Density, viscosity, conductivity, ultrasonic velocity, and refractive index studies of aqueous solutions of citric acid at different temperatures.IntroductionPolybasic acids play an important role in biological and industrial processes and accurate knowledge of their properties is therefore required. Citric acid is a tribasic, environmentally acceptable, and versatile chemical. As it occurs in metabolism of almost all living things, its interactions in an aqueous solution is of great value to the biological scientists. In pharmaceutical industry, citric acid is used as a stabilizer in various formulations, as a drug component and as a anticoagulant in blood for transfusions and also used as an acidifier in many pharmaceuticals. In industry, it is used in the manufacture of the alkyl resins, as a sequestering agent to remove trace metals, in special inks, in electroplating, a chelate to form stable complexes with multivalent metal ions [1, 2]. It is used in personal care products [2, 3]. Literature survey shows that there are few data on thermodynamic and transport properties for aqueous citric acid solutions. Marcia [4] reported the water activities and pH for aqueous solutions of citric acid at 298.15 K. The measurements were made from 5 to 50 mass % of citric acid. Apelblat [5, 6] and Parmer [7] studied partial molar volumes of citric acid in water at 298.15 and 298.15, 303.15, 308.15, 308.15, and 313.15 K respectively. Sijpkes [8] measured heat capacities and partial molar heat capacities at infinite dilution of citric acid in water at 298.15 K. Levien [9] carried the studies of apparent osmotic coefficients and molar conductivities. The measurements were made from 0.01 to 1 mol. [lit.sup.-1] at 298.15 K. The aim of this research work is to create accurate data on thermodynamic and transport properties of aqueous solutions of citric acid and to know more about solute--solvent interactions, and ion-solvent interactions. This paper reports density, viscosity, ultrasonic velocity, conductivity, and refractive index studies of aqueous solutions of citric acid at different temperatures. Experimental Materials Anhydrous citric acid (purity > 99.5 %, Qualigens Fine Chemicals, India) was used as received. Aqueous solutions of citric acid were prepared in triply distilled-deionized water. Methods Aqueous solutions of citric were prepared by mass in an airtight, stoppered glass bottle. Masses were recorded on an electronic Dhona balance (India) with a precision of [+ or -] 1 x [10.sup.-7] kg. The densities [rho] of aqueous solutions were measured with the help of a 15 x [10.sup.-6] [m.sup.3] double arm pycnometer. The uncertainty in density measurements was [+ or -] 1 x [10.sup.-7] kg x [m.sup.-3]. Dynamic viscosities [eta] of aqueous solutions were measured using an Ubbelohde suspended-level viscometer. The uncertainty in the viscosity measurements was 0.003 mPa.s. The details of experimental methods for density and viscosity measurements have been reported previously. [10, 11] Ultrasonic velocities were measured by using a Multifrequency Ultrasonic Interferometer (M-83, Mittal Enterprises, India) at 2 MHz. Uncertainty in ultrasonic velocity measurements was 0.03%. The ultrasonic interferometer was calibrated with triply distilled water. Cyber Abbe Refractometer (USA) with an accuracy of [+ or -] 0.0002 was used for refractive index measurements. Refractometer was calibrated with standard specimen, water, and toluene. For measurement of refractive indices at different temperatures, water at different temperatures was circulated through the refractometer by a pump. Conductivity measurements were made by using Digital Conductometer (India). Conductivity cell immersed in a sample solution was placed in thermostat. The cell constant 1.11 [cm.sup.-1] was determined by using 0.1mol [kg.sup.-1] aqueous KCl solution at different temperatures. The experimental uncertainty in conductivity values was less than 0.2 %. Density, viscosity, ultrasonic velocity, conductivity, and refractive index have been measured as a function of concentration (0.3351 to 2.3422) mol x [kg.sup.-1] and temperature (298.15, 303.15, 308.15, and 313.15) K at atmospheric pressure. Results and Discussion Density Study Table 1 includes the densities ([rho]) and apparent molar volumes ([V.sub.[phi], m]) of aqueous solutions of citric acid at (298.15, 303.15, 308.15, and 313.15) K and at atmospheric pressure. From Table 1 it is observed that density of aqueous solution varies linearly with molality (m). At higher temperatures [rho] values become smaller. Figure 1 depicts the variations of densities of solutions of citric acid in water as a function of molality at different temperatures. From [rho] values, ([V.sub.[phi], m]) have been calculated by using the following equation [12,13] [V.sub.[phi], m] = (M/[rho]) - [([rho] - [([[rho].sub.0]) /(m[rho][[rho].sub.0])] (1) [FIGURE 1 OMITTED] M is the molar mass of the citric acid and [[rho].sub.0] is density of the water. [V.sub.[phi], m] value becomes larger at higher temperature. Partial molar volume [V.sup.o.sub.[phi], m] of citric acid has been calculated by using the Masson's equation [14,15] [V.sub.[phi], m] = [V.sup.o.sub.[phi], m] + [V.sub.S] [m.sup.1/2] + [V.sub.B] m (2) In this equation, [V.sub.S] and [V.sub.B] are solute, solvent and temperature dependent empirical parameters. [V.sup.o.sub.[phi], m], [V.sub.S] and [V.sub.B] have been estimated by the least square fitting of the apparent molar volume data in the equation 2. The values of [V.sup.o.sub.[phi], m], [V.sub.S] and [V.sub.B] at various temperatures are summarized in Table 2. The reported values for [V.sup.o.sub.[phi], m] by Apelblat [6] and Parmar [7] are 112.44 and 94.76 [cm.sup.3] x [mol.sup.-1], respectively. The observed value for [V.sup.o.sub.[phi], m] at 298.15 K is 110.321 [cm.sup.3] x [mol.sup.-1]. The small differences between observed value and literature [7] value may be due to the term [B.sub.v]m in equation 2. The [V.sup.o.sub.[phi], m] and [V.sub.S] values provide information regarding solute-solvent and ion--solvent interactions, respectively. The positive values of [V.sup.o.sub.[phi], m] at all temperatures suggest the strong solute-solvent interactions [16]. The VS values are positive which is an indication of ion-solvent interactions. [V.sub.S] values are smaller than [V.sup.o.sub.[phi], m] suggesting the dominance of solute-solvent interactions over ion-solvent interactions. The [V.sup.o.sub.[phi], m] value increases and VS value decreases with rise of temperature. Viscosity Study Table 3 presents the viscosities [eta] of aqueous solutions at different temperatures. From Table 3, it is clear that [eta] increases with an increase in the m. The [eta] value becomes smaller at higher temperatures. Variations of viscosities of solutions of citric acid at different temperatures are illustrated in Figure 2. The viscosity data have been analyzed by using the Jones-Dole equation [17] [eta]/[[eta].sub.o] = 1 + A [m.sup.1/2] + Bm (3) [FIGURE 2 OMITTED] Where [eta] and [[eta].sub.o] are the viscosities of solution and solvent, respectively. A is a constant independent of concentration and Jones-Dole coefficient B is related to the effect of the ions on the structure of water. B is interpreted as a measure of the structure-forming and structure-making capacity of an electrolyte in solutions. [18] Least squares method was used to calculate the constant A and Jones-Dole coefficient B. The values of A and B calculated from equation 3 are compiled in Table 4. The values of A and B are negative and positive, respectively. Parmar [19] also observed positive value for B (0.628 [dm.sup.3]/mol at 303.15 K). The positive values of B at all temperatures are an indicative of water-structuring [18] behavior of citric acid. Ultrasonic Velocity Study Ultrasonic velocities (u) of aqueous solutions of citric acid at 298.15, 303.15, 308.15, 313.15 K are given in Table 5. The plots of variations of ultrasonic velocities of solutions of citric acid with molality are shown in the Figure 3. From u values, the values of isentropic compressibility KS have been calculated by using the Laplace equation [20] [K.sub.S] = 1/([u.sub.2] [rho]) (4) [FIGURE 3 OMITTED] [K.sub.S], u, and [rho] are the isentropic compressibility ([Pa.sup.-1]), ultrasonic velocity ([m x [s.sup.-1]), and density (kg x [m.sup.-3]) of the solution, respectively. From Table 5, it follows that the [K.sub.S] values are positive and become smaller at higher concentration of citric acid. The apparent molar isentropic compressibility ([K.sub.[phi], S]) values are calculated by using the following equation [21] [K.sub.[phi], S] = [(1/m [[rho].sub.o]) x (([K.sub.S] - [K.sub.Sol])] + [K.sub.S] [V.sub.[phi], m] (5) [K.sub.Sol] is the isentropic compressibility of water. The negative values of [K.sub.[phi], S] suggest that the water molecules around the citric acid molecules are less compressible than water molecules in the bulk [22, 23]. The limiting molar isentropic compressibility [K.sup.0.sub.[phi],S] is estimated by fitting of [K.sub.[phi], S] data in the equation [21]: [K.sub.[phi], S] = [K.sup.0.sub.[phi],S] + a [m.sup.1/2] + bm (6) The [K.sup.0.sub.[phi],S], a and b values are included in Table 6. Electrical Conductivity Study Electrical conductivities [kappa] of aqueous solutions of citric acid in water are listed in Table 7. Levien [8] reported electrical conductivities of solutions of citric acid in water up to 1M. Our experimental values of electrical conductivities are around 3% lower than the literature [8] values at 298.15 K. From Table 7, it is observed that the electrical conductivity increases and reaches to maximum and then falls down. The conductivity also increases with an increase in the temperature. Figure 4 presents the variations of conductivities with molality of solutions of citric acid in water. At 298.15 K, the maximum is observed at about 1.4362 mol x [kg.sup.-1]. It is revealed from Table 7 and Figure 4 that the maximum shifts towards higher concentration of citric acid at higher temperature. [FIGURE 4 OMITTED] Refractive Index Study The refractive indices n of aqueous solutions of citric acid at four temperatures are collected in Table 8. The refractive index increases with an increase in concentration of citric acid and decreases with an increase in temperature. The graphical representation of variations of refractive indices as a function of molality at different temperatures is shown in the Figure 5. The molar refractivity [R.sub.m] of citric acid in water was calculated by using the Lorent-Lorenz equation (24, 25). [R.sub.m] = ([n.sup.2]-1/[n.sup.2] +2) x (([x.sub.1] [M.sub.1] + [x.sub.2] [M.sub.2])/ [rho]) (7) [FIGURE 5 OMITTED] Where [x.sub.1], [x.sub.2], [M.sub.1], and [M.sub.2] are the mole fractions and molar masses of citric acid and water respectively. [R.sub.m] increases with an increase in concentration of citric acid. Conclusions Positive values of partial molar volume are an indicative of strong citric acid-water interaction. Positive value for Jones-dole coefficient suggests water structure forming behavior of citric acid. Limiting molar isentropic compressibility has higher negative value that supports the conclusion drawn from partial molar volume. Maximum in conductivity concentration curve is at about 1.4362 mol x [kg.sup.-1]. At higher temperature the maximum shifts towards the higher concentration of citric acid. Molar refractivity of citric acid in water increases with increase in the molality of solution and decreases with an increase in the temperature. Acknowledgement The author gratefully acknowledges the financial support of the University Grants Commission (Western Region), Pune, India (File No: 47-117/06) References [1] The Merck index- An Encyclopedia of Chemicals, Drugs, Biologicals, 13th ed; Merck and Co., Inc: 2001, 405. [2] Kirk-Othmer Encyclopedia of Chemical Technology, 4th ed.: John Willey and Sons: New York (1993), 354-380. [3] Kent, J. A. Kent and Riegels Handbook of Industrial Chemistry and Biotechnology; Spingerlink: 2008 XIV, 1386. [4] Maffia, M. C., Meirelles, J. A. 2001 "Water Activity and pH in Aqueous Polycarbonic Acid Systems", J. Chem. Eng. Data, 46, pp. 582-587. [5] Apelblat, A., Manzurola, E., 1990, "Apparent Molar Volumes of Organic Acids and Salts at 298.15 K", Fluid Phase Equilibria, 60, pp. 157-171. [6] Apelblat, A; Manzurola, E., 1985, "Apparent Molar Volumes of Citric, Tartaric, Malic, Succinic, Maleic, and Acetic Acids in Water at 298.15 K", J. Chem. Thermodyn., 6, pp. 579-584. [7] Parmar, M. L., Awasthi, R. K., Guleria, M. K., 2004, "A Study of Partial Molar Volumes of Citric Acid and Tartaric Acid in Water and Binary Mixtures of Ethanol at various Temperatures", J. Chem. Sci., 116, pp. 33-38. [8] Sijpkes, A. H.; Rossum, P. A.; Raad, J. S.; Somsen, G., 1989, "Heat Capacities and Volumes of Some Polybasic Carboxylic Acids in Water at 298.15 K", J. Chem. Thermodyn., 9, pp. 1061-1067. [9] Levien, B. J., 1955, "A Physicochemical Study of Aqueous Citric Acid Solutions", J. Phys. Chem., 59, pp. 640-644. [10] Kharat, S. J., 2008, "Density, Viscosity, and Ultrasonic Velocity Studies of Aqueous Solutions of Sodium Acetate at Different Temperatures" J. Mol. Liq., 140, pp. 10-14. [11] Kharat, S. J., 2008, "Density, and Viscosity Studies of Aqueous Solutions of Cesium Trifluroacetate at Different Temperatures", J. Chem. Eng. Data, 53, pp. 1292-1294. [12] Kupke, D. W., 1973, "Physical Principles and Techniques of Physical Chemistry", Part C; Academic Press: New York, London. [13] Plotz, I. M., 1972, "Rosenberg, R. M. Chemical Thermodynamic Theory and Methods", 3rd ed; W. A Benjamin: CA. [14] Redlich, D., Mayer, D. M., 1964, "The Molal Volumes of Electrolytes" Chem. Rev., 64, pp. 222-227. [15] Sadeghi, R., Goodarzi, B., 2008, "Volumetric Properties of Potassium Dihydrogen Citrate and Tripotassium Citrate in Water and in Aqueous Solutions of Alanine at T = (283.15 to 308.15) K", J. Chem. Eng. Data, 53, pp. 26-35. [16] Ali, A., Nain, A.K., Kumar, N., Ibrahim, M., 2002, " Density and Viscosity of Magnesium Sulfate in Formamide + Ethylene Glycol Mixed Solvents"' J. Chem. Sci., 114(5), pp. 495-500. [17] Jones, G., Dole, M., 1929, "The Viscosity of Aqueous Solutions of Strong Electrolytes with Special Reference to Barium Chloride", J. Am. Chem. Soc., 5 (1), pp. 2950-2964. [18] Hribar, B. N., Southall, T., Vlachy, V., Dill, K. A., 2002, "How Ions Affect the Structure of Water", J. Am. Chem. Soc., 124 (41), pp.12302-12311. [19] Parmar, M. L., Awasthi, R. K., Guleria, M. K., 2004, "A Study of Viscosities of Citric Acid and Tartaric Acid in Water and Binary Mixtures of Ethanol at various Temperatures", Indian J. Chem., 43 (A), pp. 41-44. [20] Robinson, R.A., Stokes, R. H., 1959, Electrolytic solutions; Butter Worth Scientific Publications, London. [21] Harned, H.S., Owen, B.B., 1957, "Physical Chemistry of Electrolyte Solutions", Chapman and Hall, London. [22] Sadeghi, R., Ziamajidi, F., 2007, "Volumetric Properties and Isentropic Compressibility Behavior of Aqueous Solutions of Polyvinylpyrrolidone + Sodium Citrates at T = (283.15 to 308.15) K", J. Chem. Thermodyn, 39 (8), pp. 1118-1124. [23] Soto, A., Arce A., 1998, "Khoshkbarchi, M. K. Experimental Data and Modeling of Apparent Molar Volumes, Isentropic Compressibility and Refractive Indices in Aqueous Solutions of Glycine + Water", Biophysical Chemistry, 74(3), 165-175. [24] Pacak, P. Kodejs, J. 1988, " Molar Volumes and Refractions of Highly Concentrated Solutions of Ammonium and Potassium Thiocyantaes in Water and DMSO" Can. J. Chem, 66, 2244. [25] Moelwyn-Hughes, E.A., 1961, Physical Chemistry, Pergamon, London. Sanjeevan J. Kharat * P. G. Department of Chemistry, HPT Arts & RYK Science College, Nashik- 422005, India Corresponding authors: E-mail: ksanjeevan@dataone.in
Table 1: Density [rho] and Apparent Molar Volume [V.sub.[phi], m] of
Citric Acid in water from T = (298.15 to 313.15) K
m (a) [10.sup.-3] [rho] (b) [10.sup.6] x [V.sub.[phi], m] (c)
T = 298.15 K
0.0000 0.9970
0.3351 1.0225 113.246
0.5175 1.0353 113.868
0.8848 1.0594 114.577
1.0321 1.0685 114.773
1.3109 1.0850 115.012
1.5615 1.0990 115.197
1.7697 1.1101 115.322
2.0790 1.1257 115.509
2.3422 1.1383 115.620
T = 308.15 K
0.0000 0.9940
0.3351 1.0191 114.576
0.5175 1.0317 115.179
0.8848 1.0555 115.768
1.0321 1.0645 115.923
1.3109 1.0807 116.205
1.5615 1.0945 116.373
1.7697 1.1053 116.573
2.0790 1.1207 116.721
2.3422 1.1331 116.824
m (a) [10.sup.-3] x [rho] (b) [10.sup.6] x [V.sub.[phi], m] (c)
T = 303.15 K
0.0000 0.9956
0.3351 1.0209 113.906
0.5175 1.0336 114.518
0.8848 1.0576 115.108
1.0321 1.0666 115.342
1.3109 1.0830 115.562
1.5615 1.0968 115.813
1.7697 1.1078 115.941
2.0790 1.1233 116.109
2.3422 1.1358 116.215
T = 313.15 K
0.0000 0.9922
0.3351 1.0171 115.289
0.5175 1.0297 115.652
0.8848 1.0534 116.203
1.0321 1.0623 116.414
1.3109 1.0785 116.616
1.5615 1.0922 116.806
1.7697 1.1031 116.908
2.0790 1.1185 117.025
2.3422 1.1309 117.107
(a) mol x [kg.sup.-1], (b) kg x [m.sup.-3], (c) [m.sup. 3] x
[mol.sup.-1]
Table 2: Least Square Fitted Values of Partial Molar Volume
[V.sup.0.sub.[phi], m], Ion-Solvent Interaction Parameter [V.sub.S],
and Constant [V.sub.B] of Equation 2 of Citric Acid in water from
T = (298.15 to 313.15) K
T/K [10.sup.6] x [V.sup.0.sub.[phi], m] (c)
298.15 110.321 [+ or -] 0.1878
303.15 111.281 [+ or -] 0.1729
308.15 112.099 [+ or -] 0.1888
313.15 113.007 [+ or -] 0.0750
T/K [10.sup.6] x [V.sub.S] (d) [10.sup.6] x [V.sub.B] (e)
298.15 6.1541 [+ or -] 0.3736 ?1.7755 [+ or -] 0.1751
303.15 5.4610 [+ or -] 0.3439 ?1.4674 [+ or -] 0.1612
308.15 5.1518 [+ or -] 0.3755 ?1.3542 [+ or -] 0.1761
313.15 4.5978 [+ or -] 0.1490 ?1.2532 [+ or -] 0.0699
[+ or -] Standard errors (d) [m.sup.3] x [mol.sup.-3/2] x [kg.sup.1/2],
(e) [m.sup.3] x [mol.sup.-2] x kg
Table 3: Viscosity [eta] of Citric Acid in Water from T = (298.15 to
313.15) K
m (a) [10.sup.3] x [eta] (f)
T = 298.15 K T = 303.15 K
0.0000 0.894 0.800
0.3351 1.045 0.920
0.5175 1.118 0.985
0.8848 1.280 1.131
1.0321 1.365 1.205
1.3109 1.532 1.345
1.5615 1.693 1.482
1.7697 1.843 1.631
2.0790 2.122 1.857
2.3422 2.432 2.120
m (a)
T = 308.15 K T = 313.15 K
0.0000 0.722 0.658
0.3351 0.813 0.725
0.5175 0.869 0.772
0.8848 1.002 0.885
1.0321 1.068 0.943
1.3109 1.193 1.059
1.5615 1.331 1.179
1.7697 1.445 1.275
2.0790 1.632 1.454
2.3422 1.825 1.613
(f) [m.sup.-1] x kg x [s.sup.-1]
Table 4: Least Square Fitted Values of Constant A and Jones Dole
Coefficient B of Equation 3 for Citric Acid in water from T = (298.15
to 313.15) K
T/K A (g) B (h)
298.15 -0.278 0.837
303.15 -0.295 0.826
308.15 -0.313 0.811
313.15 -0.354 0.809
(g) [(mol x [kg).sup.-1/2] (h) kg x [mol.sup.-1]
Table 5: Ultrasonic Velocity u, Isentropic Compressibility [K.sub.S],
and Apparent Molar Isentropic Compressibility [K.sub.[phi], S], of
Citric Acid in Water from T = (298.15 to 313.15) K
m (a) [10.sup.-3] x u (i) [10.sup.10] x [10.sup.15] x
[K.sub.S] (j) [K.sub.[phi], S] (k)
T = 298.15 K
0.0000 1.4960 4.482 --
0.3351 1.5064 4.310 -2.640
0.5175 1.5128 4.221 -2.550
0.8848 1.5260 4.054 -2.094
1.0321 1.5316 3.990 -2.026
1.3109 1.5424 3.874 -1.927
1.5615 1.5520 3.778 -1.707
1.7697 1.5600 3.702 -1.525
2.0790 1.5720 3.595 -1.265
2.3422 1.5824 3.508 -1.114
T = 308.15 K
0.0000 1.5196 4.357 --
0.3351 1.5300 4.192 -1.471
0.5175 1.5364 4.106 -1.402
0.8848 1.5496 3.946 -1.074
1.0321 1.5548 3.886 -0.8286
1.3109 1.5656 3.775 -0.759
1.5615 1.5754 3.681 -0.671
1.7697 1.5838 3.607 -0.585
2.0790 1.5954 3.506 -0.262
2.3422 1.6062 3.421 -0.233
m (a) [10.sup.-3] x u (i) [10.sup.10] x [10.sup.15] x
[K.sub.S] (j) [K.sub.[phi], S] (k)
T = 303.15 K
0.0000 1.5092 4.410 --
0.3351 1.5196 4.242 -2.022
0.5175 1.5260 4.155 -1.941
0.8848 1.5392 3.991 -1.581
1.0321 1.5444 3.931 -1.281
1.3109 1.5552 3.818 -1.253
1.5615 1.5648 3.724 -1.021
1.7697 1.5732 3.647 -0.991
2.0790 1.5848 3.545 -0.651
2.3422 1.5956 3.458 -0.619
T = 313.15 K
0.0000 1.5288 4.312 --
0.3351 1.5392 4.150 -0.958
0.5175 1.5452 4.067 -0.631
0.8848 1.5584 3.909 -0.523
1.0321 1.5640 3.848 -0.495
1.3109 1.5748 3.739 -0.487
1.5615 1.5844 3.647 -0.315
1.7697 1.5928 3.573 -0.310
2.0790 1.6044 3.473 -0.024
2.3422 1.6152 3.389 -0.016
(i) [ms.sup.-1] (j) [Pa.sup.-1]
(k) [m.sup.3] x [mol.sup.-1] x [Pa.sup.-1]
Table 6: Least Squares Fitted Values of Parameter of Equation 6 at T =
(298.15 to 313.15) K
T/K [10.sup.15] x [K.sup.0.sub.[phi], S] (k)
298.15 -3.132 [+ or -] 0.252
303.15 -2.849 [+ or -] 0.370
308.15 -2.155 [+ or -] 0.329
313.15 -1.242 [+ or -] 0.393
T/K [10.sup.15] x a (l) [10.sup.15] x b (m)
298.15 0.515 [+ or -] 0.501 0.525 [+ or -] 0.235
303.15 1.266 [+ or -] 0.737 0.140 [+ or -] 0.346
308.15 1.037 [+ or -] 0.655 0.151 [+ or -] 0.307
313.15 0.571 [+ or -] 0.782 0.147 [+ or -] 0.367
[+ or -] Standard errors
(l) [m.sup.3] x [mol.sup.-2] x [Pa.sup.-1] x kg
(m) [m.sup.3] x [mol.sup.-3] x [Pa.sup.-1] x [kg.sup.2]
Table 7: Conductivity [kappa] of Citric Acid in Water from T = (298.15
to 313.15) K
m (a) [10.sup.5] x
[kappa] (p)
T = 298.15 K T = 303.15 K T = 308.15 K T = 313.15 K
0.3351 4.31 5.05 5.65 6.12
0.5175 5.81 6.40 6.85 7.35
0.8848 6.86 7.49 8.10 8.80
1.0321 7.20 7.80 8.39 9.02
1.3109 7.31 7.94 8.54 9.16
1.5615 7.28 7.91 8.56 9.19
1.7697 7.11 7.74 8.37 8.99
2.0790 6.85 7.47 8.11 8.74
2.3422 6.56 7.81 7.81 8.45
(p) S x [m.sup.-1]
Table 8: Refractive indices n and Molar Refractions [R.sub.M] of Citric
Acid in Water from T = (298.15 to 313.15) K.
m (a) N [10.sup.3] x n [10.sup.3] x
[R.sub.M.sup.q] [R.sub.M.sup.q]
T = 298.15 K T = 303.15 K
0.0000 1.3325 1.3320
0.3351 1.3400 3.9265 1.3395 3.9260
0.5175 1.3440 4.0659 1.3435 4.0645
0.8848 1.3515 4.3840 1.3510 4.3823
1.0321 1.3542 4.5306 1.3537 4.5301
1.3109 1.3592 4.8391 1.3587 4.8372
1.5615 1.3635 5.1584 1.3630 5.1565
1.7697 1.3668 5.4371 1.3663 5.4363
2.0790 1.3715 5.9747 1.3710 5.9719
2.3422 1.3752 6.5011 1.3747 6.4977
T = 308.15 K T = 313.15 K
0.0000 1.3313 1.3305
0.3351 1.3387 3.9251 1.3380 3.9249
0.5175 1.3428 4.0637 1.3420 4.0622
0.8848 1.3502 4.3827 1.3495 4.3819
1.0321 1.3530 4.5290 1.3523 4.5284
1.3109 1.3579 4.8362 1.3572 4.8349
1.5615 1.3622 5.1562 1.3615 5.1546
1.7697 1.3655 5.4348 1.3648 5.4324
2.0790 1.3702 5.9712 1.3695 5.9678
2.3422 1.3740 6.4948 1.3733 6.4905
(q) mol x [m.sup.-3]
Anil shirsat (Member): 7/18/2010 1:25 PM
A very good excellent work, I must appreciate the effort of author creating such a data.
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