CHAPTER 3 PARTIAL MOLAL VOLUME, PARTIAL MOLAL...

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/KNO3 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 (V0), Hepler

coefficient (2V

0/ T

2), transfer volumes ( V

0) and hydration number (nH)

are evaluated using density data. Apparent molal compressibility (K ), partial

molal compressibility (K0), transfer compressibility ( K

0) and hydration

number (nH) 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

µ10*

) and solute ( µ20*

) are estimated from viscosity data. Pair and triplet

interaction coefficients have also been calculated from transfer parameters.

The linear correlation of V0, 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 (NH3+, COO

-), methylene group (CH2) 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 mS 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.

52

Table 3.1 Density, and apparent molal volume, V of – amino acids in aqueous sodium fluoride solutions at

different temperatures

mS = 0 mol·kg-1

mS = 0.1 mol·kg-1

mS = 0.3 mol·kg-1

mS = 0.5 mol·kg-1

m

(mol kg-1

)*10

3

(kg m-3

)

V *106

(m3 mol

-1)

*103

(kg m-3

)

V *106

(m3 mol

-1)

*103

(kg m-3

)

V *106

(m3 mol

-1)

*103

(kg m-3

)

V *106

(m3 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

53

Table 3.1 (Continued)

mS = 0 mol·kg-1

mS = 0.1 mol·kg-1

mS = 0.3 mol·kg-1

mS = 0.5 mol·kg-1

m

(mol kg-1

) *103

(kg m-3

)V *10

6

(m3 mol

-1)

*103

(kg m-3

)V *10

6

(m3 mol

-1)

*103

(kg m-3

)V *10

6

(m3 mol

-1)

*103

(kg m-3

)V *10

6

(m3 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

54


mS = 0 mol·kg-1

mS = 0.1 mol·kg-1

mS = 0.3 mol·kg-1

mS = 0.5 mol·kg-1

m

(mol kg-1

) *103

(kg m-3

)V *10

6

(m3 mol

-1)

*103

(kg m-3

)V *10

6

(m3 mol

-1)

*103

(kg m-3

)V *10

6

(m3 mol

-1)

*103

(kg m-3

)V *10

6

(m3 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

55


mS = 0 mol·kg-1

mS = 0.1 mol·kg-1

mS = 0.3 mol·kg-1

mS = 0.5 mol·kg-1

m

(mol kg-1

) *103

(kg m-3

)V *10

6

(m3 mol

-1)

*103

(kg m-3

)V *10

6

(m3 mol

-1)

*103

(kg m-3

)V *10

6

(m3 mol

-1)

*103

(kg m-3

)V *10

6

(m3 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

56


mS = 0 mol·kg-1

mS = 0.1 mol·kg-1

mS = 0.3 mol·kg-1

mS = 0.5 mol·kg-1

m

(mol kg-1

) *103

(kg m-3

)V *10

6

(m3 mol

-1)

*103

(kg m-3

)V *10

6

(m3 mol

-1)

*103

(kg m-3

)V *10

6

(m3 mol

-1)

*103

(kg m-3

)V *10

6

(m3 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

57


mS = 0 mol·kg-1

mS = 0.1 mol·kg-1

mS = 0.3 mol·kg-1

mS = 0.5 mol·kg-1

m

(mol kg-1

) *103

(kg m-3

)V *10

6

(m3 mol

-1)

*103

(kg m-3

)V *10

6

(m3 mol

-1)

*103

(kg m-3

)V *10

6

(m3 mol

-1)

*103

(kg m-3

)V *10

6

(m3 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

58

Usually the partial molal volumes (V0) 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, V0

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 V0 are evaluated

by taking an average of all the data points. The values of partial molal

volumes V0, along with the literature values of partial molal volumes of

amino acids in water, are given in Table 3.2.

Table 3.2 Partial molal volume (0

V ) of – amino acids in aqueous

sodium fluoride solutions at different temperatures

0V * 106 / m3 mol-1 at various ms / mol kg-1

0.00 (Water)Amino

AcidPresent Work Literature 0.1 0.3 0.5

T = 303.15 K

Glycine 43.76 (0.42) 39.5a 43.59b 43.89c 44.10 (0.61) 44.81 (0.64) 45.25 (0.32)

Alanine 60.36 (0.50) 59.80a 60.63c 61.12 (0.63) 61.94 (0.47) 63.14 (0.21)

Valine 90.25 (0.84) 90.22c 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) 43.90d 43.98e 44.37(0.63) 45.33(0.26) 45.90(0.53)

Alanine 60.41(0.51) 60.44d 60.88e 61.77(0.61) 62.94(0.35) 63.84(0.25)

Valine 90.30(0.81) 91.42f 91.51g 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) 44.15c 44.52j 44.85(0.84) 45.75(0.57) 46.38(0.73)

Alanine 61.43(0.63) 61.35f 62.9b 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) 109.00k 109.84(0.44) 110.91(0.33) 111.23(0.48)

T = 318.15 K

Glycine 44.79(0.34) 44.17l 45.59(0.77) 46.57(0.74) 47.11(1.09)

Alanine 61.55(0.83) 61.46g 63.75(0.30) 64.86(0.40) 65.46(0.50)

Valine 91.87(0.37) 91.93l 94.09(0.75) 95.58(0.53) 96.30(0.49)

Leucine 108.80(0.51) 109.37g 110.50(0.49) 111.87(0.49) 112.28(0.50)

Values within parenthesis indicates the error in0

V

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).

59

The contribution of the zwitterionic end group V0

(NH3+, COO

-),

the methylene group V0(CH2) and other alkyl chains of homologous series of

amino acids to V0

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 (NH3+, COO

-), CH2 and

other alkyl side chains to partial molal volumes (0

V ) of

– amino acids in aqueous sodium fluoride solutions at


0V * 10

6 / m

3 mol

-1 at various ms / mol kg

-1

Group0.00 (Water) 0.1 0.3 0.5

T = 303.15 K

NH3+, COO

-28.26 28.55 29.26 30.09

CH2- 15.73 15.96 15.98 15.94

CH3CH- 31.46 31.92 31.96 31.88

(CH3)2CHCH- 62.92 63.84 63.92 63.76

(CH3)2CH CH2 CH - 78.65 79.80 79.90 79.70

T = 308.15 K

NH3+, COO

-28.35 28.95 30.00 30.86

CH2- 15.75 15.98 15.95 15.89

CH3CH- 31.50 31.96 31.90 31.78

(CH3)2CHCH- 63.00 63.92 63.80 63.56

(CH3)2CH CH2 CH - 78.75 79.90 79.75 79.45

T = 313.15 K

NH3+, COO

-28.92 29.56 30.41 31.41

CH2- 15.79 16.05 16.14 15.96

CH3CH- 31.58 32.10 32.28 31.92

(CH3)2CHCH- 63.16 64.20 64.56 63.84

(CH3)2CH CH2 CH - 78.95 80.25 80.70 79.80

T = 318.15 K

NH3+, COO

-29.25 30.44 31.32 31.93

CH2- 15.83 16.01 16.13 16.11

CH3CH- 31.66 32.02 32.26 32.22

(CH3)2CHCH- 63.32 64.04 64.52 64.44

(CH3)2CH CH2 CH - 79.15 80.05 80.65 80.55

60

The partial molal volumes of transfer 0

V 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 (0

V ) of – amino acids in

aqueous sodium fluoride solutions at different temperatures

0V * 10

6 / m

3 mol


-1

Amino Acid0.1 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 V0

(NH3+, COO

-), the

methylene group contribution V0

(CH2) and the contribution from other

alkyl chains of homologous series of amino acids to V0

are evaluated using

equations (1.4) to (1.7) and are given in Table 3.5

61

Table 3.5 Contributions of zwitterionic groups (NH3+, COO

-), CH2 and

other alkyl side chains to partial molal volumes of transfer

(0

V ) of – amino acids in aqueous sodium fluoride

solutions at different temperatures

0V * 10

6 / m

3 mol


-1

Group0.1 0.3 0.5

T = 303.15 K

NH3+, COO

-0.287 1.000 1.830

CH2- 0.235 0.256 0.208

CH3CH- 0.470 0.512 0.416

(CH3)2CHCH- 0.940 1.024 0.832

(CH3)2CH CH2 CH - 1.175 1.280 1.040

T = 308.15 K

NH3+, COO

-0.594 1.642 2.500

CH2- 0.229 0.196 0.143

CH3CH- 0.458 0.392 0.286

(CH3)2CHCH- 0.916 0.784 0.572

(CH3)2CH CH2 CH - 1.145 0.980 0.715

T = 313.15 K

NH3+, COO

-0.638 1.485 2.488

CH2- 0.257 0.347 0.170

CH3CH- 0.514 0.694 0.340

(CH3)2CHCH- 1.028 1.388 0.680

(CH3)2CH CH2 CH - 1.285 1.735 0.850

T = 318.15 K

NH3+, COO

-1.187 2.076 2.680

CH2- 0.181 0.296 0.284

CH3CH- 0.362 0.592 0.568

(CH3)2CHCH- 0.724 1.184 1.136

(CH3)2CH CH2 CH - 0.905 1.480 1.420

The standard partial molal volumes of amino acids are used to

determine the number of water molecules, nH, hydrated to the amino acid by

using equations (1.9) to (1.13) and are given in Table 3.6.

The hydration number nH 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 (nH) of – amino acids in aqueous sodium

fluoride solutions at different temperatures

nH at various ms / mol kg-1

0.1 0.3 0.5Amino

AcidFrom

volume

data

From

compressibility

data

From

volume

data

From

compressibility

data

From

volume

data

From

compressibility

data

T = 303.15 K

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 VAB /

KAB / AB and VABB / KABB / ABB are given in Table 3.7.

Table 3.7 Pair interaction coefficients, VAB / KAB / AB and Triplet

interaction coefficients VABB / KABB / ABB of – amino acids

in aqueous sodium fluoride solutions at different

temperatures

Amino

Acid

VAB * 106

m3mol

-2kg

VABB * 106

m3

mol-3

kg2

KAB * 1014

m3

mol-1

kg Pa-1

KABB * 1014

m3mol

-1kg Pa

-1AB * 10

3

m3

mol-2

kgABB * 10

3

m3

mol-3

kg2

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

Glycine2.070 -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 V0 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

Acida coefficient

b coefficient

m3·mol

-1·K

-1

c coefficient

m6·mol

-2·K

-2

ms = 0.1 / mol kg-1

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

ms = 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

ms = 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

u / m s-1

at various ms / mol kg-1

m

(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


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


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


66


u / m s-1


m

(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


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


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


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


67


u / m s-1


m

(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


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


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


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


68


u / m s-1


m

(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


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


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


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


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


K * 1015

/ m3

mol-1

Pa-1


m

(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


K * 1015

/ m3

mol-1

Pa-1


m

(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


K * 1015

/ m3

mol-1

Pa-1


m

(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


K * 1015

/ m3

mol-1

Pa-1


m

(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

K /

(10

-15m

3.m

ol

-1.P

a-1

)

The partial molal compressibility (K0) of the homologous amino

acids has been evaluated using equation (1.17) by least square fit method

(Figure 3.1). The calculated values of K0 (along with error) and the

experimental slope values Sk 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.

-24.0

-20.0

-16.0

-12.0

-8.0

-4.0

0.0

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

74

Table 3.11 Partial molal compressibility (K0), slopes (Sk) of – Amino acids in aqueous sodium fluoride solutions at


K0 * 10

15Sk * 10

18K

0 * 10

15Sk * 10

18K

0 * 10

15Sk * 10

18K

0 * 10

15Sk * 10

18Amino

acids m3mol

-1Pa

-1kg m

3mol

-2Pa

-1m

3mol

-1Pa

-1 kg m

3mol

-2Pa

-1m

3mol

-1Pa

-1 kg m

3mol

-2Pa

-1m

3mol

-1Pa

-1 kg m

3mol

-2Pa

-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) -23.5m

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

75


K0 * 10

15Sk * 10

18K

0 * 10

15Sk * 10

18K

0 * 10

15Sk * 10

18K

0 * 10

15Sk * 10

18Amino

acids m3mol

-1Pa

-1kg m

3mol

-2Pa

-1m

3mol

-1Pa

-1kg m

3mol

-2Pa

-1 m

3mol

-1Pa

-1 kg m

3mol

-2Pa

-1m

3mol

-1Pa

-1 kg m

3mol

-2Pa

-1


0.00 (Water) 0.1 0.3 0.5

T = 313.15 K

Glycine -22.34(0.07) -22.4n

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) -19.8n

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) -19.2n

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) -17.8n

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) -21.56g 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) -17.85g

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) -18.23g

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) -16.35g

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 K0

mWadi and Ramasami (1997),

nKharakoz (1991),

gKikuchi et al (1995).

76

The contributions of charged end groups K0 (NH3

+, COO

-), K

0

(CH2) group and other alkyl chain of the amino acids to K0 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 (K0) of



K0* 10

15 / m

3 mol

-1 Pa


-1

Group 0.00 (Water) 0.1 0.3 0.5

T = 303.15 K

NH3+, COO

--25.34 -22.35 -18.06 -14.71

CH2- 0.47 0.13 -0.58 -1.01

CH3CH- 0.94 0.27 -1.16 -2.02

(CH3)2CHCH- 1.88 0.54 -2.32 -4.04

(CH3)2CH CH2 CH - 2.35 0.67 -2.90 -5.05

T = 308.15 K

NH3+, COO

--24.060 -19.360 -15.310 -10.990

CH2- 0.943 0.038 -0.713 -1.313

CH3CH- 1.886 0.076 -1.426 -2.626

(CH3)2CHCH- 3.772 0.152 -2.852 -5.252

(CH3)2CH CH2 CH - 4.715 0.190 -3.565 -6.565

T = 313.15 K

NH3+, COO

--22.750 -16.630 -12.090 -8.220

CH2- 1.025 -0.134 -0.902 -1.399

CH3CH- 2.050 -0.268 -1.804 -2.798

(CH3)2CHCH- 4.100 -0.536 -3.608 -5.596

(CH3)2CH CH2 CH - 5.125 -0.670 -4.510 -6.995

T = 318.15 K

NH3+, COO

--22.250 -12.980 -8.080 -5.210

CH2- 1.085 -0.668 -1.455 -1.781

CH3CH- 2.170 -1.336 -2.910 -3.562

(CH3)2CHCH- 4.340 -2.672 -5.820 -7.124

(CH3)2CH CH2 CH - 5.425 -3.340 -7.275 -8.905

77

The transfer partial molal compressibilities K0

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 ( K0) of – Amino

acids in aqueous sodium fluoride solutions at different

temperatures

K0* 10

15 / m

3 mol

-1 Pa


-1

0.1 0.3 0.5Amino Acid

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 K0 (NH3

+, COO

-), K

0 (CH2) and other

alkyl chain of the homologous amino acids to transfer partial molal

compressibilities K0 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 ( K0) of – Amino acids in Aqueous

Sodium Fluoride solutions at different temperatures

K0* 10

15 / m

3 mol

-1 Pa


-1

Group 0.1 0.3 0.5

T = 303.15 K

NH3+, COO

-2.881 7.284 10.630

CH2- -0.317 -1.048 -1.479

CH3CH- -0.634 -2.096 -2.958

(CH3)2CHCH- -1.268 -4.192 -5.916

(CH3)2CH CH2 CH - -1.585 -5.240 -7.395

T = 308.15 K

NH3+, COO

-4.695 8.748 13.070

CH2- -0.905 -1.656 -2.256

CH3CH- -1.810 -3.312 -4.512

(CH3)2CHCH- -3.620 -6.624 -9.024

(CH3)2CH CH2 CH - -4.525 -8.280 -11.280

T = 313.15 K

NH3+, COO

-6.122 10.660 14.530

CH2- -1.159 -1.927 -2.424

CH3CH- -2.318 -3.854 -4.848

(CH3)2CHCH- -4.636 -7.708 -9.696

(CH3)2CH CH2 CH - -5.795 -9.635 -12.120

T = 318.15 K

NH3+, COO

-9.271 14.170 17.040

CH2- -1.753 -2.540 -2.866

CH3CH- -3.506 -5.080 -5.732

(CH3)2CHCH- -7.012 -10.160 -11.464

(CH3)2CH CH2 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 Pa s at various ms / mol kg-1

m

(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


= 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


= 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


= 5.83×10-3

= 5.92×10-3

= 5.87×10-3

80



m

(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


= 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


= 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


= 5.16×10-3

= 5.26×10-3

= 5.41×10-3

81



m

(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


= 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


= 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


= 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


= 4.59×10-3

= 4.78×10-3

= 4.76×10-3

82



m

(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


= 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


= 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


= 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


= 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

B * 103 / m

3 mol


-1

0.00 (Water)

Amino

Acid

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) 0.241o

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)

T = 308.15 K

Glycine 0.147 (0.010)0.1466

i

0.148p 0.148 (0.008) 0.154 (0.015) 0.159 (0.007)

Alanine 0.246 (0.007) 0.247p

0.249 (0.017) 0.251 (0.012) 0.257 (0.007)

Valine 0.417 (0.017) 0.418i

0.426 (0.006) 0.427 (0.007) 0.430 (0.013)

Leucine 0.488 (0.018) 0.483i

0.495 (0.018) 0.499 (0.025) 0.505 (0.025)

T = 313.15 K

Glycine 0.142 (0.012)0.144

q

0.145r 0.147 (0.000) 0.148 (0.013) 0.154 (0.007)

Alanine 0.241 (0.015) 0.247s

0.244 (0.007) 0.248 (0.011) 0.249 (0.013)

Valine 0.413 (0.007) 0.413t

0.423 (0.028) 0.426 (0.015) 0.426 (0.013)

Leucine 0.484 (0.022) 0.480t

0.491 (0.018) 0.499 (0.015) 0.501 (0.019)

T = 318.15 K

Glycine 0.141 (0.017) 0.139t

0.146 (0.009) 0.147 (0.012) 0.147 (0.015)

Alanine 0.230 (0.009) 0.238s

0.235 (0.012) 0.240 (0.015) 0.243 (0.007)

Valine 0.410 (0.009) 0.408t

0.416 (0.016) 0.420 (0.015) 0.422 (0.007)

Leucine 0.471 (0.026) 0.471t

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, CH2 and other alkyl side chains of amino acids in

aqueous sodium fluoride solution at different temperatures

B * 103 / m

3 mol


-1

Group0.1 0.3 0.5

T = 303.15 K

NH3+, COO

-0.072 0.075 0.077

CH2- 0.087 0.088 0.089

CH3CH- 0.174 0.176 0.178

(CH3)2CHCH- 0.348 0.352 0.356

(CH3)2CH CH2 CH - 0.435 0.440 0.445

T = 308.15 K

NH3+, COO

-0.068 0.073 0.078

CH2- 0.087 0.086 0.086

CH3CH- 0.174 0.172 0.172

(CH3)2CHCH- 0.348 0.344 0.344

(CH3)2CH CH2 CH - 0.435 0.430 0.430

T = 313.15 K

NH3+, COO

-0.066 0.066 0.071

CH2- 0.086 0.088 0.087

CH3CH- 0.172 0.176 0.174

(CH3)2CHCH- 0.344 0.352 0.348

(CH3)2CH CH2 CH - 0.430 0.440 0.435

T = 318.15 K

NH3+, COO

-0.066 0.066 0.066

CH2- 0.083 0.085 0.086

CH3CH- 0.166 0.17 0.172

(CH3)2CHCH- 0.332 0.340 0.344

(CH3)2CH CH2 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

B*103

B(R)*103

B *103

B(R *103

B *103

B(R *103

m3mol

-1m

3mol

-1 m

3mol

-1 m

3mol

-1 m

3mol

-1 m

3mol

-1


Amino

acids

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


(dB/dT) / m3

mol-1

K-1


Amino

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 / V0(Zhao 2006). The values of B /V

0are given in Table 3.20.

Table 3.20 Ratio of B - coefficient to partial molal volume (B / V0) of



B / V0 at various ms / mol kg

-1Amino

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 ( µ10*

)

and solute ( µ20*

) as suggested by Feakins et al (1993) and Eyring et al (1941)

from equations (1.26) and (1.27). The values of ( µ10*

) and the partial molal

volume of solvent ( 0

1V ) are given in Table 3.21. The values of the free energy

of activation per mole of the solute ( µ20*

) are given in Table 3.22.

Table 3.21 Free energy of activation of solvent 0*

1 and mean volume of

solvent ( 0

1V ) of Aqueous Sodium Fluoride solution at


ms

mol kg-1

0*

1

kJ mol-1

0

1V

m3

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 ; 8.93u

18.12 ; 18.11u

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 18.03u Lark et al (2006)

88

Table 3.22 Free energy of activation of solute 0*

2 of – Amino acids

in Aqueous Sodium Fluoride solution at different

temperatures

0*

2 / kJ mol-1

at various ms / mol kg-1Amino

acids 0.00 (Water) 0.1 0.3 0.5

T = 303.15 K

Glycine 32.82 34.10 34.96 35.66

Alanine 49.34 50.30 51.37 52.10

Valine 78.43 79.77 81.36 83.09

Leucine 90.72 91.52 92.90 94.09

T = 308.15 K

Glycine

33.37

33.05v

33.72 34.89 35.89

Alanine

49.69

50.54v

50.50 51.19 52.44

Valine 78.05 79.95 80.53 81.48

Leucine

90.60

89.76v

92.03 93.15 94.44

T = 313.15 K

Glycine 32.94 33.91 34.37 35.52

Alanine 49.60 50.43 51.39 51.92

Valine 78.53 80.55 81.56 81.98

Leucine 91.17 92.69 94.40 95.14

T = 318.15 K

Glycine 33.11 34.11 34.60 34.88

Alanine 48.48 49.72 50.87 51.65

Valine 79.06 80.51 81.68 82.44

Leucine 90.40 91.35 93.28 94.76v Lark et al (2007)

89

3.4 DISCUSSION

The density values (Table 3.1) increase with increase in

concentration of amino acids. The increase in density with concentration is

due to the shrinkage in the volume which in turn is due to the presence of

solute molecules. Increase of density also indicates the increase in solute -

solvent and solvent - solvent interactions (Thirumaran and Sabu 2009).

It is observed (Table 3.1) that V values increase with increase in

concentration of sodium fluoride as well as at different temperatures for all

amino acids studied, thereby showing the presence of strong solute -solvent

interactions. Similar conclusions are obtained for some – amino acids in

aqueous metformin hydrochloride (Rajagopal and Jayabalakrishnan 2010c).

The values of V0 are by definition free from solute-solute interactions and

therefore provide information regarding solute-solvent interactions (Belibagli

and Agranci 1990). Further, the increase in V0

for all the amino acid

concentration (Table 3.2) indicates that the solute - cosolute interactions

increase with the increase in sodium fluoride concentration. Similar trend in

V0 values has been reported for some amino acids in aqueous sodium

chloride (Yuan et al 2006) and sodium caproate (Wang et al 2004). The

values of V0 increase with increase in temperature. This may be due to the

release of some solvent molecules from the loose solvation layers of the

solutes in solution (Wadi and Ramasami 1997). The increase in V0 values

from glycine to leucine (Figure 3.2) may be attributed to the increased

hydrophobicity/non polar character of the side chain in the homologous

– amino acids and hence glycine would cause the largest volume contraction

followed by alanine, valine and leucine. Similar increase in V0

values with

increasing side chain length from glycine to valine have been reported by

Banipal and Kapoor (1999).

90

V0/(

10

6m

3m

ol-1

)

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

0 .0 0 1. 00 2 .0 0 3 .0 0 4 .00 5.0 0 6 .0 0

nc

Figure 3.2 Plot of partial molal volume (V0) against number of carbon

atoms in alkyl side chain (nc) of ( ) 0 M, ( ) 0.1 M, ( ) 0.3

M, ( ) 0.5 M of sodium fluoride solution at T = 303.15K

It is seen from Table 3.3 that the values of V0 (NH3

+, COO

-)

increase with increasing concentration of sodium fluoride while no regular

trend is noted with V0 (CH2). This indicates that the interactions between

cosolute and charged end groups (NH3+, COO

-) of amino acids are much

stronger than those between the cosolute and (CH2). This leads to the

reduction in the electrostriction of the solvent water due to increased amino

acid - sodium fluoride interactions, thereby contributing to the more positive

values of the partial molal volume. It is also seen that the contribution to V0

increases with increase in the size of alkyl side of the amino acids for all

temperatures. Similar results are available in literature for some amino acids

in aqueous CaCl2 (Yan et al 2004).

91

The values of V0 and V

0 for all amino acids are positive and

increase with the molality of sodium fluoride in the solutions (Tables 3.2 and

3.4). These results can be explained by the cosphere overlap model, as

developed by Friedman and Krishnan (1973 b). Properties of the water

molecules in the hydration cosphere depend on the nature of the solute

species. The types of the interaction occurring between the sodium and

fluoride ions and amino acids can be classified as (Bhat et al 1988):

(1) Ion-ion interaction between Na+

of cosolute and the COO-

group of amino acid.

(2) Ion-ion interaction between F– of cosolute and the NH3

+

group of amino acid.

(3) Ion-nonpolar group interactions between cosolute – amino

acid.

The first two types of interactions will produce positive V0

values whereas the last type of interactions results in negative V0. For polar

species, the volume of water molecules is smaller in the solvation sphere due

to the effect of electrostriction and a decrease in the hydrogen-bonded

network of water molecules in the solvation sphere than in the bulk. So the

overlap of two hydrophilic hydration cospheres relaxes some water molecules

to the bulk giving rise to a positive change in volume. For nonpolar species,

the hydrophobic hydration gives a positive volume contribution. So the

overlap of two hydrophobic hydration cospheres relaxes some water

molecules from the solvation sphere of the bulk giving rise to a negative

change in volume. The influence of hydrophilic species on the hydrophobic

hydration sphere of apolar species gives a negative volume effect. The

positive value of V0 indicates the interaction between the charge centres of

amino acids dominates other forms of interactions. A similar conclusion has

been reported for some amino acids and peptides in aqueous sodium acetate

92

(Wang et al 1999), sodium caproate (Wang et al 2004), sodium chloride

(Yuan et al 2006) and glycylglycine in aqueous sodium fluoride (Lin et al

2006).

Table 3.5 shows that the values of V0 (NH3

+, COO

-) are greater

than V0 (CH2) and increases with increasing concentration of sodium

fluoride and the contribution to V0 increases with increase in the size of

alkyl side of the amino acids. This also indicates that the interactions between

sodium fluoride and charged end groups (NH3+, COO

-) of amino acids are

stronger. A similar linear correlation has also been reported for some amino

acids in aqueous guanidine hydrochloride (Yan et al1998) and potassium

thiocynate (Wadi and Goyal 1992) solutions.

The nH values (obtained by both volume and compressibility data)

show a tendency to decrease with an increase in the concentration of sodium

fluoride as well as temperature (Table 3.6). The decrease in nH values with the

increase in the concentration of sodium fluoride also shows that sodium

fluoride has dehydration effect on amino acids. Further, increase in

temperature also reduces the electrostriction. The reduction in the

electrostriction with increasing sodium fluoride concentration and

temperature is confirmed by the decrease in nH. Also the decrease of the

hydration number of the amino acids with the increasing NaF molalities

indicates that the interactions involving ions (Na+, F

-) with the charged

centres of amino acids become stronger, that weakens the electrostriction of

the charged centres with the water molecules, and strengthens the hydration

competitions between ions and the charged centres of the amino acids, then nH

decrease. This is in consistent with the observed increase in V0 with

increasing sodium fluoride concentrations. This also supports the view that

electrolytes have a dehydration effect on the amino acids in solution (Ogawa

et al 1984b, Wang et al 1999). The observed nH values follow the order: Leu

> Val > Ala > Gly.

93

It is seen from Table 3.7 that the VAB values are positive and VABB

are negative showing the dominance of pair interactions over triplet

interactions. The positive values of the pair interaction coefficients VAB also

suggest that interaction occurs due to the overlap of hydration spheres of the

solute-cosolute molecules (Rajagopal and Jayabalakrishnan 2010c) which

again supports the conclusion drawn from the cosphere overlap model.

The values of KAB are positive and KABB are negative

(Table 3.7). The change in KAB values from glycine to L-leucine comes from

the difference in the interactions of the alkyl side chains of the amino acids

with sodium fluoride, as the interactions of zwitterionic end groups for

different amino acids with sodium fluoride are almost same. This suggests

that alkyl side chains of the amino acids play an important role in modulating

the volume of transfer. Similar conclusions are given by Banipal and Singh

(2004b) for some amino acids, diglycine and lysozyme in aqueous n-propanol.

The positive AB values and negative ABB values (Table 3.7)

suggest the dominance of pair interaction that occur due to the overlap of

hydration spheres of amino acids and sodium fluoride molecules, which

supports the conclusion drawn from the cosphere overlap model using

volumetric data. Similar results are also available in literature (Lark et al

2006).

According to Hepler’s criteria, when V0 / T > 0 and

2V

0/ T

2

< 0 the solute has the hydrophilic character while V0 / T < 0 and

2V

0 / T

2

> 0 the solute has hydrophobic character. It is observed from Table 3.8 that

values of (2V

0/ T

2) are greater than 0 (i.e. The temperature derivative

coefficient c positive), indicating that all studied amino acids have

hydrophobic character and also these amino acids act as structure maker in

aqueous sodium fluoride solutions (Gekko and Noguchi 1979, Soto et al

94

2004). Therefore, the effects of the charged end groups of amino acids are the

prominent factor for the feature of temperature dependence of V0 of amino

acids.

The ultrasonic speed (Table 3.9) increases with increase in the

concentration of amino acids as well as increasing of sodium fluoride

concentrations. Molecular association is thus responsible for the observed

increase in ultrasonic speed in these mixtures. The increase in ultrasonic

speed in these solutions may be attributed to the cohesion brought about by

the ionic hydration.

It can be seen from Table 3.10 that the K values of the amino acid

in aqueous sodium fluoride solutions are negative indicating that the water

molecules around ionic charged groups of amino acids are less compressible

than the water molecules in the bulk solution (Soto et al 2004). This further

supports the conclusion that the interaction of ions with amino acid

zwitterions localized at the head groups decreases the electrostriction of water

caused by the charged centres of amino acids resulting in an increase in

volume, therefore, increasing the compressibility of the solution.

Hydrophobic solutes often show negative compressibility as well, due to the

ordering that is induced by them in water structure (Iqbal and Verrall 1989,

Conway and Verrall 1966).

It is also found that K0 values are negative (Table 3.11) and

increase linearly with the increase in concentration of sodium fluoride in

solutions. It indicates that the solute – solvent interactions increase on

increasing concentration of sodium fluoride in solutions. Sk values are

positive for all the amino acids studied which indicate the presence of weak

solute – solute interactions. A similar observation was made by Ogawa et al

(1984b) for some amino acids in aqueous alkali-chloride solutions.

95

A linear regression analysis of the K0 values as a function of nc at

various sodium fluoride concentrations gives the contributions of (NH3+,

COO-) and (CH2). It is seen from Table 3.12 that the contributions of (NH3

+,

COO-) to K

0 is less than that of (CH2) and increases with increasing

concentration of sodium fluoride. This indicates that the interactions between

cosolute and charged end groups (NH3+, COO

-) of amino acids are much

stronger than those between the cosolute and (CH2). Similar conclusion is

obtained by Pal and Kumar (2005b) for some amino acids in aqueous

magnesium chloride.

The apparent molal compressibilities of transfer ( K0) from water

to sodium fluoride at infinite dilution are given in Table 3.13 and are found to

be positive. These positive values of transfer may be attributed to the

interactions occurring between Na+ and COO

-, and F

- and NH3

+ ions. This

observation states that the dehydration of solute and cosolute is high.

Table 3.14 shows that the contributions of (NH3+, COO

-) to K

0 is

larger than that of (CH2) and increases with increasing concentration of

sodium fluoride. This indicates that the interactions between sodium fluoride

and charged end groups (NH3+, COO

-) of amino acids are stronger. Thus

supports the conclusion drawn from volumetric studies.

From Table 3.15, it is observed that the values of viscosity increase

with increase in solute as well as sodium fluoride concentration. Viscosity

variation is attributed to the structural changes. This increasing trend indicates

the existence of molecular interaction occurring in these systems. Also the

increase in viscosity of the solution on addition of solute indicate the structure

making ability of the solutes (Iqbal and Chaudhry 2009)

It is well established that viscosity B coefficient is a measure of

solute solvent interactions and is directly dependent on the size, shape and

charge of the solute molecules. Thus, the B values reflect the net structural

96

r

effects of the charged groups and the hydrophobic CH2 groups on the solvent.

The values of viscosity B coefficient for all the amino acids studied in water

and in aqueous sodium fluoride solutions at the four different temperatures

are positive indicating that the ion – solvent interactions are strong. Further,

Table 3.16 shows that the B values of the amino acids increase with increase

in molality of aqueous sodium fluoride (Figure 3.3), which shows that the ion

solvent interactions become stronger with the increase in concentration of

sodium fluoride. The viscosity B coefficient decreases with the increase in

temperature thereby showing that the ion solvent interactions are further

weakened with the increase in temperature, which may be attributed to the

decrease in solvation of ions by water. The viscosity B coefficient values for

amino acids in aqueous sodium fluoride solutions show the following order:

glycine < L-alanine < L-valine < L-leucine.

1.00

1.01

1.02

1.03

1.04

1.05

0.00 0.02 0.04 0.06 0.08 0.10 0.12

c/ (mol.dm-3

)

Figure 3.3 Plot of relative viscosity ( r) against molarity ( c ) of ( )

glycine, ( ) alanine, ( ) valine, ( ) leucine of 0.1 M sodium

fluoride solution at T = 303.15K

97

It is observed from Table 3.17, that viscosity B-coefficient

increases with increase in number of carbon atoms (nc), in the alkyl chain of

the amino acids. From Table 3.18, it is seen that the contributions of (NH3+,

COO-) and (CH2) groups to viscosity B-coefficient in water, at T = 308 K,

agree well with the literature values (Lark et al 2007). Moreover, the

magnitudes of B (NH3+, COO

-) systematically increase, in negligible manner,

with the increase in the concentration of sodium fluoride. The variation of B

(CH2) with concentration of sodium fluoride is almost insensitive. Similar

results on group contribution to B-coefficient are available in literature

(Banipal and Singh 2004b, Yan et al 2001). Furthermore, the values of B

(NH3+, COO

-) decrease with increase in temperature, whereas, no such regular

trend is observed for B (CH2). This indicates the predominance of the

interactions between zwitterionic centres with sodium fluoride in the structure

making ability of the solute.

The transfer B coefficients, B are positive (Table 3.18) for the

studied concentration range of the solvent. The B (W NaF) values reflect

the net effect of the interactions of sodium fluoride with R groups and

charged centres of amino acids. To get the contributions of these interactions

separately, transfer B coefficient of R group B(R) (W NaF) are calculated

by subtracting the transfer B coefficient of glycine from transfer B coefficient

of each amino acid. It is observed that the contribution due to the interactions

between charged centres of amino acids and sodium fluoride molecules are

much greater than that due to interactions between R groups of amino acids

and sodium fluoride molecules. This result is identical to the conclusion

obtained by Belibagli and Agranci (1990).

The sign of dB/dT values is found to provide important information

regarding structure making or structure breaking ability of the solute in the

solvent media (Sharma and Ahluwalia 1973). In general, the dB/dT is

98

negative for structure maker and positive for structure breaker solutes in

solutions (Zhao 2006). From Table 3.19, it is seen that dB/dT values are

negative for all amino acids studied. This shows that all the amino acids

studied act as structure makers in aqueous sodium fluoride solutions.

The solvation of any solute can be judged from the magnitude of

B /V0 (Zhao 2006). A value between 0 and 2.5 indicates an unsolvated

spherical species, and any higher value is an indication of solvated ones

(Stokes 1965). Table 3.20 shows that values of B /V0 are greater than 2.5 and

hence all amino acids studied are highly solvated. Also, it is observed that

temperature is having negligible effect on the solvation characters of the

amino acids reported in this work.

It is evident from Tables 3.21 and 3.22, that µ20*

values are

positive and much larger than µ10*

which indicate that ion-solvent

interactions are stronger. It further suggests that the interactions between

solute and solvent molecules in the ground state are stronger than in the

transition state. Thus, the solvation of the solute in the transition state is

unfavourable in free energy terms. Similar results are obtained for Glycine in

aqueous solutions of transition metal chlorides by Mishra and Gautam (2001).

Further, µ20*

increases in the order glycine < L-alanine < L-valine

< L-leucine at a given temperature, indicating that the solvation of amino acid

molecules becomes increasingly unfavourable as the hydrophobicity or the

number of carbon atoms of the side chain increases from glycine to L-leucine.

Similar results are available in literature for - amino acids in aqueous and

mixed aqueous solutions (Palecz 2000, Frank and Wen 1957).

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