Ions in solution

To prepare for the discussion of bioiogioai redox reactions and the roie of ions in 

The most significant difference between the solution of an electrolyte and a nonelectrolyte is that there are long-range Coulombic interactions between the ions in the former. As a result, electrolyte solutions exhibit nonideal behavior even at very low concentrations because the solute particles, the ions, do not move independently of one another. Some idea of the importance of ion-ion interactions is obtained by noting their average separations in solutions of different molar concentration c and, to appreciate the scale, the typical number of HjO molecules that can fit between them  

Checklist of key concepts 211 Checklist of key equations 212 Discussion questions 212 Exercises 212 

The largest body of data for electrolyte solutions pertains to water as the solvent, and values for other solvents are best described in terms of the transfer functions of the ions from water as the source to the required solvent as the target (Section 4.3). This is because the transfer quantities are only a small fraction of the total and can be determined much more accurately than can the difference between the large values in the source and target solvents. Attention is, therefore, first directed toward aqueous solutions. After the relevant properties of the solvents that are involved in solutions of electrolytes have been dealt with in Chapter 3, the transfer of ions from aqueous solutions to solutions in these solvents, and eventually also to solutions in mixed solvents (Section 6.1) is presented and discussed. 

The restricted primitive model is the simplest approximation. It considers the ions as charged conducting particles dispersed uniformly in a continuum fluid made up of a compressible dielectric. The ions are characterized by their masses, charges (magnitudes), and sizes (radii), and are assumed to be spherical. The sign of the charge does not play a role in this model. The solvent is characterized by its permittivity, compressibility, and thermal expansibility. The standard state properties of the ions may then be estimated by the application of electrostatic theory and compared with the experimental values. 

More sophisticated models allow for the molecular nature of the solvent and take into account the interactions between its molecules. It is then possible to ascribe concentric solvation shells to the ions made up with an average number of solvent molecules in the first and sometimes a second shell. This (first shell) solvation nnmber becomes a definite integer if the solvent molecules form coordinate bonds with the ion. Snch a model may still be treated by appropriate theoretical tools and used in compnter simulations. 

The more common process that can be carried out experimentally is to dissolve in the solvent an entire electrolyte, consisting of a matched number of cations and anions to produce a neutral species. Infinite dilution may be very well approximated as a limit of extrapolation from low, finite, and diminishing concentrations. This limit corresponds to the dissolution of a mole of electrolyte in a huge amount of solvent or of an infinitesimal amount of electrolyte in a finite amount of solvent. The molar quantities pertaining to the electrolyte at infinite dilution may then be dealt with. Some means to deduce from the measured quantities those pertaining to the individual ions must still be devised, in order to relate experimental values to those obtained from theory or computer simulations. 

The individual ionic quantities contributing to the measured molar properties of the infinitely dilute electrolyte are additive, because then each ion is surrounded by solvent molecules only and is remote from other ions and does not interact with them. These quantities are weighted by their stoichiometric coefficients and V in the electrolyte Q+AJI. It follows that if the value for one ion is known, those of other ions (of opposite sign) can be derived by subtracting this value, appropriately weighted, from the values for electrolytes containing it and so forth. 

What is the pH of the solution phase of a hydrogen electrode that is connected to an Fe/Fe half-reaction if the voltage of the spontaneous reaction is 0.300 V Assume that the concentration of Fe is 1.00 M and all other conditions are standard. 

According to the half-reactions in Table 8.2, the only possible spontaneous reaction is 

Because we are reversing the Fe standard reduction reaction, the value for E° (other half-reaction) thatwe use in equation 8.35 isthenegativeof —0.447 V, or +0.447 V. Using equation 8.35, we have 

This is a fairly acidic pH, corresponding to an approximate concentration of 

It is oversimplified to think that ions in solution behave ideally even for dilute solutions. For molecular solutes like ethanol or CO2, interactions between solute and solvent are minimal or are dominated by hydrogen bonding or some other polar interaction. However, we usually assume that individual solute molecules do not 

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K2 is called the hydrolysis constant for sodium ethanoate. Hydrolysis occurs when salts involving weak acids or bases are dissolved in water. It is often also found with metal ions in solution. The ion [M(H20) ] dissociates to the hydroxy species [M(H20) , (OH)]f 1. ... 

In addition to the case of a metal in contact with its ions in solution there are other cases in which a Galvani potential difference between two phases may be found. One case is the innnersion of an inert electrode, such as platinum metal, into an electrolyte solution containing a substance S that can exist m either an oxidized or reduced fomi tlirough the loss or gain of electrons from the electrode. In the sunplest case, we have... 

Diflfiision-controlled reactions between ions in solution are strongly influenced by the Coulomb interaction accelerating or retarding ion diffiision. In this case, die dififiision equation for p concerning motion of one reactant about the other stationary reactant, the Debye-Smoluchowski equation. 

Time-resolved spectroscopy has become an important field from x-rays to the far-IR. Both IR and Raman spectroscopies have been adapted to time-resolved studies. There have been a large number of studies using time-resolved Raman [39], time-resolved resonance Raman [7] and higher order two-dimensional Raman spectroscopy (which can provide coupling infonuation analogous to two-dimensional NMR studies) [40]. Time-resolved IR has probed neutrals and ions in solution [41, 42], gas phase kmetics [42] and vibrational dynamics of molecules chemisorbed and physisorbed to surfaces [44]- Since vibrational frequencies are very sensitive to the chemical enviromnent, pump-probe studies with IR probe pulses allow stmctiiral changes to... 

Intermolecular quadrupolar 2 Fluctuation of the electric field gradient, moving multipoles Common for />1 In free Ions In solution [la... 

Taking francium as an example, it was assumed that the minute traces of francium ion Fr could be separated from other ions in solution by co-precipitation with insoluble caesium chlorate (VII) (perchlorate) because francium lies next to caesium in Group lA. This assumption proved to be correct and francium was separated by this method. Similarly, separation of astatine as the astatide ion At was achieved by co-precipitation on silver iodide because silver astatide AgAt was also expected to be insoluble. 

Electron transfer can be established experimentally in reactions involving only ions in solution. Inert electrodes, made from platinum, are used to transfer electrons to and from the ions. The apparatus used is shown in Figure 4.3. the redox reaction being considered... 

When M is a voltmeter an indication of the energy difference between the reactants and products is obtained (see below). A current passes when M is an ammeter, and if a little potassium thiocyanate is added to the Fe (aq) a red colour is produced around the electrode, indicating the formation of iron(III) ions in solution the typical bromine colour is slowly discharged as it is converted to colourless bromide Br . 

For the equilibrium M(s) M (aq) + 2e, it might then be (correctly) assumed that the equilibrium for copper is further to the left than for zinc, i.e. copper has less tendency to form ions in solution than has zinc. The position of equilibrium (which depends also on temperature and concentration) is related to the relative reducing powers of the metals when two different metals in solutions of their ions are connected (as shown in Figure 4.1 for the copper-zinc cell) a potential difference is noted because of the differing equilibrium positions. 

The problem in any quantitative volumetric analysis for ions in solution is to determine accurately the equivalence point. This is often found by using an indicator, but in redox reactions it can often... 

The solid has a layer structure (p. 434). Lead(ir) iodide, like lead(Il) chloride, is soluble in hot water but on cooling, appears in the form of glistening golden spangles . This reaction is used as a test for lead(II) ions in solution. 

Aqueous ammonia can also behave as a weak base giving hydroxide ions in solution. However, addition of aqueous ammonia to a solution of a cation which normally forms an insoluble hydroxide may not always precipitate the latter, because (a) the ammonia may form a complex ammine with the cation and (b) because the concentration of hydroxide ions available in aqueous ammonia may be insufficient to exceed the solubility product of the cation hydroxide. Effects (a) and (b) may operate simultaneously. The hydroxyl ion concentration of aqueous ammonia can be further reduced by the addition of ammonium chloride hence this mixture can be used to precipitate the hydroxides of, for example, aluminium and chrom-ium(III) but not nickel(II) or cobalt(II). 

Because of ammine formation, when ammonia solution is added slowly to a metal ion in solution, the hydroxide may first be precipitated and then redissolve when excess ammonia solution is added this is due to the formation of a complex ammine ion, for example with copper(II) and nickel(II) salts in aqueous solution. 

The hydrogensulphate ion dissociates into hydrogen and sulphate ions in solution hence hydrogensulphates behave as acids. 

The many possible oxidation states of the actinides up to americium make the chemistry of their compounds rather extensive and complicated. Taking plutonium as an example, it exhibits oxidation states of -E 3, -E 4, +5 and -E 6, four being the most stable oxidation state. These states are all known in solution, for example Pu" as Pu ", and Pu as PuOj. PuOl" is analogous to UO , which is the stable uranium ion in solution. Each oxidation state is characterised by a different colour, for example PuOj is pink, but change of oxidation state and disproportionation can occur very readily between the various states. The chemistry in solution is also complicated by the ease of complex formation. However, plutonium can also form compounds such as oxides, carbides, nitrides and anhydrous halides which do not involve reactions in solution. Hence for example, it forms a violet fluoride, PuFj. and a brown fluoride. Pup4 a monoxide, PuO (probably an interstitial compound), and a stable dioxide, PUO2. The dioxide was the first compound of an artificial element to be separated in a weighable amount and the first to be identified by X-ray diffraction methods. 

The first term represents the forces due to the electrostatic field, the second describes forces that occur at the boundary between solute and solvent regime due to the change of dielectric constant, and the third term describes ionic forces due to the tendency of the ions in solution to move into regions of lower dielectric. Applications of the so-called PBSD method on small model systems and for the interaction of a stretch of DNA with a protein model have been discussed recently ([Elcock et al. 1997]). This simulation technique guarantees equilibrated solvent at each state of the simulation and may therefore avoid some of the problems mentioned in the previous section. Due to the smaller number of particles, the method may also speed up simulations potentially. Still, to be able to simulate long time scale protein motion, the method might ideally be combined with non-equilibrium techniques to enforce conformational transitions. 

Finally, the solvent also interacts with sites of the Lewis acid and the Lewis base that are not directly involved in mutual coordination, thereby altering the electronic properties of the complex. For example, delocalisation of charges into the surrounding solvent molecules causes ions in solution to be softer than in the gas phase . Again, water is particularly effective since it can act as an efficient electron pair acceptor as well as a donor. 

Because of the mentioned leveling effect of the solvent (or excess acid itself acting as such) the acidity cannot exceed that of its conjugate acid. In the case of water the limiting acidity is that of HsO. Proton-ated water, H30 (hydronium ion), was first postulated in 1907, and its preeminent role in acid-catalyzed reactions in aqueous media was first realized in the acid-base theory of Bronsted and Lowry. Direct experimental evidence for the hydronium ion in solution and in the... 

Note that the concentration of Ca + is multiplied by 2, and that the concentrations of H3O+ and OH are also included. Charge balance equations must be written carefully since every ion in solution must be included. This presents a problem when the concentration of one ion in solution is held constant by a reagent of unspecified composition. For example, in many situations pH is held constant using a buffer. If the composition of the buffer is not specified, then a charge balance equation cannot be written. 

Precipitate particles grow in size because of the electrostatic attraction between charged ions on the surface of the precipitate and oppositely charged ions in solution. Ions common to the precipitate are chemically adsorbed, extending the crystal lattice. Other ions may be physically adsorbed and, unless displaced, are incorporated into the crystal lattice as a coprecipitated impurity. Physically adsorbed ions are less strongly attracted to the surface and can be displaced by chemically adsorbed ions. 

At the equivalence point, the moles of acetic acid initially present and the moles of NaOH added are identical. Since their reaction effectively proceeds to completion, the predominate ion in solution is CH3COO-, which is a weak base. To calculate the pH we first determine the concentration of CH3COO-. 

An electrode in which the membrane potential is a function of the concentration of a particular ion in solution. 

Three techniques, one of which is ion chromatography, are used to determine the concentrations of three ions in solution. The combined concentrations of Na+ and K+ are determined by an ion exchange with H+, the concentration of which is subsequently determined by an acid-base... 

If the liquid that is being bombarded contains ions, then some of these will be ejected from the liquid and can be measured by the mass spectrometer. This is an important but not the only means by which ions appear in a FAB or LSIMS spectrum. Momentum transfer of preformed ions in solution can be used to enhance ion yield, as by addition of acid to an amine to give an ammonium species (Figure 4.3). 

The reaction medium plays a very important role in all ionic polymerizations. Likewise, the nature of the ionic partner to the active center-called the counterion or gegenion-has a large effect also. This is true because the nature of the counterion, the polarity of the solvent, and the possibility of specific solvent-ion interactions determines the average distance of separation between the ions in solution. It is not difficult to visualize a whole spectrum of possibilities, from completely separated ions to an ion pair of partially solvated ions to an ion pair of unsolvated ions. The distance between the centers of the ions is different in... 

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