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Reply to Comments on "The Quest to Demystify Water. Ideal Solution Behaviors are Obtained by Adhering to the Equilibrium Mass Action Law" Andreas A. Zavitsas J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.9b01212 • Publication Date (Web): 19 Feb 2019 Downloaded from http://pubs.acs.org on February 19, 2019
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The Journal of Physical Chemistry
Reply to: “Comments on ‘Quest to Demystify Water. Ideal Solution Behaviors are Obtained by Adhering to the Equilibrium Mass Action Law’ by Z.-H. Yang J. Phys. Chem. B 2019, XXX, XXX–XXX.” Andreas A. Zavitsas* Department of Chemistry and Biochemistry, Long Island University, 1 University Plaza, Brooklyn, New York 11201, United States
We demonstrated that aqueous solutions of electrolytes exhibit ideal behavior by adhering to Raoult’s law when the mole fraction of water is calculated by eq 1.1 xw = (55.509 m∙Hd)/(55.509 m∙Hd m∙ie)
(1)
There are 55.509 moles of water in one kilogram at 25 °C, m is the molality of solute, Hd is the dynamic average of the moles of water with decreased degrees of freedom per mole of solute, and ie is the extent of dissociation of the electrolyte. In eq 1, the moles of “free” water not strongly bound to solutes is the numerator; the same moles of “free” water is in the denominator; and the moles of solute particles are added in the denominator. Aspects of our method were questioned by Yang,2 who presented a different model for correlating p/p0 with molality, the model described as being “Within the framework of complete dissociation of strong electrolytes.” According to the assumption of complete dissociation, our value for ie should be 2 for all 1:1 electrolytes. Because this is not so, Yang concluded that the excellent agreements we obtained between p/p0 and xw for 77 electrolyte solutions are just the result of a two-parameter fit, by Hd and ie, to the values of p/p0, and that Hd and ie have no physical meaning. For NaCl solutions, our method obtains ie = 1.77 indicating that each mole produces (ie 1) = 0.77 mole of species containing Na+, 0.77 mole containing Cl, (2 ie) = 0.23 mole of species containing both ions as ion pairs, and 0.23 mole of waters as the dynamic average of waters released from hydrated ions upon ion pair formation. When ion pairing occurs between counterions, some waters of hydration are released and ie quantifies the amount. A 2006 review3 provides estimated values of the waters released upon ion pairing of counter-ions. Yang stated that eq 1 is wrong because it does not include the m∙(2 ie) moles of released water in the moles
*
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[email protected]. Tel: (718)488-1351 1 ACS Paragon Plus Environment
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of “free” water and corrected eq 1 to be eq 2. Then he pointed out that eq 2 is quite different from eq 1, thus proving that our method is wrong. xw = (55.509 m∙Hd)/(55.509 m∙Hd m∙(2 ie) m∙ie)
(2)
Both eq 1 and eq 2 must have the same moles of “free” water in the numerator and in the denominator. However, the eq 2 suggested by Yang has the moles of “free” water to be 55.509 m∙Hd in the numerator and the same moles of “free” water to be 55.509 m∙Hd m∙(2 ie) in the denominator. It cannot be both. In a previous similar criticism of our method, Yang stated that the correct form of our approach should have been as in eq 3.3 xw = (55.509 m∙Hd m∙(2 ie))/(55.509 m∙Hd 2∙m)
(3)
In eq 3, the released water m∙(2 ie) was added to the moles of “free” water in the numerator, but not to the “free” water in the denominator. This is the reverse of what is done in the recent criticism.2 When the moles of “free” water in the numerator and denominator are made unequal, eq 1 is proven wrong. Also, the term 2∙m in the denominator of eq 3 indicates complete dissociation, while m∙(2 ie) in the numerator indicates incomplete. One cannot have both in the same equation, because the result will be absurd, and prove that eq 1 is wrong! To complete the discussion of this aspect, the moles of “free” water in our eq 1 are the total moles of water that cause the vapor pressure minus the moles of bound water: 55.509 – m∙Hd. This accounts for all the “free” water, including any water released upon formation of ion pairs, and is the same in numerator and denominator. One cannot add more “free” water to the total “free” water. Yang states that for NaCl solutions “ie violated the law of mass action and Zavitsas furtherly [sic] assumed…”. Nothing further was assumed to fix this problem, because there is no problem. The value ie = 1.77 is the constant extent of dissociation required by the mass action law for NaCl solutions. Adherence to the law is obtained by this one-and-only correct ie. The claim that we indicated in any way that ie violated anything is baseless. However, it does violate Yang’s assumption of complete dissociation. Yang says that “Zavitsas implicitly defined a species, so-called water clusters (H2O)d as ion pairs.”2 There are no ions in water-water clusters, and there is no implication in our article that such clusters were defined as ion pairs. It is not clear what motivated this assertion. Yang claimed that “we found that Hd of NaCl, NaBr, and NaI are different”; also “this violates the additivity because ascribed [sic] no bound waters to Cl, Br, and I. Therefore, the 2 ACS Paragon Plus Environment
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The Journal of Physical Chemistry
assigned Hd and ie by Zavitsas have not his claimed physical meaning.” It is not Yang who discovered these differences in Hd numbers. We focused on them explicitly, described them as an apparent conundrum, and explained them as follows: “The differences are caused primarily because the extents of dissociation are not the same.” Our Figure 7 showed the linear relation between ie and Hd for several 1:1 electrolytes.1 In comparing Hd of NaCl, NaBr, and NaI, the ie values are 1.77, 1.82, and 1.89 respectively. One mole of NaCl produces 0.77 mole of Na; NaBr produces 0.82 mole of Na; and NaI produces 0.89 mole of Na. We pointed out the obvious: “The greater the extent of dissociation, the greater is the fraction of free cations binding water and increasing Hd.” We are perplexed by Yang’s failure to notice the section of our article regarding the subject of this paragraph. We emphasized that our method is valid for molalities of 0.1 and greater. However, Yang extrapolated our method to infinite dilution to demonstrate that the convention of complete dissociation at infinite dilution will be violated. It has been known for a long time that the idea of complete dissociation at infinite dilution is only a convention.4 There is no experimental evidence for it by direct vapor pressure measurements applicable to Raoult’s law. Below about 1.0 m such direct measurements “are rarely accurate or precise enough to yield meaningful values of .”5 We pointed out that many reported p/p0 values for concentrations of about 0.5 m or lesser are not actually measured vapor pressures but values adjusted so that ionic activity coefficients derived from them will smoothly converge to the assumed value of unity at infinite dilution, as required by the convention. Our method was stated not to venture into such extrapolations, which are based on assumptions and beliefs unrelated to Raoul’s law.1 The fundamental fault in Yang’s approach is that it maintains that all strong electrolytes dissociate completely, independent of concentration. Should this eventually prove to be true, not only ours but all of the hundreds of studies mentioning ion pairing would be wrong. AUTHOR INFORMATION *E-mail:
[email protected]. Tel: (718) 488-1351 ORCD Andreas A. Zavitsas: 0000-0002-1310-8307 Notes The author declares no competing financial interest. REFERENCES 3 ACS Paragon Plus Environment
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(1) Zavitsas, A. A. Quest to Demystify Water: Ideal Solution Behaviors Are Obtained by Adhering to the Equilibrium Mass Action Law. J. Phys. Chem. B 2019, 119, 869–883. (2) Yang, Z.-H. Comments on “Quest to Demystify Water: Ideal Solution Behaviors Are Obtained by Adhering to the Equilibrium Mass Action Law.” J. Phys. Chem. B 2019, XXX, XXX–XXX. (3) Yang, Z.-H. Reply to the ‘Comment on “the Size and Structure of Selected Hydrated Ions and Implications for Ion Channel Selectivity” by A. Zavitsas, RSC Adv., 2016, 6, 92771’. RSC Adv. 2016, 6, 93217–93218. (4) Daniels, F.; Alberty, R. A. Physical Chemistry, 3rd ed. John Wiley & Sons, Inc. New York, 1966. (5) Rard, J. A.; Clegg, S. L. Critical Evaluation of the Thermodynamic Properties of Aqueous Calcium Chloride. 1. Osmotic and Activity Coefficients of 0–10.77 mol∙kg Aqueous Calcium Chloride Solutions at 298.15 K and Correlation with Extended Pitzer Ion-Interaction Models. J. Chem. Eng. Data 1997, 42, 819–849.
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