Reactions of Ions with Polar Molecules

Simple electrostatic models can be used to interpret the activity coefficients of polar molecules in terms of just three parameters a radius, the dipole moment of the solute, and the dielectric constant of the solvent. The continuum model of the solvent can be used to deduce a value for the free energy of solvation of a spherical molecule of radius r containing a point dipole at its center. The value obtained by Kirkwood from electrostatic theory is 

This gives for the activity coefficient of the solute, relative to the gas phase (I = 1), 

This expression has been used to correlate activities of polar molecules in mixtures of solvents of low dielectric constant with a success which is 

In H20-dioxane mixtures, for example, we may expect to find serious changes in solvation in the low H2O range of composition. 

In the case of the reactions of ions with polar molecules, there have been several approaches used. The simplest of these has been to calculate the coulombic energy of a transition complex consisting of a charge za and a dipole This is given by Eq. (XV.6.6)  

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Fast Reactions of Ions with Polar Molecules... 

In the Langevin orbiting theory, only the ion-induced dipole interaction was considered as a long-range force operative between the ion—molecule pair. Thus the theory applies only to the reactions of ions with non-polar molecules. In fact, it has been pointed out that some ion—molecule reactions in which the neutral molecule has a permanent dipole have reaction cross-sections greater than those predicted by the Langevin theory [56—63]. Such ion—polar molecule reactions have also been treated classical mechanically by several authors [57, 58, 61, 64—68]. 

Any substance whose aqueous solution contains ions is called an electrolyte. Any substance that forms a solution containing no ions is a nonelectrolyte. Electrolytes that are present in solution entirely as ions are strong electrolytes, whereas those that are present partly as ions and partly as molecules are weak electrolytes. Ionic compounds dissociate into ions when they dissolve, and they are strong electrolytes. The solubility of ionic substances is made possible by solvation, the interaction of ions with polar solvent molecules. Most molecular compounds are nonelectrolytes, although some are weak electrolytes, and a few are strong electrolytes. When representing the ionization of a weak electrolyte in solution, half-arrows in both directions are used, indicating that the forward and reverse reactions can achieve a chemical balance called a chemical equilibrium. 

Table III - Reactions of He, C and N ions with polar molecules (excepted trans C2H2CI2). The listed rate coefficients are in units of lO cm s" ...

If the reactants are ionic with opposite charges, the rate constant can be greater than 1010 L mol -1 s-1 due to the favorable attractive forces. For example, the rate constant for the reaction of H+ with OH- in aqueous solutions at 25°C is 10n L mol-1 s-1. On the other hand, the electrostatic repulsion between ions of like sign can significantly slow their reaction. Similarly, if the reactants are polar molecules, electrostatic forces between them and the solvent may come into play. 

For ions and polar molecules, the nature of the solvent is an important factor in solution-phase reactions. Following the derivation of Laidler and Meiser (1982), we first consider the reaction between two ions A and B with charges ZAe and ZL e, respectively, where e is unit electronic charge and ZA and Zu are the number of unit charges on the ions, i.e., are whole positive or negative numbers. The electrostatic force (F) between these two ions separated by a distance r in a vacuum is given by Coulomb s law,... 

The ionic states are highly reactive because of polarization forces and in the solid state the parent ion radical or parent carbonium ion is the main reactant. The reactions of these ions with neutral molecules can be understood on the basis of energetics, the isoelectronic principle, and charge-exchange bonding. 

Debye and Huckel (J) have derived an expression for the work function of an ion in an ion atmosphere in solution. They and others (J, S, 4) have applied this function to various phenomena in liquid media. The authors (2) have previously deduced, in a similar way, the field around a dipole and have combined it with Onsagers (5) theory of polar liquids to obtain an equation that explains the electrostatic effects on the rates of reaction between ions and dipolar molecules (2). The equation has been applied (2,6,7,8) to the rates of several ion-dipolar molecular reactions. 

In eukaryotic cells, electron transport and oxidative phosphorylation occur in mitochondria. Mitochondria have both an outer membrane and an inner membrane with extensive infoldings called cristae (fig. 14.2). The inner membrane separates the internal matrix space from the intermembrane space between the inner and outer membranes. The outer membrane has only a few known enzymatic activities and is permeable to molecules with molecular weights up to about 5,000. By contrast, the inner membrane is impermeable to most ions and polar molecules, and its proteins include the enzymes that catalyze oxygen consumption and formation of ATP. The role of mitochondria in 02 uptake, or respiration, was demonstrated in 1913 by Otto Warburg but was not fully confirmed until 1948, when Eugene Kennedy and Albert Lehninger showed that mitochondria carry out the reactions of the TCA cycle, the transport of electrons to 02, and the formation of ATP. 

Polar solvents help to stabilize ions and polar molecules. To understand the effect of the solvent polarity on reaction rates, the polarity of the reactant must be compared with the polarity of the transition state. The one (reactant or transition state) that is more polar (has more charge separation) will be stabilized more by an increase in the polarity of the solvent. If the transition state is more polar than the reactants, increasing the solvent polarity will stabilize the transition state more than the reactants. This will decrease AG, resulting in a faster reaction. In contrast, if the reactants are more polar than the transition state, increasing the solvent polarity will stabilize the reactants more, resulting in a larger JG and a slower reaction. 

In Cl plasma, all the ions are liable to associate with polar molecules to form adducts, a kind of gas-phase solvation. The process is favoured by the possible formation of hydrogen bonds. For the adduct to be stable, the excess energy must be eliminated, a process which requires a collision with a third partner. The reaction rate equation observed in the formation of these adducts is indeed third order. Ions resulting from the association of a reagent gas molecule G with a protonated molecular ion MH+ or with a fragment ion F+, of aprotonated molecular ion MH+ with a neutral molecule, and so on, are often found in Cl spectra. Every ion in the plasma may become associated with either a sample molecule or a reagent gas molecule. Some of these ions are useful in the confirmation of the molecular mass, such as... 

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