Metallic and non-metallic anionic interaction activities estimated with sound velocity and refractive index

2.1 Chemicals and solvents

Chemicals (99.99%, AR, K₂Cr₂O₇, K₂HPO₄, KMnO₄, KH₂PO₄, KCl, KOH, Ranbaxy, India) were used as received. Milli-Q water was used as a solvent.

2.2 Analytical conditions

The experiment was done at 293.15 K. Solutions w/w were prepared with Milli-Q water of 10⁻⁶ μ S cm⁻¹ conductance with electronic Kern ABS 220-4 model balance with ±0.01 mg accuracy. The ρ and V_S data with 10⁻³kg m⁻³ and 10⁻² ms⁻¹, respectively, were measured with density and sound velocity meter DSA 5000M whose quartz U tube was cleaned with acetone after each measurement. The equipment works on a theory of oscillation periods of U tube for air, solvent and solutions (Pal et al., 2010). The μ_ri was measured with ±10⁻⁴ using Rudolph Research analytical J series Refractometer model 57. Its sample plate was properly cleaned and dried each time with acetone. The measurements for water values were repeated several times to ensure calibration and reproducibility of the equipment. The μ_ri literature value of the water was 1.3328 which very closely matched with experimental values of water. The precision and reproducibility of measured data along with 95.5% confidence variance were noted with highly reproducibility. Similarly the V_S experimental value was 1482.69 ms⁻¹ for water and had shown striking agreements with literature values.

4.1 The V_S, V_L, and $V_{\text{S}}^0$ , ${\mu }_{\text{ri}}^0$ and concentration study for comparative ionic interactions

The concentration effect on V_S and μ_ri was analyzed from data given in Table 1 and showed increases in V_S and μ_ri with increase in concentration and V_L was decreased. The V_S and μ_ri directly determined internal pressure and ionic hydration with salt’s interactions which formed a high compact continuous medium through which the sound and light waves traveled. Thus the ISI forces developed a denser medium that manifolded the sound speed with a decrease in light velocity. The ISI created anion-hydration and partly the unengaged water with the similar molecules as a homogeneous medium. Thus a pattern of ion-hydration is different with each salt and inferred interaction as important information about a medium characterization that increased V_S and decreased V_L. It is observed that an increase in concentration is accompanied with an increase in internal pressure. For example, V_S is 343.2 m/s in air and 1482.69 m/s with water while V_L is 3 × 10⁸ m/s in vacuum but V_L in water is 2.5209 m/s. Thus, the K₂Cr₂O₇, K₂HPO₄, KMnO₄, KH₂PO₄, KCl, and KOH interactions have increased and decreased V_S and V_L, respectively (Table 1). It inferred that the ISI enhanced and exerted a higher internal pressure where an increase in V_S is accompanied with a decrease in V_L, depicted in Fig. 1. Both V_S and V_L are mutually inversely proportional due to an additional resistance and compressibility, respectively, with concentration. With salts Table 1 shows a percentage increase in V_S with approximately equal decrease in V_L. It is similar to energy conservation as partly the energy is consumed and the same amount of energy is appeared in another form. Thereby it seems an interesting property of solution that inferred absorption of a certain amount of a particular wave and the same amount of another form is exhibited as wave conservation.

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Figure 1

Relation between sound and light velocity.

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The $V_S^0$ with KH₂PO₄ > K₂HPO₄ > KOH > K₂Cr₂O₇ > KCl > KMnO₄ sequence inferred higher internal pressure with the KH₂PO₄ and lowest for KMnO₄ (Table 2). It is explained with pressure p = 1/volume v (Boyle’s law) relation where the density ρ = mass m/v. It marked the KH₂PO₄ with higher density that caused stronger ionic interactions and the KMnO₄ with lower density due to weaker ionic interactions. Such observation inferred that a metallic anion weakened the ionic interactions and the non-metallic anion strengthened the same. Similarly, the ${\mu }_{\mathit{ri}}^0$ as KMnO₄ > KH₂PO₄ > KOH > K₂HPO₄ > KCl > K₂Cr₂O₇, with highest values with KMnO₄ and lowest with K₂Cr₂O₇ (Table 2) inferred that the ${\text{MnO}}_4^{-}$ a metallic anion with weaker internal pressure and also the ${\text{Cr}}_2{\text{O}}_7^{-}$ with two metallic anion with variable valence inferred weaker shear stress and strain due to moderately weaker ionic interaction. The $V_S^0$ values of the K₂Cr₂O₇, K₂HPO₄, KH₂PO₄, KCl and KOH are rationalized w.r.t. those of the KMnO₄ with the 1.000067, 1.000169, 1.000175, 1.000040, and 1.000162 times higher than of the KMnO₄, respectively. Similarly, the ${\mu }_{\mathit{ri}}^0$ of the K₂HPO₄, KMnO₄, KH₂PO₄, KCl, and KOH are rationalized w.r.t. the K₂Cr₂O₇ and noted 1.000068, 1.000135, 1.000105, 1.000038 and 1.000075 times higher than of the K₂Cr₂O₇, respectively (Table 3). In comparison to the K₂HPO₄ and KH₂PO₄, there is no specific effect of 1 and 2 K⁺ on V_S and μ_ri while the ${\text{PO}}_4^{3-}$ anions are the same because both V_S and μ_ri for the KH₂PO₄ are higher than of the K₂HPO₄. However, in comparison to K₂Cr₂O₇ and KMnO₄ the V_S are higher with K₂Cr₂O₇ and μ_ri with KMnO₄ due to an effect of anionic metals on V_S and μ_ri. The two anionic metallic atoms such as Cr in the K₂Cr₂O₇ has increased V_S more than single anionic metallic atom such as Mn in the KMnO₄ that decreased the μ_ri. The Mn and Cr are in +7 and +6 oxidation states in KMnO₄ and K₂Cr₂O₇, respectively, so another information is also important that the metal having high oxidation number decreased V_S and increased μ_ri while the metal having low oxidation number increased V_S and decreased μ_ri. In comparison of K₂Cr₂O₇ and KCl, the effect of ionic size and symmetrical arrangement of the ISI existed. The metallic anion such as K₂Cr₂O₇ increased V_S more than of the KCl where the K⁺ and Cl⁻ have the same sizes due to the same electronic configuration such as 1s², 2s², 2p⁶, 3s², 3p⁶. These variations could be due to the same sizes of the ions which might have created symmetrical arrangement of the ISI while the different size of the ions such as the K⁺ and ${\text{Cr}}_2{\text{O}}_7^{2-}$ with metallic anionic property developed unsymmetrical ISI which increased the compressibility. This effect is opposite for the μ_ri such as the KCl increased μ_ri higher than of K₂Cr₂O₇.

4.2 Adiabatic (β) and apparent molal compressibilities (ϕk)

The negative values of the ϕk, Δβ, and Δβ/β₀ (Sumathi and Varalakshmi, 2010; Anwar, 1998; Anwar and Anil Kumar, 2002) given in Table 1 which is due to ISI, where the Δβ and Δβ/β₀ values increased with increase in salts concentration. It may be attributed to an overall increase in the cohesive forces in the solution (Sumathi and Varalakshmi, 2010; Pandey and Akhatar, 1996). These cohesive forces may result into interaction between water–water, salt–water and salt–water adjacent molecules, where the β values decreased with increase in concentration (Table 1). The β⁰ are as KMnO₄ > KCl > K₂Cr₂O₇ > KOH > KH₂PO₄ > K₂HPO₄ (Table 2) shows that KMnO₄ has the highest and K₂HPO₄ has the lowest β⁰ value with 0.0053 pa⁻¹ difference in their values due to creating high adiabatic compress medium (ACM). A decrease in β⁰ is due to an increase in ion-dipolicstriction where the salts caused a compression with the decrease in the compressibility (Riyazudden and Khan, 2009). A comparison of KH₂PO₄ and K₂HPO₄ salts inferred that a replacement of an H⁺ from K₂HPO₄ caused a weaker ISI with contribution of K⁺ for creating ACM. Thus the cations matter a lot toward an ACM effect on the water structure. Thus KH₂PO₄ with only single K⁺ created a stronger ACM while K₂HPO₄ with 2K⁺ caused a weaker ACM. Thus the K₂HPO₄ interaction is two times weaker effective for ACM than of the KH₂PO₄. The difference of their β⁰ values are very low with 0.0002 pa⁻¹ which has obtained from (KH₂PO₄–K₂HPO₄) that inferred the more cation numbers had partially caused ACM effect. Similarly the KMnO₄ has created stronger ACM than of the K₂Cr₂O₇ due to the number of cation and number of transitional metal in their anions. It inferred that the low number of a metal such as Mn (+7) in MnO₄^- caused stronger ACM than of the high number of a metal such as Cr (+6). Thus extensively and explicitly constituted a concept of molionic mixtures where nature of salts had caused structural impacts on the water structure with variable resultants values of V_S, β and ϕk. The ratio of their β⁰ values is 1.0008 pa⁻¹ derived from (KMnO₄/K₂Cr₂O₇) had inferred the partially affected ACM by less number of anionic metals. A linear fitting of the ϕk⁰ with the composition are found as K₂HPO₄ > KH₂PO₄ > K₂Cr₂O₇ > KOH > KCl > KMnO₄ (Table 2) due to a reverse relation of ϕk⁰ with β⁰ except KOH and K₂Cr₂O₇. It inferred that those factors which are accountable for strong β⁰ or ACM such as numbers of cation or anionic metals are weaker for ϕk. The similar trend of V_S and ϕk with opposite trends of the β⁰ showed a special relationship among V_S, β, and ϕk as V_S = ϕk/β as such as relation among the density = mass/volume.