P

mole/l, the surface tension increases with increasing concentration. This result and also presented by them densities are inconsistent with all available in the literature data causing that the reported values of parachor are clearly incorrect. From physicochemical properties of aqueous solutions of citric acid densities are much better documented in the literature than other properties [1]. There are many reported sets of densities and an additional set, determined in this investigation as a byproduct in the surface tension determinations, is presented in Table 2. These densities d(T;m), served to calculate the apparent molar volumes V2, (T;m) of citric acid (Table 3) from

V2, (T ; m) 

 M2 1000  1 1     d (T , m) m  d (T ; m) d H2O (T ) 

(2)

where M2 denotes the molar mass of citric acid. The values of apparent molar volumes are very sensitive to errors in density, and their presentation in Fig. 2 shows a very large scattering of them not only in very dilute solutions but also in a rather moderate concentrated solutions, m < 3.0 mol.kg-1. It should

ACCEPTED MANUSCRIPT be mentioned that the apparent molar volumes of citric acid at 298.15 K, as plotted in Fig. 2, are limited only to the 112 - 120 cm3.mol-1 region, when their actual scattering in various investigations significantly exceeds these limits [1]. It is evident, that in

PT

concentrated solutions, where only undissociated citric acid exists, V2, (T;m) decreases linearly with m, but its decrease is considerably stronger in dilute solutions due to the

RI

dissociation process. The insufficient accuracy of densities in very dilute solutions and an

SC

uncertain representation of three dissociation steps of the acid prevent to obtain the partial molar volume at infinite dilution of citric acid. This difficult problem of 1:3 type

NU

weak electrolyte, will probably found solution only when a very accurate densities will be determined by the dilatometric technique and not by a oscillating tube densimeter. Most

MA

likely, the scattering of the apparent molar volumes in concentrated solutions results from measurements performed with not completely transparent, containing very fine solid particles, solutions of citric acid.

D

Using surface tensions (T;m) and densities d(T;m), it possible to evaluate the

temperature [19,20]

TE

parachor P(T;m) values. This is an additive quantity which is nearly independent of

M av.   1/ 4 (T ; w)  d(T ; w) M av.  x1M1  x 2 M 2

AC CE P

P(T ; w) 

(3)

where xi are the mol fraction of components, Mi are their molar masses and <(T;m)> denotes the average value of surface tension at constant m in the investigated temperature range. Parachor values based on our surface tensions and densities determined from 283.15 K to 323.15 K, for unsaturated solutions, can be correlated with mass fractions w in the following way

P(T ; w) / g1/4  cm3  s-1/2  mol-1  55.545  35.546w - 60.171w 2  162.20w 3 R 2  0.9994

(4)

And, the expected error in surface tensions, if calculated from this equation, is about ± 0.65 mN.m-1.

ACCEPTED MANUSCRIPT 4. Conclusions In this investigation surface tension and densities of aqueous solutions of citric acid were determined by applying the pendant drop method and the oscillation tube

PT

densimeter in a wide concentration, from 0.1 to 12 mol.kg-1 and temperature from 283.15 K to 323.15 K regions. Some measurements were also performed in supersaturated

RI

solutions. Reported here surface tensions are more consistent with those of Averbukh et

SC

al [6] than with other results in the literature [3,5,8,9]. Parachor values were calculated and correlated using surface tensions and densities from this investigation. The

NU

volumetric properties of citric acid solutions are still far from being satisfactorily represented taking into account the significant scattering of available apparent molar

D

MA

volutes.

TE

References.

A. Apelblat, Citric Acid, Springer, Cham Heidelberg, 2014.

[2]

J. Taube, J. Prakt. Chemie, Capillary constants of certain aqueous and alcoholic

AC CE P

[1]

solutions. 31 (1885) 177-219. [3]

C.E. Linebarger, The surface-tension of aqueous solutions of oxalic, tartaric, and citric acids. J. Amer. Chem. Soc. 20 (1889) 128-130.

[4]

J. Livingston, R. Morgan, W.W. McKirahan, The weight of a falling drop and the laws of Tate. XIV. The drop weights of aqueous solutions of the salt of organic acids. J. Amer. Chem. Soc. 35 (1913) 1739-1767.

[5]

D.A. Averbukh, V.P. Metkin, B.M. Petrov, Determination of the surface tension of citric acid and filtrate solutions. Khlebopekarnaya i Konditerskaya Promyshlennost 16 (1972) 20-22.

[6]

D.A. Averbukh, V.P. Metkin, T.G. Chistova, Thermophysical and physicochemical parameters of solutions in citric acid production.

CNIITENI Food

Scientific-Technical Reference Book No 2, p.15, 1977. [7]

D.O. Topping, G,B. McFiggans, G. Kiss. Z. Varga, M.C. Facchini, S. Decesari, M. Mircea, Surface tension of multicomponent mixed inorganic/organic aqueous

ACCEPTED MANUSCRIPT solutions of atmospheric significance: measurements, model prediction and importance for cloud activation predictions. Atmos. Chem. Phys. 7 (2007) 23712396. Z. Varga, G. Kiss, H.C. Hansson, Modelling the cloud condensation nucleous

PT

[8]

activity of organic acids on the basis of surface tension and osmolality

S. Mahiuddin, B. Minofar, J.M. Borah, M.R. Das, P. Jungwirth, Propensities of

SC

[9]

RI

measurements. Atmos. Chem. Phys. 7 (2007) 4601-4611.

oxalic, citric, succinic and maleic acids for the aqueous solution/vapour interface:

NU

Surface tension measurements and molecular dynamics simulation. Chem. Phys. Lett. 462 (2008) 217-221.

B.J. Levien, A physicochemical study of aqueous citric acid solutions. J. Phys. Chem. 59 (1955) 640-644.

[11]

MA

[10]

C. Laguerie, M. Aubry, J.P. Couderc, Some physicochemical data on

D

monohydrate citric acid in water: solubility, density, viscosity, diffusivity, pH of

[12]

TE

standard solutions, and refractive index. J. Chem. Eng. Data 21 (1976) 85-87. E. Manzurola, A. Apelblat, Apparent molar volumes of citric, tartaric, malic,

AC CE P

succinic, maleic and acetic acids in water. J. Chem. Thermodyn. 17 (1985) 579584. [13]

A.H. Sijpkes, P. Van Rossum, J.S. Raad, G.J. Somsen, Heat capacities and volumes of some polybasic carboxylic acids in water at 298.15 K. J. Chem. Thermodyn. 21 (1989) 1061-1067.

[14]

A. Apelblat, E. Manzurola, Apparent molar volumes of organic acids and salts in water at 298.15 K. Fluid Phase Equil. 60 (1990) 157-171.

[15]

D.R. Lide (ed.) CRC Handbook of Chemistry and Physics, 82nd edn. Pp. 8-61, CRC, Boca Raton, 2001.

[16]

B.A. Patterson, E.M. Woolley, Thermodynamics of proton dissociation from aqueous citric acid: apparent molar volumes and apparent heat capacities of citric acid and its sodium salts at the pressure of 0.35 MPa and at temperatures from 278.15 to 393.15 K. J. Chem. Thermodyn. 33 (2001) 1735-1364.

ACCEPTED MANUSCRIPT [17]

S.J. Kharat, Density, viscosity, conductivity, ultrasonic velocity, and refractive index studies of aqueous solutions of citric acid at different temperatures. Int. J. Appl. Chem.4 (2008) 223-235. N.K. Patel, M.S. Mehta, J. Franco, Study of surface tension of binary solutions of

PT

[18]

organic acids in aqueous media. Labdev Part A 12 (1974) 89-90. D.B. MacLeod,

On a relation between surface tension and density. Trans.

RI

[19]

S. Sugden, A relation between surface tension, density, and chemical

TE

D

MA

NU

composition. J. Chem. Soc. 125 (1924) 1167-1177.

AC CE P

[20]

SC

Faraday Soc. 19 (1923) 38-41.

ACCEPTED MANUSCRIPT TABLE 1. Surface tensions of aqueous solutions of citric acid as a function of concentration m and temperature T. m/(mol kg )

D

MA

NU

SC

RI

PT

T=283.15 K T=293.15 K T=298.15 K T=303.15 K T=313.15 K T=323.15 K 0 74.08 72.56 71.61 70.86 69.21 67.41 0.1038 73.16 71.63 70.84 70.19 68.77 67.19 0.2780 71.77 70.33 68.81 67.35 65.94 0.2812 72.45 71.05 70.08 69.59 68.23 66.72 0.5705 71.21 70.11 69.48 68.89 67.68 66.38 0.8909 70.13 69.16 68.67 68.15 67.16 66.03 0.9439 70.54 69.60 68.53 67.33 66.18 1.254 69.41 68.43 67.94 67.41 66.47 65.40 1.287 69.64 67.79 65.79 63.56 61.66 1.312 69.99 68.92 67.79 66.68 65.42 1.701 68.75 67.87 67.30 66.75 65.75 64.71 1.734 69.13 67.72 66.27 64.79 63.20 2.235 68.16 67.27 66.67 66.21 65.26 64.27 2.258 68.72 67.85 66.93 65.88 65.07 2.755 67.90 66.95 66.38 65.82 64.61 63.63 2.788 68.63 67.39 66.01 64.62 63.36 3.399 67.52 66.62 66.07 65.65 64.68 63.62 3.456 68.05 66.60 65.60 64.60 63.65 4.214 68.22 67.05 65.68 64.26 63.07 4.299 67.45 66.45 65.82 65.46 64.46 63.53 5.212 67.04 66.07 65.49 65.11 64.04 63.12 5.232 67.50 66.57 65.62 64.48 63.39 * 6.395 66.63 65.55 65.03 64.50 63.43 62.41 * 7.126 66.37 65.49 64.86 64.30 63.39 62.42 * * 7.654 66.29 65.53 64.99 64.54 63.66 62.81 * * * 8.652 66.38 65.44 64.91 64.47 63.50 62.38 * 9.662 68.06 67.35 66.80 65.98 * * * * 9.800 66.50 65.34 64.66 64.29 63.30 62.40 * * * * 10.33 66.09 64.91 64.38 63.94 62.90 62.03 * * * * 12.33 70.58 69.71 68.84 67.85 67.14 * Supersaturated solutions of citric acid. Solubilities of citric acid in water is given in [1].

TE

0 0.0195 0.0507 0.0513 0.0988 0.1461 0.1535 0.1941 0.1982 0.2013 0.2464 0.2499 0.3004 0.3026 0.3461 0.3488 0.3950 0.3990 0.4474 0.4523 0.5003 0.5013 0.5513 0.5779 0.5952 0.6244 0.6499 0.6531 0.6650 0.7032

(T;m)/(mN.m-1)

-1

AC CE P

w

.

ACCEPTED MANUSCRIPT

PT

TABLE 2. Densities d of aqueous solutions of citric acid as a function of concentration m and temperature T. d(T;m)/(kg.m-3)

0.0000 0.1038 0.2812 0.5705 0.8909 1.254 1.701 2.235 2.755 3.399 4.299 5.212 6.395 7.126 7.654 8.652 9.662 9.800 10.33 12.33

T=283.15 K T=288.15 K T=293.15 K T=298.15 K T=303.15 K T=308.15 K T=313.15 K T=318.15 K T=323.15 K 999.72 999.12 998.23 997.07 995.68 994.06 992.24 990.24 988.07 1008.14 1007.42 1006.41 1005.14 1003.66 1001.96 1000.06 997.99 995.75 1021.92 1020.98 1019.81 1018.29 1016.75 1014.90 1012.99 1010.67 1008.35 1043.03 1041.80 1040.35 1038.69 1036.83 1034.80 1032.60 1030.20 1027.82 1064.72 1063.18 1061.54 1059.72 1057.64 1055.39 1053.00 1050.46 1047.80 1087.30 1085.49 1083.54 1081.38 1079.13 1076.68 1074.15 1071.24 1068.65 1112.72 1110.60 1108.40 1106.02 1103.51 1100.98 1098.12 1095.10 1091.98 1139.92 1137.47 1135.02 1132.38 1129.65 1126.71 1123.86 1120.77 1117.66 1163.74 1161.10 1158.38 1155.50 1152.61 1149.57 1146.47 1143.26 1139.96 1190.35 1187.48 1184.51 1181.45 1178.32 1175.11 1171.83 1168.47 1165.03 1221.55 1218.41 1215.21 1211.93 1208.59 1205.18 1201.71 1198.17 1194.57 1248.98 1245.64 1242.23 1238.78 1235.26 1231.71 1228.08 1224.43 1220.69 1275.57 1271.97 1268.33 1264.65 1260.93 1257.17 1253.37 1249.53 1287.67 1283.93 1280.18 1276.36 1272.54 1268.66 1264.76 1294.26 1290.48 1286.61 1282.75 1278.81 1274.90 1308.19 1304.38 1300.34 1296.35 1292.39 1323.54 1319.57 1315.58 1311.57 1307.54 1321.72 1317.74 1313.72 1309.69 1331.12 1327.08 1323.00 1318.93 1346.75 1342.64

AC

CE

PT ED

MA

NU

SC

RI

m/(mol.kg-1)

ACCEPTED MANUSCRIPT

V2,(T;m)/(cm-3.mol-1)

-1

m/ (mol kg )

RI

.

PT

TABLE 3. The apparent molar volumes V2, of citric acid as a function of concentration m and temperature T.

SC

110.07

111.28

112.43

113.56

115.34

116.13

116.88

117.63

0.2812

110.74

111.98

113.02

114.35

114.93

115.86

116.25

117.48

118.13

0.5705

111.40

112.54

113.58

114.54

115.42

116.24

117.01

117.83

118.31

0.8909

111.90

113.01

113.92

114.74

115.61

116.42

117.18

117.90

118.59

1.254

112.43

113.47

114.40

115.29

116.08

116.87

117.56

118.44

118.90

1.701

112.96

113.94

114.81

115.64

116.42

117.08

117.85

118.60

119.33

2.235

113.49

114.43

115.24

116.04

116.77

117.52

118.14

118.79

119.38

2.755

113.92

114.78

115.58

116.35

117.04

117.73

118.36

118.98

119.58

3.399

114.27

115.08

115.85

116.57

117.25

117.89

118.51

119.10

119.68

4.299

115.02

115.78

116.49

117.16

117.80

118.42

119.01

119.58

120.13

5.212

115.52

116.23

116.91

117.54

118.16

118.74

119.31

119.85

120.38

6.395

116.70

117.33

117.93

118.51

119.07

119.61

120.13

120.64

7.126

116.99

117.60

118.19

118.75

119.30

119.82

120.33

120.83

7.654

117.18

117.78

118.35

118.90

119.44

119.95

120.46

120.95

8.652

117.46

118.05

118.61

119.13

119.63

120.15

120.64

121.11

9.662

119.91

120.40

120.88

121.34

9.800

119.91

120.39

120.87

121.33

10.33

119.68

120.17

120.64

121.10

12.33

CE

PT ED

MA

0.1038

NU

114.39

AC

T=283.15 K T=288.15 K T=293.15 K T=298.15 K T=303.15 K T=308.15 K T=313.15 K T=318.15 K T=323.15 K

121.42

ACCEPTED MANUSCRIPT 14

PT

74.0

RI SC

70.0

68.0

NU

(w;T)/mNm

-1

72.0

0.20

D

64.0 0.00

MA

66.0

0.40

0.60

0.80

w

TE

FIGURE 1. Surface tension of aqueous solutions of citric acid as a function of concentration in the 288.15 - 298.15 K temperature range.

AC CE P

288.15 K: ■ - [3]; 293.15 K: ■ - [5]; ■ - [6]; ■ - this work; 298.15 K: ■ - [8]; ■ - [9].

ACCEPTED MANUSCRIPT 15

PT

120.0

RI

3

V2, /cm mol

-1

118.0

NU

SC

116.0

2.0

4.0

D

112.0 0.0

MA

114.0

m/molkg

6.0

8.0

10.0

-1

298.15 K.

TE

FIGURE 2. The apparent molar volume of citric acid as a function of concentration at

work.

AC CE P

■ - [10]; ■ - [11]; ■ - [12]; ■ - [13]; ■ - [14]; ■ - [15]; ■ - [16]; ■ - [17] and ■ - this

ACCEPTED MANUSCRIPT

AC CE P

TE

D

MA

NU

SC

RI

PT

16

PICTURE 1. Pendant drop of unsaturated aqueous solution of citric acid (molality m = 0.2812 molkg-1) at 298.15 K.

ACCEPTED MANUSCRIPT

AC CE P

TE

D

MA

NU

SC

RI

PT

17

PICTURE 2. Pendant drop of supersaturated aqueous solution of citric acid (molality m = 10.33 molkg-1) at 298.15 K. One can observe a large and several smaller solid citric acid crystals at high magnification of the pendant drop.

ACCEPTED MANUSCRIPT 18

PT

74.0

RI SC

70.0

68.0

NU

(w;T)/mNm

-1

72.0

0.20

AC CE P

TE

D

64.0 0.00

MA

66.0

Graphical abstract

0.40

w

0.60

0.80