Reaction Kinetics in Solution with special reference to Kinetic salt Effect

Reaction Kinetics in Solution with special reference to Kinetic salt Effect

What is Reaction Kinetics in Solution?

Most of the complications of kinetics and rate processes in liquid solutions arise from the much higher density of the liquid phase.

In a typical gas at atmospheric pressure, the molecules occupy only about 0.2 per cent of the volume; the other 99.8 percent is empty space. In a liquid, molecules may take up more than half the volume, and the "empty" spaces are irregular and ever-changing as the solvent molecules undergo thermal motions of their own.

In a typical liquid solution, the solvent molecules massively outnumber the reactant solute molecules, which tend to find themselves momentarily (~10–11 sec) confined to a "hole" within the liquid. This trapping is especially important if the solvent is strongly hydrogen-bonded, as is the case with water or alcohol.

When thermal motions occasionally release a solute molecule from this trap, it jumps to a new location. The jumps are very fast (10–12 to 10–13 sec) and short (usually a few solvent-molecule diameters), and follow an entirely random pattern, much like Brownian motion.

The collision theory of bimolecular reactions is not expected to apply in solution since the solvent would hinder the collisions. And yet, surprisingly, there are certain reactions for which the rate constant and the activation energy are almost the same when the reactions are studied in solvent as when they are investigated in the gas phase .We conclude, therefore, that the Arrhenius factors for these cases are nearly the same. So, in case of solution, the word collision is replaced by the word encounter.

When the two molecules collide with each other in solution they are hindered from separating after an unreactive  collision(encounter) since they are surrounded by a cage of solvent molecule . thus, they make many encounters before separating . These encounters compensate for the relatively slow diffusion of the reactant molecules towards each othes in the liquid phase.

Solvent cages and encounter pairs

Consider a simple bimolecular process. The reactant molecules jump from between holes in the solvent matrix, only occasionally finding themselves in the same solvent cage, where thermal motions are likely to bring them into contact.

1. A pair of reactants end up in the same solvent cage, where they bounce around randomly and exchange kinetic energy with the solvent molecules.

2. Eventually the two reactants form an encounter pair. If they fail to react the first time, they have many more opportunities during the lifetime of the cage.

3. Finally, after about 10–11 sec, the solvent cage breaks up and the products diffuse away.

4. The products form and begin to move away from each other.

The process can be represented as

A + B{AB}Products

in which the {AB} term represents the caged reactants, including the encounter pair and the activated complex.


Compare this scenario with a similar reaction in the gas phase; the molecules involved in the reaction are often the only ones present, so a significant proportion of the collisions will be (A-B) encounters. However, if the collision is not energetically or geometrically viable, the reactant molecules fly apart and are unlikely to meet again quickly.

In a liquid, however, the solute molecules are effectively in a constant state of collision—if not with other reactants, then with solvent molecules which can exchange kinetic energy with the reactants. Once an A-B encounter pair forms, the two reactants have multiple chances to collide, greatly increasing the probability that they obtain the kinetic energy required to overcome activation energy hump before the encounter pair disintegrates.

TWO IMPORTANT LIMITING CASES FOR REACTIONS IN SOLUTION 

For water at room temperature, k1 is typically 109-1010 dm–3 mol–1 s–1 and k2 is around 10–9-10–10 dm–3 mol–1 s–1. Given these values, k3 >1012, s-1 implies diffusion control, whereas values less than 109 s–1 are indicative of activation control.

  • Diffusion controlled: If the activation energy of the A+B reaction is very small or if the escape of molecules from the {AB} cage is difficult, the kinetics are dominated by K1, and thus by the activation energy of diffusion. Such a process is said to be diffusion controlled. Reactions in aqueous solution in which Ea > 20 kJ/mol are likely to fall into this category.

  • Activation-controlled: In the reverse case, the activation energy of the A+B reaction dominates the kinetics, and the reaction is activation-controlled.

Several general kinds of reactions are consistently very fast, and thus are diffusion-controlled in most solvents. Gas-phase rate constants are normally expressed in units of mol s–1, but rate constants of reactions in solution are conventionally given in units of mol L​-1 or dm3 mol–1 s–1. Conversion between these units depends on a number of assumptions and is non-trivial.

  • Recombination of atoms and radicals: for example, for the formation of (I2) from Iodine atoms in hexane at 298 K, k3 = 1.3×1012 dm3 mol–1 s–1.
  • Acid-base reactions that involve the transport of (H+) and (OH-) ions tend to be very fast. The most famous of these is one of the fastest reactions known:

[H+ + OH- H2O]

for this k3 = 1.4×10 dm3 mol–1 s–1 at 298 K.

Solvent Polarity Effect

Polar solvents such as water and alcohols interact with ions and polar molecules through attractive dipole-dipole and ion-dipole interactions, leading to lower-energy solvated forms which stabilize these species. In this way, a polar solvent can alter both the thermodynamics and kinetics of a reaction.

Solvent thermodynamic effect

If the products of the reaction are markedly more or less polar than the reactants, solvent polarity can change the overall thermodynamics (equilibrium constant) of the reaction. Nowhere is this more apparent than when an ionic solid such as salt dissolves in water.  The  Na+  and Cl- ions are bound together in the solid by strong coulombic forces; pulling the solid apart in a vacuum or in a non-polar solvent is a highly endothermic process. In contrast, dissolution of NaCl in water is slightly exothermic and proceeds spontaneously.

The water facilitates this process in two important ways. First, its high dielectric constant of 80 reduces the force between the separated ions to 1/80 of its normal value. Second, the water molecules form a solvation shell around the ions (lower left), rendering them energetically (thermodynamically) more stable than they are in the NaCl solid.

Solvent Kinetic Effect

In the same way, the activation energy and therefore rate of a reaction whose mechanism involves the formation of an intermediate or activated complex with polar or ionic character is subject to change as the solvent polarity is altered. As an example, consider an important class of reactions in organic chemistry. When an aqueous solution of a strong base such as KOH is added to a solution of tertiary-butyl chloride in ethanol, the chlorine is replaced by a hydroxyl group, leaving t-butyl alcohol as a product:

This reaction is one of a large and important class known as SN1 nucleophilic substitution processes. In these reactions, a species with a pair of non-bonding electrons (also called a nucleophile or Lewis base) uses them to form a new bond with an electrophile: a compound in which a carbon atom has a partial positive charge owing to its bonds to electron-withdrawing groups. In this example, other nucleophiles such as NH3 or even H2O would serve as well.

To reflect the generality of this process and to focus on the major changes that take place, this reaction is represented as follows:

Extensive studies of this class of reactions in the 1930's revealed that it proceeds in two activation energy-controlled steps, followed by a simple dissociation into the products:

In step 1, which is rate-determining, the chlorine leaves the alkyl chloride, leaving an intermediate known as a carbocation ("cation"). These ions, in which the central carbon atom lacks a complete octet, are highly reactive, and in step 2 the carbocation is attacked by the (water molecule) which supplies the missing electron. The immediate product is another cation in which the positive charge is on the oxygen atom. This oxonium ion is unstable and rapidly dissociates (3) into the alcohol and a hydrogen ion.

The reaction coordinate diagram illustrates the effect of solvent polarity on this reaction. Polar solvent molecules interact most strongly with species in which the electric charge is concentrated in one spot. Therefore, the carbocation is stabilized to a greater extent than are the activated complexes in which the charge is spread out between the positive and negative ends. As the heavy green arrows indicate, a more polar solvent stabilizes the carbocation more than it does either of the activated complexes; the effect is to materially reduce the activation energy of the rate-determining step, and thus speed up the reaction. Because neither the alkyl chloride nor the alcohol is charged, the change in solvent polarity has no effect on the equilibrium constant of the reaction. This is dramatically illustrated by observing the rate of the reaction in solvents composed of ethanol and water in varying amounts:

% water

10

20

30

40

50

60

k1 × 106

1.7

9.1

40.3

126

367

1294

The kinetic study of reactions in solution phase is very complicated and is governed by many factors:

        (a) The movement of ions in solution depends upon the viscosity of the solvent. Therefore, the rate constants of reactions vary with nature of solvent. The rate of reaction between oppositely charged ions is expected to be higher than that for a reaction involving an ion and a neutral molecule or two neutral molecules.

       (b) Extent of solvation:- The degree of solvation of any reacting species affects the rate of the reaction. The reaction rate will be larger in solvents which have least solvation tendency for the reactants. e.g. rate of formation of quaternary ammonium salts is faster in nitrobenzene than in benzene.

       (c) Nature of reacting species:- The reaction is faster in that solvent in which the activated complex is more stable. If the activated complex is polar, the reaction would be faster in polar solvent. If the activated complex is non-polar, the reaction would be fast in non-polar solvent. Ionic strength.

In ionic reactions, due to electrostatic interactions between the reacting ions, the rate of the reaction is influenced by the charges of reacting ions and also ionic strength in solution.

These effects are generally known as salt effects and are of two types-

(a) Primary salt effect:

It is observed in non-catalytic reactions where the added salt doesn’t have any ion common with the ions of the reacting species. But it’s addition changes the ionic strength of the solution, as a result of which the degree of dissociation of substances change.

A simple and satisfactory treatment of Primary salt effect was made by Bjerrum. He proposed that reacting molecules first form an activated complex which is in equilibrium with the reactants. The activated complex decomposes to yield the products.

(b) Secondary salt effect:

It refers to the actual change in the concentration of reacting ions by addition of electrolyte in catalytic reactions. Arrhenius discovered when a salt of the acid catalyzing a reaction is added to it, the catalytic effect is enhanced. Because this addition increases the concentration of anion and undissociated acid (due to common ion effect). This indicates that both undissociated acid and it’s anion have catalytic activity. Thus, the reaction rate indirectly depends upon the amount of salt added in the catalytic reactions. This is called Secondary salt effect.

The addition of a salt having no common ion with the acid catalyzing a reaction can also sometimes lead to an increase in catalytic action of acid. It is called as Primary Salt effect. e.g.The rate of inversion of cane sugar in presence of acetic acid increases by 30 % when 10 % of NaCl is added.

The secondary salt effect can either increase or decrease the rate constant. It can be either larger or smaller than a primary salt effect. For uncharged reactants (neutral molecules), the rate constant is independent of ionic strength.

The existence of salt effects indicate the necessity of adequate control of ionic strength in a kinetic investigation. Either the ionic strength must be kept low so that the effects are small or a series of measurements must be made and extrapolated to zero ionic concentration. Another method is to add small quantities of electrolytes in the reaction which may involve ions, and study the influence of ionic strength. If salt effects are observed, they must be interpreted with care in terms of mechanism because of many possible sources of these effects.

Reactions of ions in solution: Reactions of ionic species in liquids are one exception to the rule that reactions in the liquid phase usually have similar rates as in the gas phase (the other exception being electron transfer reactions). The reason is that the charged species are very sensitive to their environment, in particular solvation. Changes of the charge distribution are accompanied by correspondingly large solvation shell rearrangements.

Effect of the ionic strength of the solution: The main effect arises from the stabilization of shielding every ion in solution by the op-positely charged ”ionic atmosphere” or “ion cloud” (⇒Debye-Hückel theory, Appendix??)

Equilibrium constant for [AB]:

Activity coefficient from Debye-Hückel theory:

Ionic Strength:

Kinetic salt effect:

Dependence of rate constant on Ionic Strengyh:

Conclusions:


Kinetic salt effect for reactions of ions in solution:
Thankyou

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