48 CHAPTER 3 PARTIAL MOLAL VOLUME, PARTIAL MOLAL COMPRESSIBILITY AND VISCOSITY B-COEFFICIENT OF FOUR HOMOLOGOUS -AMINO ACIDS IN AQUEOUS SODIUM FLUORIDE SOLUTIONS AT DIFFERENT TEMPERATURES 3.1 INTRODUCTION Proteins are the most vital of all the biological molecules evolved for a variety of specific purposes. To be functional and active, a very specific three dimensional structure is required. An array of vital forces, i.e., hydrophobic interactions, hydrogen bonding, ionic interactions, van der Waals interactions constitute the main forces responsible for the specific structure and conformation of proteins. Some covalent forces like disulphide linkage also contribute in maintaining the structure of protein (Privalov 1979. Hydration of proteins plays a significant role in the stability, dynamic, structural characteristics and fundamental activities of biopolymers. Proteins are complex molecules and their behaviour in solutions is governed by number of specific interactions. To reduce the degree of complexity in the study of these interactions, the study of the interactions in systems containing smaller bio-molecules, such as amino acids and peptides are preferred by many authors (Riyazuddeen and Bansal 2006, Yan et al 1998.
49 The zwitterionic nature of amino acids has an important bearing on biological functions in the physiological media such as blood, membranes, cellular fluids etc., where water happens to be important (Zubay 1996. The properties of proteins such as their structure, solubility, denaturation, activity of enzymes, etc. are greatly influenced by electrolytes (Von Hippel and Schleich 1969 a,b, Jencks 1969, Makhatadze and Privalov 1992, Robinson and Jencks 1965. The apparent and partial molal volumes of electrolyte solutions have proven to be a very useful tool in elucidating the structural interactions occurring in solutions (Millero 1971. The partial molal volumes, which are the first derivative of Gibbs energy with respect to pressure, are also used to calculate the effect of pressure on ionic equlibria for processes of engineering and oceanographic importance (Millero 1971. Since amino acids are zwitterions in aqueous solutions, their hydrations and interactions with proteins have resemblance with those of electrolytes (Zhao 2006, Millero et al 1978. The compressibility property, which is the second derivative of the Gibbs energy, also is a sensitive indicator of molecular interactions, particularly in cases where partial molal volume data fail to provide an unequivocal interpretation of the interactions (Iqbal and Verrall 1989. Viscosity has also been proven to be a sensitive and accurate probe for solution studies (Wang et al 2000. Study of interactions of some amino acids with KCl/KNO 3 at T= (298.15 to 323.15 K and that of L-alanine with potassium di-hydrogen citrate and tri-potassium citrate at T = (283.15 to 308.15 K have been reported by Riyazuddeen and Altamash (2010, Sadeghi and Goodarizi (2008 respectively. Wang et al (1999 have reported the partial molar volumes of some -amino acids in aqueous sodium acetate solutions at 308.15K. Apparent molar volumes and viscosity B-coefficients of caffeine in aqueous thorium nitrate solutions at T = (298.15, 308.15, and 318.15 K are
50 determined by Sinha et al (2010. The viscosity B-coefficients of some amino acids have been investigated in aqueous potassium thiocyanate (Wadi and Goyal 1992, sodium butyrate (Yan et al 2001 and ammonium chloride (Natarajan et al 1990 solutions. Effect of temperature on volumetric and viscometric properties of some amino acids in aqueous metformine hydrochloride (Rajagopal and Jayabalakrishnan 2010c and salbutamol sulphate (Rajagopal and Jayabalakrishnan 2009 have also been reported. The effectiveness of fluoride as anion in stabilising proteins is greater than chloride, bromide and iodide. Similarly, sodium cation is having the order of stabilising proteins as Na + > Li + > Ca 2+ > Mg 2+ (Wiggins 1997. Sodium fluoride is colourless crystalline salt used in the treatment of tooth decay (Bourne 1986. Literature survey shows that the influence of sodium fluoride on the volumetric properties of glycylglycine alone has been reported by Lin et al (2006. In this chapter the data on density, ultrasonic speed and viscosity of some amino acids (glycine, L-alanine, L-valine and L-leucine in aqueous sodium fluoride at T= (303.15, 308.15, 313.15 and 318.15 K are reported. Apparent molal volumes (V, partial molal volumes (V 0, Hepler coefficient ( 2 V 0 / T 2, transfer volumes ( V 0 and hydration number (n H are evaluated using density data. Apparent molal compressibility (K, partial molal compressibility (K 0, transfer compressibility ( K 0 and hydration number (n H have been calculated using ultrasonic speed data. Viscosity B-coefficients of Jones-Dole equation, transfer B-coefficient ( B, variation of B with temperature (db/dt, free energy of activation per mole of solvent µ 0* 1 and solute ( µ 0* 2 are estimated from viscosity data. Pair and triplet interaction coefficients have also been calculated from transfer parameters. The linear correlation of V 0, V 0, K 0, K 0, and B for the homologous
51 series of amino acids have been used to calculate the contribution of charged end groups (NH 3 +, COO -, methylene group (CH 2 and other alkyl chain of the amino acids. 3.2 EXPERIMENTAL The densities ( of the solutions of sodium fluoride are measured using a single stem pycnometer. The ultrasonic speed (u are determined using a multifrequency ultrasonic interferometer (M-84, Mittal make, India at a frequency of 2 MHz. Viscosity ( are measured by means of a suspended level Ubbelohde viscometer. Densities, ultrasonic speeds and viscosities are measured at temperatures T = (303.15, 308.15, 313.15 and 318.15 K as discussed in detail in Chapter 2. 3.3 RESULTS The experimental densities of the homologous amino acids in aqueous sodium fluoride solutions at temperatures T = (303.15, 308.15, 313.15 and 318.15 K are given in Table 3.1. The uncertainty values for density are calculated and are included in Table 3.1. Throughout this chapter m denotes molality of amino acids and m S molality of sodium fluoride. The apparent molal volumes (V are calculated from the measured densities using the equation (1.1 and the error values associated with them are evaluated using equation (1.2 and are given in Table 3.1.
Table 3.1 Density, and apparent molal volume, V of amino acids in aqueous sodium fluoride solutions at different temperatures m S = 0 mol kg -1 m S = 0.1 mol kg -1 m S = 0.3 mol kg -1 m S = 0.5 mol kg -1 m (mol kg -1 *10 3 V *10 6 *10 3 V *10 6 *10 3 V *10 6 *10 3 V *10 6 (kg m -3 (m 3 mol -1 (kg m -3 (m 3 mol -1 (kg m -3 (m 3 mol -1 (kg m -3 (m 3 mol -1 T = 303.15 K Glycine 0 0.9956 1.0002 1.0088 1.0171 0.02 0.9962 45.11 (0.06 1.0008 45.04(0.06 1.0094 44.91(0.05 1.0177 44.78(0.05 0.04 0.9969 42.56(0.05 1.0015 42.51(0.05 1.0101 42.43(0.04 1.0183 44.76(0.04 0.06 0.9975 43.37(0.04 1.0021 43.32(0.04 1.0106 44.86(0.04 1.0188 46.34(0.04 0.08 0.9981 43.77(0.04 1.0027 43.71(0.04 1.0111 46.06(0.04 1.0195 44.70(0.04 0.1 0.9987 43.99(0.04 1.0031 45.93(0.04 1.0117 45.79(0.04 1.0200 45.64(0.04 = 4.8 10-4 = 4.5 10-4 = 4.4 10-4 = 4.4 10-4 Alanine 0 0.9956 1.0002 1.0088 1.0171 0.02 0.9962 59.18 (0.06 1.0008 59.05 (0.06 1.0093 63.72 (0.06 1.0176 63.39 (0.05 0.04 0.9968 59.15 (0.05 1.0013 61.52 (0.05 1.0099 61.22 (0.05 1.0181 63.36 (0.04 0.06 0.9973 60.80 (0.05 1.0019 60.65 (0.04 1.0104 62.01 (0.04 1.0186 63.33 (0.04 0.08 0.9978 61.60 (0.04 1.0024 61.45 (0.04 1.0110 61.16 (0.04 1.0191 63.30 (0.04 0.1 0.9984 61.06 (0.04 1.0028 62.92 (0.04 1.0115 61.62 (0.04 1.0197 62.30 (0.04 = 4.2 10-4 = 4.0 10-4 = 4.2 10-4 = 3.9 10-4 Valine 0 0.9956 1.0002 1.0088 1.0171 0.02 0.9962 87.35 (0.07 1.0007 92.09 (0.06 1.0093 91.52 (0.06 1.0175 95.81 (0.06 0.04 0.9966 92.35 (0.06 1.0012 92.04 (0.05 1.0097 93.94 (0.05 1.0180 93.35 (0.05 0.06 0.9972 90.62 (0.05 1.0017 92.00 (0.05 1.0102 93.07 (0.05 1.0185 92.50 (0.05 0.08 0.9978 89.73 (0.05 1.0022 91.95 (0.05 1.0107 92.62 (0.04 1.0189 93.27 (0.04 0.1 0.9982 91.20 (0.05 1.0026 92.91 (0.05 1.0111 93.31 (0.04 1.0194 92.74 (0.04 = 4.0 10-4 = 3.7 10-4 = 3.5 10-4 = 3.5 10-4 52
Table 3.1 (Continued m S = 0 mol kg -1 m S = 0.1 mol kg -1 m S = 0.3 mol kg -1 m S = 0.5 mol kg -1 m (mol kg -1 *10 3 (kg m -3 V *10 6 (m 3 mol -1 *10 (kg m -3 V *10 6 (m 3 mol -1 *10 (kg m -3 V *10 6 (m 3 mol -1 *10 (kg m -3 V *10 6 (m 3 mol -1 = 4.0 10-4 = 3.7 10-4 = 3.5 10-4 = 3.5 10-4 Leucine 0 0.9956 1.0002 1.0088 1.0171 0.02 0.9961 106.48(0.07 1.0007 106.11(0.06 1.0092 110.34(0.06 1.0175 109.60(0.05 0.04 0.9965 108.96(0.06 1.0011 108.57(0.05 1.0096 110.30(0.05 1.0179 109.56(0.05 0.06 0.9970 108.07(0.06 1.0016 107.68(0.05 1.0101 108.61(0.05 1.0183 109.51(0.04 0.08 0.9975 107.59(0.05 1.0019 109.73(0.05 1.0105 108.97(0.05 1.0186 110.69(0.04 0.1 0.9981 106.27(0.05 1.0023 109.93(0.04 1.0110 108.18(0.05 1.0191 109.43(0.04 = 3.8 10-4 = 3.2 10-4 = 3.4 10-4 = 3.0 10-4 T = 308.15 K Glycine 0 0.9940 0.9987 1.0071 1.0154 0.02 0.9946 45.13(0.06 0.9993 45.06(0.06 1.0077 44.94(0.05 1.016 44.81(0.05 0.04 0.9953 42.57(0.05 1.0000 42.53(0.04 1.0083 44.91(0.04 1.0166 44.78(0.04 0.06 0.9959 43.39(0.04 1.0006 43.34(0.04 1.0089 44.88(0.04 1.0171 46.37(0.04 0.08 0.9965 43.78(0.04 1.0011 44.98(0.04 1.0094 46.09(0.04 1.0177 45.94(0.03 0.10 0.9970 45.02(0.04 1.0016 45.96(0.04 1.0100 45.82(0.04 1.0181 47.62(0.03 = 4.6 10-4 = 4.5 10-4 = 4.4 10-4 = 4.2 10-4 Alanine 0 0.994 0.9987 1.0071 1.0154 0.02 0.9946 59.23(0.06 0.9992 64.11(0.06 1.0076 63.78(0.05 1.0159 63.46(0.05 0.04 0.9952 59.19(0.05 0.9998 61.57(0.05 1.0081 63.75(0.04 1.0164 63.43(0.04 0.06 0.9957 60.85(0.05 1.0004 60.70(0.04 1.0087 62.07(0.04 1.0169 63.40(0.04 0.08 0.9962 61.66(0.05 1.0009 61.50(0.04 1.0092 62.45(0.04 1.0173 64.58(0.03 0.10 0.9968 61.12(0.05 1.0015 60.96(0.04 1.0097 62.67(0.04 1.0178 64.31(0.03 = 4.6 10-4 = 4.3 10-4 = 4.0 10-4 = 3.6 10-4 53
Table 3.1 (Continued m S = 0 mol kg -1 m S = 0.1 mol kg -1 m S = 0.3 mol kg -1 m S = 0.5 mol kg -1 m (mol kg -1 *10 3 (kg m -3 V *10 6 (m 3 mol -1 *10 (kg m -3 V *10 6 (m 3 mol -1 *10 (kg m -3 V *10 6 (m 3 mol -1 *10 (kg m -3 V *10 6 (m 3 mol -1 Valine 0 0.9940 0.9987 1.0071 1.0154 0.02 0.9946 87.44(0.06 0.9992 92.19(0.06 1.0076 91.63(0.06 1.0158 95.94(0.06 0.04 0.9951 89.92(0.05 0.9997 92.15(0.05 1.0080 94.06(0.05 1.0162 95.90(0.05 0.06 0.9956 90.72(0.05 1.0001 93.78(0.05 1.0085 93.19(0.04 1.0168 92.61(0.04 0.08 0.9961 91.10(0.05 1.0007 92.05(0.05 1.0090 92.73(0.04 1.0172 93.39(0.04 0.10 0.9965 92.32(0.05 1.0011 93.02(0.05 1.0093 94.43(0.04 1.0176 93.83(0.04 = 3.8 10-4 = 3.9 10-4 = 3.4 10-4 = 3.4 10-4 Leucine 0 0.9940 0.9987 1.0071 1.0154 0.02 0.9945 106.62(0.07 0.9992 106.23(0.06 1.0075 110.49(0.06 1.0158 109.75(0.05 0.04 0.9949 109.10(0.06 0.9996 108.69(0.05 1.0079 110.45(0.05 1.0161 112.14(0.05 0.06 0.9954 108.20(0.05 1.0000 109.49(0.05 1.0083 110.40(0.05 1.0166 109.66(0.04 0.08 0.9959 107.73(0.05 1.0004 109.86(0.04 1.0088 109.12(0.05 1.0170 109.62(0.04 0.10 0.9964 107.42(0.05 1.0008 110.06(0.04 1.0092 109.32(0.04 1.0174 109.58(0.04 = 3.6 10-4 = 3.2 10-4 = 3.2 10-4 = 3.1 10-4 T = 313.15 K Glycine 0 0.9922 0.9968 1.0052 1.0134 0.02 0.9928 45.16(0.06 0.9974 45.09(0.05 1.0058 44.96(0.05 1.0140 44.84(0.05 0.04 0.9935 42.59(0.05 0.9981 42.55(0.04 1.0064 44.94(0.04 1.0146 44.81(0.04 0.06 0.9941 43.41(0.04 0.9987 43.36(0.04 1.0070 44.91(0.04 1.0151 46.41(0.04 0.08 0.9946 45.08(0.04 0.9991 46.27(0.04 1.0075 46.12(0.04 1.0156 47.20(0.03 0.10 0.9952 45.05(0.04 0.9996 47.00(0.04 1.0079 47.83(0.03 1.0160 48.64(0.03 = 4.6 10-4 = 4.3 10-4 = 4.2 10-4 = 4.2 10-4 54
Table 3.1 (Continued m S = 0 mol kg -1 m S = 0.1 mol kg -1 m S = 0.3 mol kg -1 m S = 0.5 mol kg -1 m (mol kg -1 *10 3 (kg m -3 V *10 6 (m 3 mol -1 *10 (kg m -3 V *10 6 (m 3 mol -1 *10 (kg m -3 V *10 6 (m 3 mol -1 *10 (kg m -3 V *10 6 (m 3 mol -1 Alanine 0 0.9922 0.9968 1.0052 1.0134 0.02 0.9928 59.28(0.06 0.9973 64.18(0.06 1.0057 63.86(0.05 1.0139 63.54(0.05 0.04 0.9933 61.79(0.05 0.9979 61.63(0.04 1.0062 63.82(0.04 1.0144 63.51(0.04 0.06 0.9939 60.91(0.04 0.9984 62.44(0.04 1.0067 63.79(0.04 1.0148 65.10(0.04 0.08 0.9943 62.99(0.04 0.9989 62.82(0.04 1.0072 63.76(0.04 1.0152 65.89(0.03 0.10 0.9949 62.19(0.04 0.9994 63.04(0.04 1.0077 63.73(0.04 1.0157 65.37(0.03 = 4.0 10-4 = 4.0 10-4 = 3.8 10-4 = 3.4 10-4 Valine 0 0.9922 0.9968 1.0052 1.0134 0.02 0.9927 92.63(0.07 0.9973 92.32(0.06 1.0056 96.71(0.06 1.0138 96.09(0.05 0.04 0.9933 90.04(0.06 0.9977 94.80(0.05 1.0061 94.19(0.05 1.0142 96.05(0.05 0.06 0.9938 90.84(0.05 0.9983 92.23(0.05 1.0065 94.98(0.04 1.0147 94.38(0.04 0.08 0.9943 91.21(0.05 0.9987 93.45(0.05 1.0070 94.11(0.04 1.0150 95.97(0.04 0.10 0.9948 91.42(0.05 0.9991 94.16(0.04 1.0074 94.56(0.04 1.0156 93.97(0.04 = 4.0 10-4 = 3.6 10-4 = 3.4 10-4 = 3.3 10-4 Leucine 0 0.9922 0.9968 1.0052 1.0134 0.02 0.9926 111.85(0.07 0.9972 111.43(0.06 1.0056 110.66(0.05 1.0138 109.93(0.05 0.04 0.9932 106.71(0.06 0.9977 108.86(0.05 1.0060 110.62(0.05 1.0141 112.33(0.04 0.06 0.9937 106.66(0.05 0.9981 109.65(0.05 1.0063 112.23(0.04 1.0144 113.11(0.04 0.08 0.9941 107.88(0.05 0.9985 110.03(0.05 1.0068 110.53(0.04 1.0149 111.02(0.04 0.10 0.9945 108.60(0.05 0.9990 109.22(0.05 1.0072 110.49(0.04 1.0154 109.75(0.04 = 3.6 10-4 = 3.3 10-4 = 3.0 10-4 = 3.0 10-4 55
Table 3.1 (Continued m S = 0 mol kg -1 m S = 0.1 mol kg -1 m S = 0.3 mol kg -1 m S = 0.5 mol kg -1 m (mol kg -1 *10 3 (kg m -3 V *10 6 (m 3 mol -1 *10 (kg m -3 V *10 6 (m 3 mol -1 *10 (kg m -3 V *10 6 (m 3 mol -1 *10 (kg m -3 V *10 6 (m 3 mol -1 T = 318.15 K Glycine 0 0.9902 0.9945 1.0029 1.0111 0.02 0.9908 45.19(0.06 0.9951 45.13(0.05 1.0035 45.00(0.05 1.0117 44.87(0.05 0.04 0.9914 45.16(0.05 0.9957 45.10(0.04 1.0041 44.97(0.04 1.0123 44.85(0.04 0.06 0.9921 43.43(0.04 0.9964 43.38(0.04 1.0046 46.60(0.04 1.0128 46.45(0.03 0.08 0.9926 45.11(0.04 0.9968 46.31(0.04 1.0051 47.41(0.03 1.0131 49.69(0.03 0.10 0.9932 45.08(0.04 0.9972 48.06(0.04 1.0055 48.88(0.03 1.0136 49.67(0.03 = 4.6 10-4 = 4.2 10-4 = 4.0 10-4 = 3.8 10-4 Alanine 0 0.9902 0.9945 1.0029 1.0111 0.02 0.9907 64.44(0.06 0.9950 64.27(0.06 1.0034 63.94(0.05 1.0116 63.63(0.05 0.04 0.9914 59.30(0.05 0.9955 64.24(0.05 1.0039 63.91(0.04 1.0120 66.04(0.04 0.06 0.9919 60.97(0.05 0.996 64.21(0.04 1.0043 65.54(0.04 1.0125 65.20(0.03 0.08 0.9924 61.79(0.04 0.9966 62.91(0.04 1.0048 65.10(0.03 1.0129 65.99(0.03 0.10 0.9930 61.24(0.04 0.9971 63.13(0.04 1.0052 65.81(0.03 1.0133 66.45(0.03 = 4.3 10-4 = 4.0 10-4 = 3.5 10-4 = 3.4 10-4 Valine 0 0.9902 0.9945 1.0029 1.0111 0.02 0.9907 92.77(0.07 0.9950 92.47(0.05 1.0033 96.89(0.05 1.0115 96.26(0.05 0.04 0.9912 92.72(0.06 0.9955 92.43(0.05 1.0038 94.36(0.05 1.0119 96.22(0.04 0.06 0.9918 90.97(0.05 0.9959 94.07(0.04 1.0042 95.15(0.04 1.0124 94.55(0.04 0.08 0.9923 91.34(0.05 0.9962 96.15(0.04 1.0045 96.77(0.04 1.0126 97.38(0.04 0.10 0.9928 91.55(0.05 0.9967 95.34(0.04 1.0051 94.73(0.04 1.0130 97.10(0.04 = 4.0 10-4 = 3.3 10-4 = 3.3 10-4 = 2.9 10-4 56
Table 3.1 (Continued m S = 0 mol kg -1 m S = 0.1 mol kg -1 m S = 0.3 mol kg -1 m S = 0.5 mol kg -1 m (mol kg -1 *10 3 (kg m -3 V *10 6 (m 3 mol -1 *10 (kg m -3 V *10 6 (m 3 mol -1 *10 (kg m -3 V *10 6 (m 3 mol -1 *10 (kg m -3 V *10 6 (m 3 mol -1 Leucine 0 0.9902 0.9945 1.0029 1.0111 0.02 0.9907 106.93(0.06 0.9949 111.64(0.06 1.0033 110.87(0.05 1.0115 110.13(0.04 0.04 0.9911 109.43(0.05 0.9954 109.06(0.05 1.0036 113.32(0.05 1.0118 112.54(0.04 0.06 0.9916 108.53(0.05 0.9958 109.85(0.05 1.0040 112.45(0.04 1.0121 113.33(0.04 0.08 0.9920 109.33(0.05 0.9961 111.50(0.05 1.0044 111.99(0.04 1.0125 112.47(0.04 0.10 0.9924 109.80(0.05 0.9966 110.44(0.04 1.0049 110.70(0.04 1.0128 112.92(0.04 = 3.4 10-4 = 3.2 10-4 = 3.0 10-4 = 2.6 10-4 Values within parenthesis indicates the error inv 57
58 Usually the partial molal volumes (V 0 are obtained using the equation (1.3 by the method of least squares. However in the cases where molality dependence of V is found to be either negligible or having no definite trend, the partial molal volumes at infinite dilution, V 0 are evaluated by taking an average of all the data points ( Bhat and Ahluwalia 1985, Wang et al 1999, Yan et al 2004. In the present case, the values of V 0 are evaluated by taking an average of all the data points. The values of partial molal volumes V 0, along with the literature values of partial molal volumes of amino acids in water, are given in Table 3.2. 0 Table 3.2 Partial molal volume ( V of amino acids in aqueous sodium fluoride solutions at different temperatures Amino Acid 0 V * 10 6 / m 3 mol -1 at various m s / mol kg -1 0.00 (Water Present Work Literature 0.1 0.3 0.5 T = 303.15 K Glycine 43.76 (0.42 39.5 a 43.59 b 43.89 c 44.10 (0.61 44.81 (0.64 45.25 (0.32 Alanine 60.36 (0.50 59.80 a 60.63 c 61.12 (0.63 61.94 (0.47 63.14 (0.21 Valine 90.25 (0.84 90.22 c 92.20 (0.18 92.89 (0.40 93.53 (0.59 Leucine 107.48 (0.50-108.40 (0.70 109.28 (0.44 109.76 (0.23 T = 308.15 K Glycine 43.98(0.49 43.90 d 43.98 e 44.37(0.63 45.33(0.26 45.90(0.53 Alanine 60.41(0.51 60.44 d 60.88 e 61.77(0.61 62.94(0.35 63.84(0.25 Valine 90.30(0.81 91.42 f 91.51 g 92.64(0.33 93.21(0.50 94.33(0.68 Leucine 107.81(0.41 108.40 i 108.87(0.70 109.96(0.30 110.15(0.50 T = 313.15 K Glycine 44.26(0.53 44.15 c 44.52 j 44.85(0.84 45.75(0.57 46.38(0.73 Alanine 61.43(0.63 61.35 f 62.9 b 62.82(0.42 63.79(0.02 64.68(0.45 Valine 91.23(0.42 91.58 f 93.39(0.50 94.91(0.48 95.29(0.46 Leucine 108.34(0.95 109.00 k 109.84(0.44 110.91(0.33 111.23(0.48 T = 318.15 K Glycine 44.79(0.34 44.17 l 45.59(0.77 46.57(0.74 47.11(1.09 Alanine 61.55(0.83 61.46 g 63.75(0.30 64.86(0.40 65.46(0.50 Valine 91.87(0.37 91.93 l 94.09(0.75 95.58(0.53 96.30(0.49 Leucine 108.80(0.51 109.37 g 110.50(0.49 111.87(0.49 112.28(0.50 Values within parenthesis indicates the error in a Yan et al (2004, b Bhattacharya and Sengupta (1985, c Lark and Bala (1983, d Munde and Kishore (2003, e Lark et al (2004, f Gopal and Agarwal (1973, g Kikuchi et al (1995, i Yan et al (1999, j Zhao et al (2004, k Duke et al (1994, l Banipal and Kapoor (1999. 0 V
59 The contribution of the zwitterionic end group V 0 (NH + 3, COO -, the methylene group V 0 (CH 2 and other alkyl chains of homologous series of amino acids to V 0 at different temperatures are evaluated using equations (1.4 to (1.7 and are reported in Table 3.3. Table 3.3 Contributions of zwitterionic groups (NH + 3, COO -, CH 2 and 0 other alkyl side chains to partial molal volumes ( V of amino acids in aqueous sodium fluoride solutions at different temperatures Group 0 V * 10 6 / m 3 mol -1 at various m s / mol kg -1 0.00 (Water 0.1 0.3 0.5 T = 303.15 K NH + 3, COO - 28.26 28.55 29.26 30.09 CH 2-15.73 15.96 15.98 15.94 CH 3 CH- 31.46 31.92 31.96 31.88 (CH 3 2 CHCH- 62.92 63.84 63.92 63.76 (CH 3 2 CH CH 2 CH - 78.65 79.80 79.90 79.70 T = 308.15 K NH + 3, COO - 28.35 28.95 30.00 30.86 CH 2-15.75 15.98 15.95 15.89 CH 3 CH- 31.50 31.96 31.90 31.78 (CH 3 2 CHCH- 63.00 63.92 63.80 63.56 (CH 3 2 CH CH 2 CH - 78.75 79.90 79.75 79.45 T = 313.15 K NH + 3, COO - 28.92 29.56 30.41 31.41 CH 2-15.79 16.05 16.14 15.96 CH 3 CH- 31.58 32.10 32.28 31.92 (CH 3 2 CHCH- 63.16 64.20 64.56 63.84 (CH 3 2 CH CH 2 CH - 78.95 80.25 80.70 79.80 T = 318.15 K NH + 3, COO - 29.25 30.44 31.32 31.93 CH 2-15.83 16.01 16.13 16.11 CH 3 CH- 31.66 32.02 32.26 32.22 (CH 3 2 CHCH- 63.32 64.04 64.52 64.44 (CH 3 2 CH CH 2 CH - 79.15 80.05 80.65 80.55
60 The partial molal volumes of transfer V 0 of amino acids from pure water to sodium fluoride water mixtures are calculated using equation (1.8 and the results are given in Table 3.4. Table 3.4 Partial molal volume of transfer ( V 0 of amino acids in aqueous sodium fluoride solutions at different temperatures Amino Acid 0 V * 10 6 / m 3 mol -1 at various m s / mol kg -1 0.1 0.3 0.5 T = 303.15 K Glycine 0.34 1.05 1.49 Alanine 0.76 1.58 2.78 Valine 1.95 2.64 3.28 Leucine 0.92 1.80 2.28 T = 308.15 K Glycine 0.39 1.35 1.92 Alanine 1.36 2.53 3.43 Valine 2.34 2.91 4.03 Leucine 1.06 2.15 2.34 T = 313.15 K Glycine 0.59 1.49 2.12 Alanine 1.39 2.36 3.25 Valine 2.16 3.68 4.06 Leucine 1.50 2.57 2.89 T = 318.15 K Glycine 0.80 1.78 2.32 Alanine 2.20 3.31 3.91 Valine 2.22 3.71 4.43 Leucine 1.70 3.07 3.48 The zwitterionic end group contribution V 0 (NH + 3, COO -, the methylene group contribution V 0 (CH 2 and the contribution from other alkyl chains of homologous series of amino acids to V 0 are evaluated using equations (1.4 to (1.7 and are given in Table 3.5
61 Table 3.5 Contributions of zwitterionic groups (NH 3 +, COO -, CH 2 and other alkyl side chains to partial molal volumes of transfer ( V 0 of amino acids in aqueous sodium fluoride solutions at different temperatures Group V 0 * 10 6 / m 3 mol -1 at various m s / mol kg -1 0.1 0.3 0.5 T = 303.15 K NH + 3, COO - 0.287 1.000 1.830 CH 2-0.235 0.256 0.208 CH 3 CH- 0.470 0.512 0.416 (CH 3 2 CHCH- 0.940 1.024 0.832 (CH 3 2 CH CH 2 CH - 1.175 1.280 1.040 T = 308.15 K NH + 3, COO - 0.594 1.642 2.500 CH 2-0.229 0.196 0.143 CH 3 CH- 0.458 0.392 0.286 (CH 3 2 CHCH- 0.916 0.784 0.572 (CH 3 2 CH CH 2 CH - 1.145 0.980 0.715 T = 313.15 K NH + 3, COO - 0.638 1.485 2.488 CH 2-0.257 0.347 0.170 CH 3 CH- 0.514 0.694 0.340 (CH 3 2 CHCH- 1.028 1.388 0.680 (CH 3 2 CH CH 2 CH - 1.285 1.735 0.850 T = 318.15 K NH + 3, COO - 1.187 2.076 2.680 CH 2-0.181 0.296 0.284 CH 3 CH- 0.362 0.592 0.568 (CH 3 2 CHCH- 0.724 1.184 1.136 (CH 3 2 CH CH 2 CH - 0.905 1.480 1.420 The standard partial molal volumes of amino acids are used to determine the number of water molecules, n H, hydrated to the amino acid by using equations (1.9 to (1.13 and are given in Table 3.6. The hydration number n H values evaluated from the compressibility data using the standard equation (1.18 are also presented in Table 3.6.
62 Table 3.6 Hydration number (n H of amino acids in aqueous sodium fluoride solutions at different temperatures Amino Acid From volume data n H at various m s / mol kg -1 0.1 0.3 0.5 From compressibility data From volume data T = 303.15 K From compressibility data From volume data From compressibility data Glycine 1.87 2.73 1.69 2.25 1.58 1.88 Alanine 2.26 2.73 2.05 2.41 1.75 2.12 Valine 3.24 2.76 3.07 2.61 2.91 2.40 Leucine 3.30 2.63 3.08 2.51 2.96 2.36 T = 308.15 K Glycine 1.80 2.36 1.56 1.92 1.42 1.44 Alanine 2.09 2.44 1.80 2.15 1.58 1.83 Valine 3.13 2.23 2.99 2.21 2.71 1.88 Leucine 3.19 2.38 2.91 2.33 2.86 2.23 T = 313.15 K Glycine 1.68 2.01 1.46 1.52 1.30 1.09 Alanine 1.83 2.14 1.59 1.82 1.36 1.54 Valine 2.94 2.18 2.56 1.97 2.47 1.57 Leucine 2.94 2.08 2.68 2.00 2.60 1.94 T = 318.15 K Glycine 1.50 1.67 1.25 1.15 1.12 0.83 Alanine 1.60 1.80 1.32 1.43 1.17 1.19 Valine 2.77 1.92 2.40 1.60 2.21 1.34 Leucine 2.78 2.02 2.44 1.96 2.33 1.85 On the basis of McMillan-Mayer theory (McMillan and Mayer 1945 of solutions, Friedman and Krishnan (1973 b considered that the thermodynamic transfer properties of solutes in aqueous solutions could be explained in terms of the cosolutes interaction. The pair and triplet volume interaction parameters are obtained by fitting transfer data to equation (1.14.
63 The pair and triplet compressibility interaction coefficients V AB / K AB / AB and V ABB / K ABB / ABB are given in Table 3.7. Table 3.7 Pair interaction coefficients, V AB / K AB / AB and Triplet interaction coefficients V ABB / K ABB / ABB of amino acids in aqueous sodium fluoride solutions at different temperatures Amino Acid V AB * 10 6 m 3 mol -2 kg V ABB * 10 6 K AB * 10 14 K ABB * 10 14 AB * 10 3 m 3 mol -3 kg 2 m 3 mol -1 kg Pa -1 m 3 mol -1 kg Pa -1 m 3 mol -2 kg ABB * 10 3 m 3 mol -3 kg 2 T = 303.15 K Glycine 1.825-0.390 1.827-1.125 0.043-0.042 Alanine 3.842-1.676 0.755-0.168 0.028-0.022 Valine 10.665-10.783 0.561-0.267 0.031-0.012 Leucine 5.065-3.920 1.075-0.967 0.015-0.002 T = 308.15 K Glycine 2.070-0.062 2.481-1.883 0.004 0.011 Alanine 7.330-5.600 0.923-0.383 0.014-0.007 Valine 10.575-12.737 0.890-0.717 0.049-0.053 Leucine 5.920-4.880 0.250-0.133 0.037-0.030 T = 313.15 K Glycine 3.169-1.422 3.253-2.758 0.025-0.022 Alanine 7.495-6.183 1.055-0.533 0.017-0.012 Valine 12.060-11.237 0.775-0.233 0.056 0.062 Leucine 8.475-8.213 0.338-0.227 0.039-0.030 T = 318.15 K Glycine 4.359-2.814 4.604-4.453 0.027-0.032 Alanine 12.145-11.840 1.347-0.533 0.027-0.020 Valine 12.260-11.147 1.504-1.083 0.033-0.030 Leucine 9.575-8.887 0.202-0.100 0.015 0.007 The variation of limiting partial molal volume V 0 with temperature is expressed using the quadratic equation (1.15 (Pal and Kumar 2004. The
64 coefficients a, b and c are determined and these coefficients are used to interpret the effect of the hydrocarbon chain on water structure using the general hydrophobicity criteria proposed by Hepler (1969. The values of a, b and c are given in Table 3.8. Table 3.8 Temperature coefficients, a, b and c of amino acids in aqueous sodium fluoride solutions Amino Acid a coefficient b coefficient c -1 m 3 mol -1 K m s = 0.1 / mol kg -1 coefficient -2 m 6 mol -2 K Glycine 467.87-2.826 0.005 Alanine 274.11-1.543 0.003 Valine 310.76-1.531 0.003 Leucine 254.97-1.083 0.002 m s = 0.3 / mol kg -1 Glycine 298.85-1.746 0.003 Alanine 72.57-0.251 0.001 Valine 372.95-1.991 0.004 Leucine 326.47-1.565 0.003 m s = 0.5 / mol kg -1 Glycine 75.10-0.308 0.001 Alanine 95.94-0.360 0.001 Valine 235.85-1.094 0.002 Leucine 690.28-3.905 0.007 The ultrasonic speed values of the homologous amino acids in aqueous sodium fluoride solutions at temperatures T = (303.15, 308.15, 313.15 and 318.15 K are given in Table 3.9. The uncertainty values u for ultrasonic speed are calculated and are included in Table 3.9.
65 Table 3.9 Ultrasonic speed (u of Amino acids in Aqueous Sodium Fluoride solutions at different temperatures m u / m s -1 at various m s / mol kg -1 (mol kg -1 0.00 (Water 0.1 0.3 0.5 T = 303.15 K Glycine 0.00 1512.0 1521.3 1538.7 1552.3 0.02 1513.1 1522.3 1539.6 1553.1 0.04 1513.9 1523.1 1540.3 1553.9 0.06 1514.9 1524.1 1541.3 1554.8 0.08 1515.9 1525.0 1542.2 1555.3 0.10 1516.8 1526.2 1543.0 1556.0 uncertainty u = 0.729 u = 0.734 u = 0.661 u = 0.569 Alanine 0.00 1512.0 1521.3 1538.7 1552.3 0.02 1513.2 1522.5 1540.0 1553.5 0.04 1514.3 1523.6 1540.9 1554.7 0.06 1515.5 1524.4 1541.9 1555.4 0.08 1516.6 1525.5 1542.5 1556.3 0.10 1517.4 1526.6 1543.6 1556.9 uncertainty u = 0.839 u = 0.793 u = 0.723 u = 0.706 Valine 0.00 1512.0 1521.3 1538.7 1552.3 0.02 1513.6 1523.0 1540.5 1554.2 0.04 1515.3 1524.4 1541.7 1555.4 0.06 1516.3 1525.7 1542.7 1556.6 0.08 1517.5 1526.4 1543.7 1557.5 0.10 1518.9 1527.6 1544.8 1558.6 uncertainty u = 1.027 u = 0.946 u = 0.903 u = 0.943 Leucine 0.00 1512.0 1521.3 1538.7 1552.3 0.02 1514.0 1523.2 1540.8 1554.4 0.04 1515.8 1525.1 1542.7 1556.4 0.06 1517.3 1526.9 1544.2 1557.9 0.08 1518.9 1528.5 1545.8 1559.8 0.10 1520.3 1529.9 1547.3 1561.4 uncertainty u = 1.262 u = 1.327 u = 1.301 u = 1.381
66 Table 3.9 (Continued m u / m s -1 at various m s / mol kg -1 (mol kg -1 0.00 (Water 0.1 0.3 0.5 T = 308.15 K Glycine 0.00 1520.4 1530.6 1547.7 1560.9 0.02 1521.4 1531.5 1548.5 1561.6 0.04 1522.3 1532.2 1549.3 1562.2 0.06 1523.2 1533.0 1550.0 1563.0 0.08 1524.0 1534.0 1550.9 1563.6 0.10 1525.0 1534.9 1551.5 1564.4 uncertainty u = 0.692 u = 0.651 u = 0.587 u = 0.531 Alanine 0.00 1520.4 1530.6 1547.7 1560.9 0.02 1521.6 1531.9 1548.9 1562.1 0.04 1522.7 1532.7 1550.0 1562.9 0.06 1523.9 1533.8 1551.1 1563.7 0.08 1525.2 1534.8 1551.9 1564.6 0.10 1526.5 1535.4 1552.5 1565.5 uncertainty u = 0.928 u = 0.741 u = 0.749 u = 0.706 Valine 0.00 1520.4 1530.6 1547.7 1560.9 0.02 1522.0 1532.2 1549.4 1562.7 0.04 1523.5 1533.7 1550.6 1563.9 0.06 1525.1 1534.7 1551.8 1565.0 0.08 1526.9 1535.8 1552.8 1566.1 0.10 1528.7 1536.8 1554.0 1567.3 uncertainty u = 1.107 u = 0.933 u = 0.938 u = 0.949 Leucine 0.00 1520.4 1530.6 1547.7 1560.9 0.02 1522.2 1532.5 1549.8 1563.0 0.04 1523.6 1534.3 1551.6 1565.0 0.06 1525.3 1536.1 1553.4 1566.6 0.08 1527.1 1537.7 1554.9 1568.3 0.10 1528.9 1539.4 1556.6 1569.9 uncertainty u = 1.286 u = 1.340 u = 1.346 u = 1.366
67 Table 3.9 (Continued m u / m s -1 at various m s / mol kg -1 (mol kg -1 0.00 (Water 0.1 0.3 0.5 T = 313.15 K Glycine 0.00 1528.0 1540.1 1555.8 1566.4 0.02 1529.0 1540.9 1556.5 1567.0 0.04 1529.8 1541.5 1557.1 1567.5 0.06 1530.7 1542.1 1557.7 1568.2 0.08 1531.8 1543.1 1558.4 1568.9 0.10 1532.7 1543.9 1559.3 1569.7 uncertainty u = 0.716 u = 0.537 u = 0.521 u = 0.501 Alanine 0.00 1528.0 1540.1 1555.8 1566.4 0.02 1529.1 1541.3 1556.9 1567.5 0.04 1530.3 1542.3 1557.9 1568.6 0.06 1531.4 1543.4 1558.9 1569.6 0.08 1532.5 1544.5 1559.6 1571.1 0.10 1533.5 1545.4 1560.1 1571.8 uncertainty u = 0.847 u = 0.812 u = 0.673 u = 0.684 Valine 0.00 1528.0 1540.1 1555.8 1566.4 0.02 1529.7 1541.7 1557.6 1568.1 0.04 1531.2 1543.2 1558.7 1569.4 0.06 1532.8 1544.2 1559.7 1570.6 0.08 1534.4 1545.4 1560.8 1571.9 0.10 1536.2 1546.5 1562.1 1572.9 uncertainty u = 1.238 u = 0.966 u = 0.923 u = 0.987 Leucine 0.00 1528.0 1540.1 1555.8 1566.4 0.02 1530.0 1542.1 1557.8 1568.5 0.04 1531.6 1543.8 1559.7 1570.3 0.06 1533.4 1545.5 1561.6 1572.1 0.08 1535.3 1547.3 1563.2 1573.9 0.10 1537.2 1549.0 1564.9 1575.6 uncertainty u = 1.390 u = 1.349 u = 1.384 u = 1.397
68 Table 3.9 (Continued m u / m s -1 at various m s / mol kg -1 (mol kg -1 0.00 (Water 0.1 0.3 0.5 T = 318.15 K Glycine 0.00 1535.2 1547.3 1562.9 1572.1 0.02 1536.2 1548.0 1563.5 1572.6 0.04 1537.1 1548.7 1564.0 1573.1 0.06 1537.8 1549.2 1564.7 1573.7 0.08 1538.9 1550.1 1565.4 1574.6 0.10 1539.8 1551.0 1566.2 1575.2 uncertainty u = 0.695 u = 0.554 u = 0.501 u = 0.485 Alanine 0.00 1535.2 1547.3 1562.9 1572.1 0.02 1536.5 1548.4 1563.9 1573.1 0.04 1537.2 1549.3 1564.8 1574.2 0.06 1538.3 1550.1 1565.5 1575.2 0.08 1539.6 1550.8 1566.4 1576.3 0.10 1540.5 1551.4 1566.9 1577.3 uncertainty u = 0.807 u = 0.625 u = 0.618 u = 0.799 Valine 0.00 1535.2 1547.3 1562.9 1572.1 0.02 1536.9 1548.8 1564.6 1573.7 0.04 1538.4 1550.4 1565.7 1575.0 0.06 1539.9 1551.6 1566.9 1576.3 0.08 1541.5 1553.0 1568.2 1577.7 0.10 1543.1 1554.2 1569.3 1578.6 uncertainty u = 1.196 u = 1.055 u = 0.962 u = 1.002 Leucine 0.00 1535.2 1547.3 1562.9 1572.1 0.02 1537.0 1549.3 1564.9 1574.1 0.04 1539.0 1550.9 1566.9 1576.2 0.06 1540.7 1552.6 1568.8 1577.9 0.08 1542.6 1554.5 1570.5 1579.8 0.10 1544.4 1556.1 1571.9 1581.7 uncertainty u = 1.408 u = 1.338 u = 1.393 u = 1.458
69 The apparent molal compressibilities (K of the homologous amino acids in aqueous sodium fluoride solutions at temperatures T = (303.15, 308.15, 313.15 and 318.15 K are calculated using the equation (1.16 and are listed in Table 3.10. Table 3.10 Apparent molal compressibility (K of amino acids in aqueous sodium fluoride solutions at different temperatures m K * 10 15 / m 3 mol -1 Pa -1 at various m s / mol kg -1 (mol kg -1 0.00 (Water 0.1 0.3 0.5 T = 303.15 K Glycine 0.02-25.56-21.87-17.81-14.23 0.04-23.40-21.19-17.17-14.23 0.06-23.14-21.41-16.91-13.79 0.08-23.01-20.82-16.12-12.96 0.10-22.35-20.44-15.92-11.92 Alanine 0.02-22.30-21.50-18.66-15.00 0.04-20.85-17.94-15.34-15.01 0.06-19.87-15.36-13.78-10.73 0.08-18.66-15.13-11.34-9.89 0.10-17.08-14.14-11.75-8.63 Valine 0.02-21.61-19.28-20.51-17.90 0.04-18.66-15.05-10.41-10.87 0.06-13.86-12.72-6.65-8.55 0.08-12.94-7.34-4.79-4.49 0.10-11.79-6.09-3.41-3.89 Leucine 0.02-22.67-18.90-18.68-17.44 0.04-17.57-16.78-16.01-16.18 0.06-14.47-16.58-12.94-11.49 0.08-13.66-12.94-11.07-10.76 0.10-12.92-10.51-10.24-10.36
70 Table 3.10 (Continued m K * 10 15 / m 3 mol -1 Pa -1 at various m s / mol kg -1 (mol kg -1 0.00 (Water 0.1 0.3 0.5 T = 308.15 K Glycine 0.02-22.35-18.75-14.90-11.50 0.04-23.11-18.10-14.91-10.23 0.06-21.90-17.39-14.03-10.21 0.08-20.57-17.36-13.90-9.91 0.10-20.05-16.79-13.05-9.19 Alanine 0.02-21.98-19.65-15.69-14.75 0.04-20.55-14.82-14.37-9.67 0.06-19.57-16.01-15.30-7.99 0.08-19.80-14.85-12.77-6.82 0.10-20.81-12.79-10.20-6.91 Valine 0.02-21.23-16.05-17.45-14.97 0.04-17.62-14.68-8.80-7.36 0.06-17.39-8.18-7.30-6.62 0.08-18.71-7.78-5.25-4.31 0.10-18.64-5.30-3.46-3.44 Leucine 0.02-20.86-18.44-18.22-17.04 0.04-17.34-14.94-14.27-13.84 0.06-17.60-13.79-12.98-12.01 0.08-18.46-11.85-11.39-10.78 0.10-18.11-11.26-10.69-9.55
71 Table 3.10 (Continued m K * 10 15 / m 3 mol -1 Pa -1 at various m s / mol kg -1 (mol kg -1 0.00 (Water 0.1 0.3 0.5 T = 313.15 K Glycine 0.02-22.12-15.73-12.12-8.92 0.04-21.46-15.11-10.81-7.66 0.06-20.73-13.49-10.38-7.64 0.08-20.69-13.32-9.82-7.63 0.10-20.41-12.96-9.72-7.35 Alanine 0.02-18.88-16.55-12.83-12.11 0.04-18.12-15.94-11.54-12.12 0.06-18.38-15.24-11.11-9.99 0.08-16.33-14.90-8.95-12.09 0.10-16.29-13.60-6.61-10.10 Valine 0.02-19.38-15.68-15.70-12.27 0.04-18.75-12.21-8.58-7.24 0.06-18.04-9.33-4.00-6.05 0.08-17.70-7.16-3.41-4.15 0.10-18.63-5.33-3.30-3.86 Leucine 0.02-17.44-16.49-15.22-16.83 0.04-16.17-14.53-13.94-11.11 0.06-16.20-12.48-12.18-9.24 0.08-15.85-12.17-11.39-10.27 0.10-15.65-12.29-10.64-10.40
72 Table 3.10 (Continued m K * 10 15 / m 3 mol -1 Pa -1 at various m s / mol kg -1 (mol kg -1 0.00 (Water 0.1 0.3 0.5 T = 318.15 K Glycine 0.02-21.92-12.89-9.43-6.37 0.04-20.51-12.90-8.14-6.39 0.06-19.62-12.50-8.10-5.94 0.08-19.81-11.86-8.09-5.65 0.10-19.67-11.47-7.80-5.54 Alanine 0.02-19.95-13.64-10.09-9.50 0.04-15.88-10.94-8.81-8.82 0.06-15.37-9.14-5.31-9.07 0.08-16.53-8.63-5.88-8.85 0.10-15.86-6.94-3.35-8.23 Valine 0.02-19.09-12.73-12.85-9.60 0.04-16.30-14.12-7.11-5.86 0.06-16.84-9.56-4.74-5.94 0.08-16.74-7.61-3.21-3.70 0.10-16.68-7.05-3.70-1.42 Leucine 0.02-15.86-16.20-14.95-14.12 0.04-16.52-12.91-12.96-13.45 0.06-15.40-11.33-12.80-9.90 0.08-15.18-10.87-11.44-10.38 0.10-14.50-10.66-9.90-9.89
73 The partial molal compressibility (K 0 of the homologous amino acids has been evaluated using equation (1.17 by least square fit method (Figure 3.1. The calculated values of K 0 (along with error and the experimental slope values S k are given in Table 3.11. The literature values of partial molal compressibility of amino acids in water are also given in Table 3.11 for comparison. 0.0-4.0 K / (10-15 m 3.mol -1.Pa -1-8.0-12.0-16.0-20.0-24.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 m/(mol.kg -1 Figure 3.1 Plot of apparent molal compressibility (K against molality (m of ( glycine, ( alanine, ( valine, ( leucine at T = 303.15 K of 0.1 M sodium fluoride solution
Table 3.11 Partial molal compressibility (K 0, slopes (S k of Amino acids in aqueous sodium fluoride solutions at different temperatures Amino acids K 0 * 10 15 S k * 10 18 K 0 * 10 15 S k * 10 18 K 0 * 10 15 S k * 10 18 K 0 * 10 15 S k * 10 18 m 3 mol -1 Pa -1 kg m 3 mol -2 Pa -1 m 3 mol -1 Pa -1 kg m 3 mol -2 Pa -1 m 3 mol -1 Pa -1 kg m 3 mol -2 Pa -1 m 3 mol -1 Pa -1 kg m 3 mol -2 Pa -1 at various m s / mol kg -1 0.00 (Water 0.1 0.3 0.5 T = 303.15 K Glycine -25.54(0.12 0.34-22.12(0.06 0.16-18.23(0.08 0.24-15.19(0.10 0.29 Alanine -23.55(0.20 0.63-22.08(0.30 0.88-19.52(0.30 0.89-17.21(0.30 0.89 Valine -23.38(0.42 1.26-22.32(0.55 1.70-21.11(0.69 1.99-19.45(0.57 1.71 Leucine -23.28(0.40 1.17-21.33(0.34 1.03-20.33(0.35 1.09-19.12(0.33 0.98 T = 308.15 K Glycine -23.74 (0.13-23.5 m 0.36-19.07(0.08 0.23-15.57(0.08 0.24-11.69(0.08 0.25 Alanine -21.47(0.09 0.15-19.74(0.25 0.69-17.44(0.22 0.63-14.79(0.33 0.93 Valine -19.94(0.15 0.20-18.92(0.47 1.42-17.91(0.54 1.57-15.18(0.46 1.30 Leucine -19.79(0.30 0.21-19.29(0.29 0.87-18.90(0.30 0.90-18.06(0.29 0.90 74
Table 3.11 (Continued Amino acids K 0 * 10 15 S k * 10 18 K 0 * 10 15 S k * 10 18 K 0 * 10 15 S k * 10 18 K 0 * 10 15 S k * 10 18 m 3 mol -1 Pa -1 kg m 3 mol -2 Pa -1 m 3 mol -1 Pa -1 kg m 3 mol -2 Pa -1 m 3 mol -1 Pa -1 kg m 3 mol -2 Pa -1 m 3 mol -1 Pa -1 kg m 3 mol -2 Pa -1 at various m s / mol kg -1 0.00 (Water 0.1 0.3 0.5 T = 313.15 K Glycine -22.34(0.07-22.4 n 0.21-16.32(0.12 0.37-12.31(0.09 0.29-8.79(0.06 0.16 Alanine -19.69(0.12-19.8 n 0.35-17.33(0.11 0.35-14.72(0.24 0.75-12.50(0.11 0.20 Valine -19.26(0.06-19.2 n 0.13-17.67(0.41 1.29-15.98(0.53 1.50-12.69(0.34 1.00 Leucine -17.43(0.07-17.8 n 0.19-16.82(0.19 0.53-16.19(0.19 0.58-15.69(0.30 0.68 T = 318.15 K Glycine -21.87(0.10-21.56 g 0.26-13.49(0.06 0.19-9.31(0.06 0.17-6.70(0.04 0.12 Alanine -18.98(0.18-17.85 g 0.38-14.57(0.25 0.79-11.61(0.27 0.82-9.65(0.05 0.13 Valine -18.45(0.11-18.23 g 0.22-15.57(0.31 0.89-12.98(0.40 1.11-10.86(0.30 0.93 Leucine -16.71(0.07-16.35 g 0.22-16.33(0.23 0.66-15.90(0.19 0.58-15.00(0.21 0.58 Values within parenthesis indicates the error in K 0 m Wadi and Ramasami (1997, n Kharakoz (1991, g Kikuchi et al (1995. 75
76 The contributions of charged end groups K 0 (NH 3 +, COO -, K 0 (CH 2 group and other alkyl chain of the amino acids to K 0 have been estimated using equations (1.4 to (1.7 and are given in Table 3.12. Table 3.12 Group contributions of partial molal compressibility (K 0 of amino acids in aqueous sodium fluoride solutions at different temperatures K 0 * 10 15 / m 3 mol -1 Pa -1 at various m s / mol kg -1 Group 0.00 (Water 0.1 0.3 0.5 T = 303.15 K NH + 3, COO - -25.34-22.35-18.06-14.71 CH 2-0.47 0.13-0.58-1.01 CH 3 CH- 0.94 0.27-1.16-2.02 (CH 3 2 CHCH- 1.88 0.54-2.32-4.04 (CH 3 2 CH CH 2 CH - 2.35 0.67-2.90-5.05 T = 308.15 K NH + 3, COO - -24.060-19.360-15.310-10.990 CH 2-0.943 0.038-0.713-1.313 CH 3 CH- 1.886 0.076-1.426-2.626 (CH 3 2 CHCH- 3.772 0.152-2.852-5.252 (CH 3 2 CH CH 2 CH - 4.715 0.190-3.565-6.565 T = 313.15 K NH + 3, COO - -22.750-16.630-12.090-8.220 CH 2-1.025-0.134-0.902-1.399 CH 3 CH- 2.050-0.268-1.804-2.798 (CH 3 2 CHCH- 4.100-0.536-3.608-5.596 (CH 3 2 CH CH 2 CH - 5.125-0.670-4.510-6.995 T = 318.15 K NH + 3, COO - -22.250-12.980-8.080-5.210 CH 2-1.085-0.668-1.455-1.781 CH 3 CH- 2.170-1.336-2.910-3.562 (CH 3 2 CHCH- 4.340-2.672-5.820-7.124 (CH 3 2 CH CH 2 CH - 5.425-3.340-7.275-8.905
77 The transfer partial molal compressibilities K 0 of amino acids from pure water to sodium fluoride water mixtures are calculated using equation (1.8 and the values are given in Table 3.13. Table 3.13 Transfer partial molal compressibility ( K 0 of Amino acids in aqueous sodium fluoride solutions at different temperatures K 0 * 10 15 / m 3 mol -1 Pa -1 at various m s / mol kg -1 Amino Acid 0.1 0.3 0.5 T = 303.15 K Glycine 3.42 7.31 10.35 Alanine 1.47 4.03 6.34 Valine 1.06 2.27 3.93 Leucine 1.95 2.95 4.16 T = 308.15 K Glycine 4.67 8.17 12.05 Alanine 1.73 4.03 6.68 Valine 1.02 2.03 4.76 Leucine 0.5 0.89 1.73 T = 313.15 K Glycine 6.02 10.03 13.55 Alanine 2.36 4.97 7.19 Valine 1.59 3.28 6.57 Leucine 0.61 1.24 1.74 T = 318.15 K Glycine 8.38 12.56 15.17 Alanine 4.41 7.37 9.33 Valine 2.88 5.47 7.59 Leucine 0.38 0.81 1.71 The contributions of K 0 (NH + 3, COO -, K 0 (CH 2 and other alkyl chain of the homologous amino acids to transfer partial molal compressibilities K 0 are evaluated using equations (1.4 to (1.7 and are listed in Table 3.14.
78 Table 3.14 Group Contributions of Transfer Partial molal compressibility ( K 0 of Amino acids in Aqueous Sodium Fluoride solutions at different temperatures K 0 * 10 15 / m 3 mol -1 Pa -1 at various m s / mol kg -1 Group 0.1 0.3 0.5 T = 303.15 K NH + 3, COO - 2.881 7.284 10.630 CH 2 - -0.317-1.048-1.479 CH 3 CH- -0.634-2.096-2.958 (CH 3 2 CHCH- -1.268-4.192-5.916 (CH 3 2 CH CH 2 CH - -1.585-5.240-7.395 T = 308.15 K NH + 3, COO - 4.695 8.748 13.070 CH 2 - -0.905-1.656-2.256 CH 3 CH- -1.810-3.312-4.512 (CH 3 2 CHCH- -3.620-6.624-9.024 (CH 3 2 CH CH 2 CH - -4.525-8.280-11.280 T = 313.15 K NH + 3, COO - 6.122 10.660 14.530 CH 2 - -1.159-1.927-2.424 CH 3 CH- -2.318-3.854-4.848 (CH 3 2 CHCH- -4.636-7.708-9.696 (CH 3 2 CH CH 2 CH - -5.795-9.635-12.120 T = 318.15 K NH + 3, COO - 9.271 14.170 17.040 CH 2 - -1.753-2.540-2.866 CH 3 CH- -3.506-5.080-5.732 (CH 3 2 CHCH- -7.012-10.160-11.464 (CH 3 2 CH CH 2 CH - -8.765-12.700-14.330 The viscosity data of the homologous amino acids in aqueous sodium fluoride solutions at temperatures T = (303.15, 308.15, 313.15 and 318.15 K are given in Table 3.15. The uncertainty values for viscosity are calculated and are also given in Table 3.15.
79 Table 3.15 Viscosity ( of Amino acids in Aqueous Sodium Fluoride solutions at different temperatures m / m Pa s at various m s / mol kg -1 (mol kg -1 0.00 (Water 0.1 0.3 0.5 T = 303.15 K Glycine 0.00 0.797 0.819 0.853 0.896 0.02 0.801 0.821 0.855 0.898 0.04 0.803 0.823 0.857 0.902 0.06 0.805 0.826 0.859 0.904 0.08 0.808 0.828 0.862 0.907 0.10 0.810 0.831 0.866 0.910 uncertainty = 1.75 10-3 = 2.17 10-3 = 1.99 10-3 = 1.80 10-3 Alanine 0.00 0.797 0.819 0.853 0.896 0.02 0.800 0.822 0.858 0.899 0.04 0.804 0.825 0.863 0.903 0.06 0.807 0.829 0.867 0.908 0.08 0.811 0.834 0.871 0.912 0.10 0.816 0.838 0.876 0.918 uncertainty = 2.87 10-3 = 3.04 10-3 = 4.08 10-3 = 2.99 10-3 Valine 0.00 0.797 0.819 0.853 0.896 0.02 0.803 0.824 0.858 0.901 0.04 0.808 0.830 0.865 0.907 0.06 0.814 0.837 0.872 0.915 0.08 0.821 0.844 0.880 0.924 0.10 0.830 0.852 0.888 0.933 uncertainty = 4.93 10-3 = 4.95 10-3 = 5.65 10-3 = 5.28 10-3 Leucine 0.00 0.797 0.819 0.853 0.896 0.02 0.804 0.825 0.859 0.901 0.04 0.809 0.832 0.866 0.907 0.06 0.817 0.841 0.875 0.916 0.08 0.827 0.849 0.884 0.927 0.10 0.834 0.857 0.893 0.937 uncertainty = 5.74 10-3 = 5.83 10-3 = 5.92 10-3 = 5.87 10-3
80 Table 3.15 (Continued m / m Pa s at various m s / mol kg -1 (mol kg -1 0.00 (Water 0.1 0.3 0.5 T = 308.15 K Glycine 0.00 0.719 0.747 0.775 0.810 0.02 0.721 0.749 0.777 0.812 0.04 0.723 0.751 0.779 0.814 0.06 0.725 0.753 0.781 0.817 0.08 0.728 0.755 0.783 0.820 0.10 0.729 0.758 0.787 0.822 uncertainty = 1.64 10-3 = 1.50 10-3 = 1.45 10-3 = 1.51 10-3 Alanine 0.00 0.719 0.747 0.775 0.810 0.02 0.722 0.750 0.781 0.815 0.04 0.726 0.753 0.786 0.819 0.06 0.729 0.756 0.790 0.823 0.08 0.733 0.760 0.793 0.827 0.10 0.736 0.765 0.797 0.832 uncertainty =2.64 10-3 = 2.47 10-3 = 3.46 10-3 = 3.33 10-3 Valine 0.00 0.719 0.747 0.775 0.810 0.02 0.724 0.753 0.780 0.814 0.04 0.730 0.759 0.786 0.820 0.06 0.736 0.766 0.793 0.827 0.08 0.743 0.772 0.800 0.834 0.10 0.747 0.778 0.806 0.842 uncertainty = 4.44 10-3 = 4.61 10-3 = 4.69 10-3 = 4.39 10-3 Leucine 0.00 0.719 0.747 0.775 0.810 0.02 0.726 0.752 0.780 0.816 0.04 0.731 0.758 0.787 0.823 0.06 0.739 0.765 0.793 0.830 0.08 0.746 0.773 0.802 0.839 0.10 0.753 0.781 0.811 0.849 uncertainty = 5.20 10-3 = 5.16 10-3 = 5.26 10-3 = 5.41 10-3
81 Table 3.15 (Continued m / m Pa s at various m s / mol kg -1 (mol kg -1 0.00 (Water 0.1 0.3 0.5 T = 313.15 K Glycine 0.00 0.653 0.682 0.707 0.738 0.02 0.655 0.684 0.709 0.740 0.04 0.656 0.686 0.712 0.742 0.06 0.658 0.688 0.714 0.744 0.08 0.660 0.690 0.715 0.747 0.10 0.662 0.692 0.718 0.749 uncertainty = 1.36 10-3 = 1.25 10-3 = 1.27 10-3 = 1.71 10-3 Alanine 0.00 0.653 0.682 0.707 0.738 0.02 0.655 0.685 0.712 0.741 0.04 0.659 0.688 0.715 0.744 0.06 0.661 0.691 0.718 0.748 0.08 0.664 0.695 0.722 0.751 0.10 0.668 0.698 0.726 0.756 uncertainty = 2.28 10-3 = 1.71 10-3 = 4.05 10-3 = 3.51 10-3 Valine 0.00 0.653 0.682 0.707 0.738 0.02 0.657 0.686 0.712 0.744 0.04 0.662 0.690 0.717 0.749 0.06 0.668 0.695 0.723 0.756 0.08 0.673 0.703 0.729 0.762 0.10 0.678 0.708 0.736 0.769 uncertainty = 3.91 10-3 = 3.93 10-3 = 4.59 10-3 = 4.50 10-3 Leucine 0.00 0.653 0.682 0.707 0.738 0.02 0.658 0.688 0.713 0.743 0.04 0.663 0.693 0.719 0.749 0.06 0.669 0.700 0.727 0.756 0.08 0.677 0.707 0.733 0.765 0.10 0.682 0.714 0.741 0.772 uncertainty = 4.55 10-3 = 4.59 10-3 = 4.78 10-3 = 4.76 10-3
82 Table 3.15 (Continued m / m Pa s at various m s / mol kg -1 (mol kg -1 0.00 (Water 0.1 0.3 0.5 T = 318.15 K Glycine 0.00 0.597 0.623 0.648 0.675 0.02 0.599 0.625 0.649 0.676 0.04 0.600 0.627 0.652 0.677 0.06 0.602 0.629 0.653 0.679 0.08 0.604 0.631 0.655 0.681 0.10 0.605 0.632 0.657 0.684 uncertainty = 1.67 10-3 = 1.12 10-3 = 1.15 10-3 = 0.98 10-3 Alanine 0.00 0.597 0.623 0.648 0.675 0.02 0.599 0.626 0.652 0.680 0.04 0.602 0.630 0.656 0.683 0.06 0.604 0.632 0.658 0.687 0.08 0.607 0.635 0.661 0.690 0.10 0.610 0.638 0.665 0.693 uncertainty = 1.99 10-3 = 2.12 10-3 = 3.74 10-3 = 2.69 10-3 Valine 0.00 0.597 0.623 0.648 0.675 0.02 0.600 0.626 0.652 0.680 0.04 0.605 0.630 0.657 0.686 0.06 0.610 0.635 0.663 0.692 0.08 0.615 0.641 0.669 0.697 0.10 0.619 0.646 0.673 0.703 uncertainty = 3.50 10-3 = 3.34 10-3 = 4.33 10-3 = 4.50 10-3 Leucine 0.00 0.597 0.623 0.648 0.675 0.02 0.601 0.628 0.653 0.680 0.04 0.605 0.634 0.658 0.686 0.06 0.611 0.640 0.663 0.693 0.08 0.618 0.646 0.670 0.700 0.10 0.622 0.651 0.678 0.706 uncertainty = 3.99 10-3 = 4.17 10-3 = 4.19 10-3 = 4.52 10-3
83 The viscosity B coefficients of amino acids in aqueous sodium fluoride solutions are obtained using equation (1.23 and are given in Table 3.16. The values of viscosity B coefficients of amino acids in water, available in literature are also given in Tables 3.16 for comparison. Table 3.16 Viscosity B - coefficient of amino acids in aqueous sodium fluoride solutions at different temperatures Amino Acid B * 10 3 / m 3 mol -1 at various m s / mol kg -1 0.00 (Water Present Work Literature 0.1 0.3 0.5 T = 303.15 K Glycine 0.145 (0.006-0.153 (0.006 0.157 (0.015 0.160 (0.008 Alanine 0.247 (0.012 0.241 o 0.252 (0.012 0.257 (0.007 0.259 (0.011 Valine 0.426 (0.028-0.432 (0.013 0.440 (0.009 0.449 (0.020 Leucine 0.497(0.030-0.500 (0.009 0.506 (0.014 0.511 (0.030 Glycine 0.147 (0.010 T = 308.15 K 0.1466 i 0.148 p 0.148 (0.008 0.154 (0.015 0.159 (0.007 Alanine 0.246 (0.007 0.247 p 0.249 (0.017 0.251 (0.012 0.257 (0.007 Valine 0.417 (0.017 0.418 i 0.426 (0.006 0.427 (0.007 0.430 (0.013 Leucine 0.488 (0.018 0.483 i 0.495 (0.018 0.499 (0.025 0.505 (0.025 Glycine 0.142 (0.012 T = 313.15 K 0.144 q 0.145 r 0.147 (0.000 0.148 (0.013 0.154 (0.007 Alanine 0.241 (0.015 0.247 s 0.244 (0.007 0.248 (0.011 0.249 (0.013 Valine 0.413 (0.007 0.413 t 0.423 (0.028 0.426 (0.015 0.426 (0.013 Leucine 0.484 (0.022 0.480 t 0.491 (0.018 0.499 (0.015 0.501 (0.019 T = 318.15 K Glycine 0.141 (0.017 0.139 t 0.146 (0.009 0.147 (0.012 0.147 (0.015 Alanine 0.230 (0.009 0.238 s 0.235 (0.012 0.240 (0.015 0.243 (0.007 Valine 0.410 (0.009 0.408 t 0.416 (0.016 0.420 (0.015 0.422 (0.007 Leucine 0.471 (0.026 0.471 t 0.474 (0.009 0.483 (0.032 0.490 (0.009 Values within parenthesis indicates the standard error in viscosity B coefficient o Zhao (2006, i Yan et al (1999, p Sandhu and Kashyap (1987, q Islam and Wadi (2004, r Bhattacharya and Sengupta (1988, s Bhattacharya and Sengupta (1980, t Rajagopal and Jayabalakrishnan (2010c
84 The zwitterionic end group, the methylene group and other alkyl side chain group contributions of amino acids to viscosity B coefficient have been calculated using equations (1.4 to (1.7. The evaluated values are given in Table 3.17. Table 3.17 Contribution to the viscosity B coefficient from zwitterionic groups, CH 2 and other alkyl side chains of amino acids in aqueous sodium fluoride solution at different temperatures Group B * 10 3 / m 3 mol -1 at various m s / mol kg -1 0.1 0.3 0.5 T = 303.15 K NH + 3, COO - 0.072 0.075 0.077 CH 2-0.087 0.088 0.089 CH 3 CH- 0.174 0.176 0.178 (CH 3 2 CHCH- 0.348 0.352 0.356 (CH 3 2 CH CH 2 CH - 0.435 0.440 0.445 T = 308.15 K NH + 3, COO - 0.068 0.073 0.078 CH 2-0.087 0.086 0.086 CH 3 CH- 0.174 0.172 0.172 (CH 3 2 CHCH- 0.348 0.344 0.344 (CH 3 2 CH CH 2 CH - 0.435 0.430 0.430 T = 313.15 K NH + 3, COO - 0.066 0.066 0.071 CH 2-0.086 0.088 0.087 CH 3 CH- 0.172 0.176 0.174 (CH 3 2 CHCH- 0.344 0.352 0.348 (CH 3 2 CH CH 2 CH - 0.430 0.440 0.435 T = 318.15 K NH + 3, COO - 0.066 0.066 0.066 CH 2-0.083 0.085 0.086 CH 3 CH- 0.166 0.17 0.172 (CH 3 2 CHCH- 0.332 0.340 0.344 (CH 3 2 CH CH 2 CH - 0.415 0.425 0.430
85 It is of interest to examine the transfer B-coefficient B from the B- coefficient data using the equation (1.8 and transfer B coefficient of R group B(R. The results are given in Table 3.18. Table 3.18 Viscosity B - Coefficient transfer ( B and transfer B coefficients of R group, B(R of Amino acids in Aqueous Sodium Fluoride solutions at different temperatures Amino acids B*10 3 B(R*10 3 B *10 3 B(R *10 3 B *10 3 B(R *10 3 m 3 mol -1 m 3 mol -1 m 3 mol -1 m 3 mol -1 m 3 mol -1 m 3 mol -1 at various m s / mol kg -1 0.1 0.3 0.5 T = 303.15 K Glycine 0.008-0.012-0.015 - Alanine 0.005-0.003 0.010-0.002 0.012-0.003 Valine 0.006-0.002 0.014 0.002 0.023 0.008 Leucine 0.003-0.005 0.009-0.003 0.014-0.001 T = 308.15 K Glycine 0.001-0.007-0.012 - Alanine 0.003 0.002 0.005-0.002 0.011-0.001 Valine 0.009 0.008 0.010 0.003 0.013 0.001 Leucine 0.007 0.006 0.011 0.004 0.017 0.005 T = 313.15 K Glycine 0.005-0.006-0.012 - Alanine 0.003-0.002 0.007 0.001 0.008-0.004 Valine 0.010 0.005 0.013 0.007 0.013 0.001 Leucine 0.007 0.002 0.015 0.009 0.017 0.005 T = 318.15 K Glycine 0.005-0.006-0.006 - Alanine 0.005 0.000 0.010 0.004 0.013 0.007 Valine 0.006 0.001 0.010 0.004 0.012 0.006 Leucine 0.003-0.002 0.012 0.006 0.019 0.013 The temperature derivatives of B coefficient (db/dt have also been calculated and are reported in Table 3.19.
86 Table 3.19 Temperature coefficient (db/dt of Amino acids in aqueous sodium fluoride solutions at different temperatures Amino (db/dt / m 3 mol -1 K -1 at various m s / mol kg -1 acids 0.00 (Water 0.1 0.3 0.5 Glycine -0.0009-0.0004-0.0007-0.0009 Alanine -0.0011-0.0011-0.0011-0.0011 Valine -0.0010-0.0010-0.0012-0.0017 Leucine -0.0016-0.0016-0.0014-0.0013 The solvation of any solute can be judged from the magnitude of B / V 0 (Zhao 2006. The values of B /V 0 are given in Table 3.20. Table 3.20 Ratio of B - coefficient to partial molal volume (B / V 0 of amino acids in aqueous sodium fluoride solutions at different temperatures Amino B / V 0 at various m s / mol kg -1 acids 0.00 (Water 0.1 0.3 0.5 T = 303.15 K Glycine 3.31 3.47 3.50 3.53 Alanine 4.09 4.12 4.14 4.10 Valine 4.72 4.68 4.74 4.80 Leucine 4.62 4.61 4.63 4.66 T = 308.15 K Glycine 3.34 3.33 3.40 3.46 Alanine 4.07 4.03 3.99 4.03 Valine 4.62 4.60 4.58 4.56 Leucine 4.53 4.55 4.54 4.58 T = 313.15 K Glycine 3.21 3.28 3.23 3.32 Alanine 3.92 3.88 3.89 3.85 Valine 4.53 4.53 4.49 4.47 Leucine 4.47 4.47 4.50 4.50 T = 318.15 K Glycine 3.15 3.20 3.15 3.12 Alanine 3.74 3.69 3.70 3.71 Valine 4.46 4.42 4.39 4.38 Leucine 4.33 4.29 4.32 4.36
87 Free energy of activation of viscous flow is another useful parameter to assess the complexity of liquid structure. The viscosity data are used to estimate the free energy of activation per mole of the solvent ( µ 1 0* and solute ( µ 2 0* as suggested by Feakins et al (1993 and Eyring et al (1941 from equations (1.26 and (1.27. The values of ( µ 1 0* and the partial molal volume of solvent ( V are given in Table 3.21. The values of the free energy 0 1 of activation per mole of the solute ( µ 2 0* are given in Table 3.22. Table 3.21 Free energy of activation of solvent 0* 1 and mean volume of solvent ( V of Aqueous Sodium Fluoride solution at 0 1 different temperatures m s mol kg -1 0* 1 0 V 1 m 3 mol -1 kj mol -1 T = 303.15 K 0.0 9.04 18.09 0.1 9.10 18.05 0.3 9.16 17.99 0.5 9.31 17.92 T = 308.15 K 0.0 8.93 ; 8.93 u 18.12 ; 18.11 u 0.1 9.02 18.08 0.3 9.11 18.02 0.5 9.21 17.95 T = 313.15 K 0.0 8.83 18.16 0.1 8.94 18.12 0.3 9.02 18.05 0.5 9.12 17.99 T = 318.15 K 0.0 8.74 18.19 0.1 8.85 18.16 0.3 8.94 18.09 0.5 9.04 18.03 u Lark et al (2006