Aqueous solution equilibria calculation

In most solutions containing an acid, we can assume that the acid dominates in the production of H+ ions. That is, we typically can assume that the acid produces so much H+ in comparison with the amount of H+ produced by water that water can be ignored as a source of H+. However, in certain cases water must be taken into account when the pH of an aqueous solution is calculated. For example, consider a 1.0 X 10-4 M solution of a very weak acid HA (Ka = 1.0 X 10-10). A quick calculation shows that if water is ignored, the [H+] produced by this acid is 1.0 X 10-7 M. This value cannot be the correct [H+] in this solution at equilibrium, because in pure water [H+] = 1.0 X 10-7 M. In this instance perhaps the thing to do to get the total [H+] is to add the two H+ concentrations ... 

Water that has been saturated with magnesia (MgO) at 25°C has a pH of 10.16. Write a balanced chemical equation for the equilibrium between MgO(s) and the ions it furnishes in aqueous solution, and calculate the equilibrium constant at 25°C. What is the solubility, in moles per litep of MgO in water ... 

ROP and RAFT polymerization techniques were combined to synthesize multiarm star-block copolymers having PeCL inner blocks and PDMAEMA outer blocks. A hyperbranched polyester core was used as a multifunctional initiator. It was calculated that the functionality of the star-blocks was equal to 19. Temperature and pH-responsive micelles were obtained in aqueous solutions. Equilibrium between unimolecular and mulrimolecular micelles was observed at pH 6.58 by dynamic LS and TEM measurements. In low-pH solutions, the PDMAEMA chains were fully protonated and therefore highly stretched, leading to maximum Rh values. When the pH was increased, the micellar Rh decreased as a result of the deprotonation of the dimethylamine groups. PDMAEMA is also a temperature-sensitive polymer, as it exhibits lower critical solution temperature (LCST) behavior. It precipitates from neutral or basic solutions between 32 and 58 °C. At pH 6.58, the Rh values were found to decrease with increasing temperature, due to the gradual collapse of the PDMAEMA outer blocks. 

To address the shortcomings in FEP results, Worth and Richards used their previously studied system of histamine monocation in aqueous solution and calculated the corresponding tautomer equilibrium constant. The intra-and intermolecular contributions to the relative SFE were evaluated separately ... 

Bromo complexes of Sb(III), Pb(II), and Bi(III) were studied in cationic CTAB/CH2CI2 reverse micelles from the viewpoint of the absorption spectra and coordination number. Since the electronic spectra of the bromomer-curate(II) complexes strongly overlapped with the spectrum of CTAB, these coordination compounds were investigated in the anionic AOT/isooctane micellar system. In some cases, for comparison, spectra were also recorded in homogeneous aqueous solutions. Equilibrium constants were not calculated for the micellar systems because the actual activities of the reactants cannot be determined in the aqueous microphase, although the formal concentrations and ionic strengths may be estimated. 

Cr(III), Frei et al. proposed that the pool of Cr(VI) delivered to the oceans should be isotopically heavy, with an isotope fractionation from the Cr(III) remaining in continental rocks possibly as large as 6%o, since that is the equilibrium fractionation between Cr(VI) and Cr(III) in aqueous solution, as calculated theoretically by Schauble et al. [42]. The higher the extent of oxidative weathering, the more heavy Cr could be dehvered to the ocean. Upon encountering dissolved Fe(II) in seawater, isotopically heavy Cr(VI) should be rapidly reduced to Cr(III) and copredpitated with Fe oxyhydroxides (sediments that will become BIF). Hence the S3/S2cr values of BIF should correlate positively with the intensity of oxidative weathering at the time of deposition. 

Aqueous solutions buffered to a pH of 5.2 and containing known total concentrations of Zn + are prepared. A solution containing ammonium pyrrolidinecarbodithioate (APCD) is added along with methyl isobutyl ketone (MIBK). The mixture is shaken briefly and then placed on a rotary shaker table for 30 min. At the end of the extraction period the aqueous and organic phases are separated and the concentration of zinc in the aqueous layer determined by atomic absorption. The concentration of zinc in the organic phase is determined by difference and the equilibrium constant for the extraction calculated. 

The standard electrode potentials , or the standard chemical potentials /X , may be used to calculate the free energy decrease —AG and the equilibrium constant /T of a corrosion reaction (see Appendix 20.2). Any corrosion reaction in aqueous solution must involve oxidation of the metal and reduction of a species in solution (an electron acceptor) with consequent electron transfer between the two reactants. Thus the corrosion of zinc ( In +zzn = —0-76 V) in a reducing acid of pH = 4 (a = 10 ) may be represented by the reaction ... 

The UV absorption spectra of sodium nitrite in aqueous solutions of sulfuric and perchloric acids were recorded by Seel and Winkler (1960) and by Bayliss et al. (1963). The absorption band at 250 nm is due either to the nitrosoacidium ion or to the nitrosyl ion. From the absorbancy of this band the equilibrium concentrations of HNO2 and NO or H20 —NO were calculated over the acid concentration ranges 0-100% H2S04 (by weight) and 0-72% HC104 (by weight). For both solvent systems the concentrations determined for the two (or three) equilibrium species correlate with the acidity function HR. This acidity function is defined for protonation-dehydration processes, and it is usually measured using triarylcarbinol indicators in the equilibrium shown in Scheme 3-15 (see Deno et al., 1955 Cox and Yates, 1983). 

C12-0062. At 25 °C, the equilibrium pressure of HCl vapor above a 0.100 M aqueous solution of HCl is 4.0 torr. Calculate the Henry s law constant and determine the equilibrium pressure of HCl vapor above a 6.0 M solution. 

The equilibrium constant for the proton transfer reaction of benzoic acid, determined in Example, is 6.4 X 10. Calculate the equilibrium concentration of benzoic acid and benzoate anions in a 5.0 X 10 M aqueous solution of the acid. 

Wolery, T.J. (1978) Some chemical aspects of hydrothermal processes at midoceanic ridges — A theoretical study I, Basalt-seawater reaction and chemical cycling between the oceanic crust and the oceans. II, Calculation of chemical equilibrium between aqueous solutions and minerals. Ph.D. Thesis, Northwestern U. 

Wolery, T.J., Calculation of Chemical Equilibrium between Aqueous Solution and Minerals The EQK3/6 Software Package, Lawrence Livermore Laboratory Report UCRL-52658, 1979, p. 41. 

E. L. Shock (1990) provides a different interpretation of these results he criticizes that the redox state of the reaction mixture was not checked in the Miller/Bada experiments. Shock also states that simple thermodynamic calculations show that the Miller/Bada theory does not stand up. To use terms like instability and decomposition is not correct when chemical compounds (here amino acids) are present in aqueous solution under extreme conditions and are aiming at a metastable equilibrium. Shock considers that oxidized and metastable carbon and nitrogen compounds are of greater importance in hydrothermal systems than are reduced compounds. In the interior of the Earth, CO2 and N2 are in stable redox equilibrium with substances such as amino acids and carboxylic acids, while reduced compounds such as CH4 and NH3 are not. The explanation lies in the oxidation state of the lithosphere. Shock considers the two mineral systems FMQ and PPM discussed above as particularly important for the system seawater/basalt rock. The FMQ system acts as a buffer in the oceanic crust. At depths of around 1.3 km, the PPM system probably becomes active, i.e., N2 and CO2 are the dominant species in stable equilibrium conditions at temperatures above 548 K. When the temperature of hydrothermal solutions falls (below about 548 K), they probably pass through a stability field in which CH4 and NII3 predominate. If kinetic factors block the achievement of equilibrium, metastable compounds such as alkanes, carboxylic acids, alkyl benzenes and amino acids are formed between 423 and 293 K. 

So far we have not touched on the fact that the important topic of solvation energy is not yet taken into account. The extent to which solvation influences gas-phase energy values can be considerable. As an example, gas-phase data for fundamental enolisation reactions are included in Table 1. Related aqueous solution phase data can be derived from equilibrium constants 31). The gas-phase heats of enolisation for acetone and propionaldehyde are 19.5 and 13 keal/mol, respectively. The corresponding free energies of enolisation in solution are 9.9 and 5.4 kcal/mol. (Whether the difference between gas and solution derives from enthalpy or entropy effects is irrelevant at this stage.) Despite this, our experience with gas-phase enthalpies calculated by the methods described in this chapter leads us to believe that even the current approach is most valuable for evaluation of reactivity. 

Figure 4 Heterocycles for which the tautomeric equilibrium in aqueous solution has been studied using free energy calculations including explicit solvent. Tautomerism occurs by exchanging a proton between the labeled atoms.

For an understanding of many systems involved in biochemistry it is important to know details of their tautomeric and ionic equilibria. For example, moving a molecule from aqueous solution to a polar environment inside a receptor may result in a different tautomer dominating the equilibrium, with consequences for the activity. In this chapter we have outlined how theoretical calculations can be used to study these systems, with the all important solvent environment treated explicitly. 

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