Chemicals

The zinc sulphate heptahydrate and the galactose of high purity (mass fraction more than 99.9) used in the present investigation were acquired from Qualigen Chemicals. All these chemicals were used without further purifications and were kept in desiccator at room temperature to avoid any possible moisture absorption.

Scheme 1 Structures of galactose and lactose. 

Solution preparation

Mixed aqueous solvents were prepared from galactose for four different concentrations (2.5, 5.0, 7.5, 10.0%) in double distilled water having density 0.9960 ×10³ kg m^-3 (w/V) at room temperature. Series of ZnSO₄ solutions of varying concentration from 0.01 to 0.1 mole.dm^-3 were made by taking the above prepared mixed solvents. The solutions were kept acquiring different temperature for 30 minutes in a thermostat with an accuracy of 0.01 K. Systems containing ZnSO₄ with aqueous lactose solvents have been studied and reported earlier [²⁶].

Apparatus and Procedure

The solutions were prepared in glass volumetric vials using a Vibra Make HTR-220E analytical balance. The densities of all solutions were measured by a bicapillary pycnometer with a reproducibility of ±3×10^-3 kg.m^-3. The viscosity of the solutions was measured by using a calibrated Ostwald viscometer, where it was immersed in a water bath to maintain constant temperature. The temperature was maintained within ±0.01 K. The speed of sound in all the solutions was measured by a single crystal variable-path ultrasonic interferometer operating at 3MHz frequency (Mittal make, India). Constant temperature was maintained by circulating water from a thermostatically regulated water bath maintained within ±0.01 K around the sample holder. The reproducibility for speeds of sound measurements was ±5 ×10^-1ms^-1.

Isentropic compressibility and molal compressibility

Isentropic compressibilities, βs, of solutions were obtained using the following Laplace equation [³²] :

where ρ and U are the density and ultrasonic velocity for the fluid samples. As per Sadeghi et al., this compressibility is the sum of two contributions, βs_{(solvent intrinsic)} and βs_{(solute intrinsic)} [³³]. The compressibility resulting from the compression of solvent molecules (galactose and lactose) is (s_{(solvent intrinsic)} whereas that of due to the compression of the hydration shell of ions is known as (s_{(solute intrinsic)} [³⁴]. Perusal of tables and figures shows that isentropic compressibility decreases with increase in concentrations of both ZnSO₄ as well as the carbohydrates contents in the solvents (Table 2). This type of variation confirms the presence of ion-solvent interactions through ion-dipole type between zinc ion and surrounding water molecules. This even supports the increasing number of H-bonding in carbohydrates. Compressibility of solvent is generally found to be higher than that of solution and it reduces with the increase in concentration of the solution [²⁷]. The closeness of the components in solutions also results in the decrease in compressibility. Again, increase in compressibility with temperatures can be attributed to the thermal expansion of the solutions resulting in a less compressible liquid [¹⁸] [Representative 3-D plots for ZnSO₄ in both aqueous galactose and lactose at different temperatures (Figs. 3 and 4)]. The (s values decrease with an increase in temperature for each binary system at a fixed composition due to an increase in thermal agitation. This happens by the release of solvent molecules from the solute and the resulting increase in solution volume. According to Bahadur et al. the decrease in isentropic compressibilities with increase in concentration of the solute is the consequence of the combined effect of solvation of ions and breaking of the structure of solvent molecules and also because of the dominating nature of (s_{(solute intrinsic)} over the (s_{(solvent intrinsic)} effect [³⁵]. In addition, another compressibility factor such as the apparent molal compressibility, ф_k was also studied, which can be determined by using the formula [³⁶]:

Fig. 3 3-D Representative plots of β_s vs Concentration (mole kg^-1) of ZnSO₄ in Galactose-water mixed solvent at T = (303.15K, 308.15K, 313.15K). 

Fig. 4 3-D Representative plots of β_s vs Concentration (mole kg^-1) of ZnSO₄ in Lactose-water mixed solvent at T = (303.15K, 308.15K, 313.15K). 

where ρ and βs0 are the density and isentropic compressibility of the solvent (aqueous-galactose), ρ and βs are those of solution, respectively; c and M are the molarity of the solution and the molar mass of the solute (zinc sulphate), respectively. Observing the variations of Φ_k from figures 5 and 6, it reveals that ф_k values decrease when increasing the concentrations of both Zn ions and carbohydrates. It also shows negative values and decreasing trends with increase in temperature. According to Bahadur et al, negative values of ф_k are attributed to strong attractive interactions between the solute and solvent due to solvation of the solute [³⁴]. It has also been reported that the negative values are indicative of electrostrictive solvation of ions [³⁷]. Again, the apparent molar compressibilty of ZnSO₄ in galactose-water systems is comparatively more than that of ZnSO₄ in lactose-water for few systems. This shows that the ion-solvent interactions are slightly more important in the former systems.

Fig. 5 Variation of apparent molar compressibility, ф_k vs Concentration (mole kg^-1) of ZnSO₄ in Galactose-water and Lactose-water mixed solvent at 303.15K. 

Fig. 6 Variation of apparent molar compressibility, ф_k of ZnSO₄ in 2.5% Galactose-water and Lactose-water vs. Temperature (303.15K, 308.15K, 313.15K). 

Free volume and partial molal volume

The free volume, V_f, internal pressure, π_i , relaxation time, τ, and relative association, R_A are other parameters that were calculated using the following relations [³⁸,³⁹,⁴⁰,⁴¹].

where, M_eff is the effective molecular mass and K is a constant equal to 4.28 x 10⁹, independent of temperature for all types of liquids; b is the space packing factor, generally 2 for liquids, R is the gas constant, T is the absolute temperature. Presently, V_f values decrease with the concentration of ZnSO₄ as well as that of galactose and lactose (Figs. 7 and 8) and increase with temperature. As per the literature, the higher values are indicative of less solute-solvent interaction [⁴²].

Fig. 7 Variation of free volume, V_f vs. Concentration (mole kg^-1) of ZnSO₄ in Galactose-water and Lactose-water mixed solvent at 303.15K. 

Fig. 8 Variation of free volume, V_f of ZnSO₄ in 2.5% Galactose-water and Lactose-water vs. Temperature (303.15K, 308.15K, 313.15K). 

The relative association, R_A, is found to be increasing regularly with the concentration of ZnSO₄ in both galactose and lactose systems (Fig. 9). But hardly any distinct variation was observed with temperature. However, it decreases slowly with the concentration of galactose and increases with lactose concentration. According to Jahagirdar et al., R_A is influenced by two factors, such as breaking of associated solvent molecules on addition of solute or electrolyte and the solvation of solute molecules. It has been reported that the former leads to decrease and the later to an increase in R_A with solute concentration [⁴³]. The relaxation time, τ, is found to be increasing with the concentrations of ZnSO₄ as well as carbohydrates (Table 3) and shows a decreasing trend with temperature [Representative 3-D plots for ZnSO₄ in aqueous galactose mixed solvent at different temperatures (Fig. 10)]. It has been reported earlier that the decrease in relaxation time is indicative of a structure breaking tendency, whereas linear or non-linear increment with concentration indicates structure formation [⁴⁴]. Kannappan et al. also reported a similar observation [⁴²]. The internal pressure, considered as the cohesive energy is supposed to be caused by the attractive and repulsive forces between the molecules [⁴⁵]. Presently, it increases with ZnSO₄ as well as with galactose and lactose concentrations. However, the values are little higher in case of ZnSO₄ in galactose than in lactose systems (Fig. 11). This enhancement is due to the strong cohesive forces that appear during the structure making of solvents in presence of solute [⁴⁶]. The values of internal pressure decrease with temperature for all the systems studied (Fig. 12). This happens due to the dispersion of solute molecules with temperature and hence there is decrease in cohesive force.

Fig. 9 Variation of Relative association, R_A vs Concentration (mole kg^-1) of ZnSO₄ in Galactose-water a nd Lactose-water mixed solvent at 303.15K. 

Fig. 10 3-D Representative plots of Relaxation time, ( vs Concentration (mole kg^-1) of ZnSO₄ in 2.5% Galactose-water mixed solvent at T = (303.15K, 308.15K, 313.15K). 

Fig. 11 Variation of internal pressure, (_i vs Concentration (mole kg^-1) of ZnSO₄ in Galactose-water and Lactose-water mixed solvent at 303.15K. 

Fig. 12 Variation of internal pressure, (_i vs Concentration (mole kg^-1) of ZnSO₄ in 2.5% Galactose-water and Lactose-water vs. Temperature (303.15K, 308.15K, 313.15K). 

The apparent molal volumes, ф_v, of ZnSO₄ have been calculated from the measured values of densities of mixed solvents and solutions using the following relation:

where, ρ₀ and ρ are the densities of mixed solvents (aqueous-galactose, -lactose) and solutions, respectively; c is the molality of the solutions, M is the molar mass of the solute (ZnSO₄). This is the shrinkage of the solution volume after mixing of the components, where same numbers of molecules are accommodated into comparatively smaller volume than the total volumes of the components. Presently, values of ф_v for ZnSO₄ in aqueous-galactose and lactose mixed solvent are positive and mostly increasing with concentrations (Fig. 13). According to Gupta G and his group, the positive values of ф_v is indicative of strong solute-solvent interaction [55]. However, the values are not in a regular increasing trend with the concentration of lactose. This type of variation suggest that the galactose molecules interact more constructively with water to strengthen the H-bonded network in the mixed solvent systems than that of lactose [⁴⁷]. In the literature there are reports showing that a higher value of ф_v is due to strong solute-solvent interaction [⁴⁸].

Fig. 13 Variation of apparent molal volume, ф_v vs. Concentration (mole kg^-1) of ZnSO₄ in Galactose-water and Lactose-water mixed solvent at 303.15K. 

Solvation number

The speed of sound measurement is used to evaluate solvation number, Sn . It was suggested by Passynski and is studied to assess the mode of association. [⁴⁹]

where, n₀ and n_i are the moles of solvent and solute, respectively. As per the literature, there are basically two solvation sheaths, primary and secondary. These can be studied with the help of speed of sound measurements [⁵⁰]. The association of solvent molecules with the ion is a strong co-ordination bond type and occurs in the primary sheath of solvation. On the other hand, in the secondary sheath, there are weak forces of attaction between solute and solvent molecules. However, the solvation indicates the association among solute with solvent molecules. Sn values are found to be positive for all systems and such variation is due to appreciable solvation of solute in solution [⁵¹]. It decreases with the concentrations of both ZnSO₄ and galactose (Table 4 and Fig. 14). This is due to the reduction of size of the secondary sheath of solvation. S_n values are also in a decreasing trend with temperature (Fig. 15). This can be attributed to the weakening of solute-solvent interaction. Marcus reported that S_n depends on both the ion and solvent as well as on the concentration through the interactions of this ion with other ions [⁵²]. Again, the non-linear variation with the concentration of ZnSO₄ indicates the increase in ion-solvent interactions [⁵³].

Fig. 14 Variation of Solvation number, S_n vs. Concentration (mole kg^-1) of ZnSO₄ in Galactose-water and Lactose-water mixed solvent at 303.15K. 

Fig. 15 Variation of Solvation number, S_n vs Concentration (mole kg^-1) of ZnSO₄ in 2.5% Galactose-water and Lactose-water vs Temperature (303.15K, 308.15K, 313.15K). 

Gibb´s free energy

The Gibb’s free energy, ΔG of the studied systems was calculated by using the relaxation time parameter and other constants.

where k is Boltzmaan’s constant (1.23x10^-23 JK^-1), T is the absolute temperature and h is Planck’s constant (6.6 x 10^-34 Js). It has been observed that the values of ΔG increase with ZnSO₄ as well as with galactose and lactose concentrations. This type of variation suggests closer approach of unlike molecules due to H-bonding. Again ΔG decreases with temperature and it is indicative of the rearrangement of molecules in the mixtures [Representative 3-D plots for ZnSO₄ in aqueous galactose mixed solvent at different temperatures (Fig. 16)]. Similar observation was reported earlier [⁵⁴] and this reveals the decrease in energy leading to dissociation [⁴⁴]

Fig. 16 3-D Representative plots of Gibb’s free energy ΔG vs Concentration (mole kg^-1) of ZnSO₄ in 2.5% Galactose-water mixed solvent at T = (303.15K, 308.15K, 313.15K).