Reactions in solution [ solution kinetics]

REACTIONS IN SOLUTION
SUBMITTED BY,
CHITHRAANILKUMAR
MAR IVANIOS COLLEGE ,
TRIVANDRUM

CONTENTS
A. SOLUTION KINETICS
B. CAGE EFFECT
C. COMPARISON BETWEEN GAS PHASE AND SOLUTION REACTIONS
D. COMPARISONS BETWEEN DIFFERENT SOLVENTS
E. CLASSES OF REACTION
F. SIGNIFICANCE OF DIFFUSION CONTROLLED AND ACTIVATION CONTROLLED PROCESSES
G. FACTORS DETERMINING THE REACTION RATES IN SOLUTION
H. EFFECT OF DIELECTRIC CONSTANT ON THE REACTION RATE
I. VOLUME OF ACTIVATION

Kinetics – how fast does a reaction proceed?
Thermodynamics – does a reaction take place?

SOLUTION KINETICS
• It is the kinetic study of chemical reactions taking place in solution phase.
• Such reactions are very common but it becomes difficult to study such reactions
theoretically.
• The rate of a chemical reaction in solution is controlled either by the rate of diffusion of the
reactants or by the activation energy of the step that leads to products.

What's different about kinetics in liquid solutions
• Most of the added 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 becomes especially important when
the solvent is strongly hydrogen-bonded as is the
case with water or alcohol.
Brownian motion of a
particle in solution
Liquid
vs.
Gases

• When thermal motions occasionally release a solute
molecule from this trap, it will jump to a new location
and follow an entirely random pattern, very much as
in Brownian motion.
• Consider a simple bimolecular process
A + B → products
• The reactant molecules will generally be jumping
from hole to hole in the solvent matrix, only
occasionally finding themselves in the same solvent
cage where thermal motions are likely to bring them
into contact.

A pair of reactants
end up in the same
solvent cage, where
they bounce
around randomly
and exchange
kinetic energy with
the solvent
molecules.
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.
The products form and
begin to move away
from
each other.
Finally, after
about
10–11 sec, the
solvent cage
breaks up
and the products
diffuse away.

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.
In solution phase, the activated complex formed by the reaction of A and B is known as
encounter pair {AB}.

• The cage effect describes how the properties of a molecule
are affected by its surroundings.
• It was first introduced by Franck and Rabinowitch in 1934
.
• Cage effect is also known as Frank – Rabinowitch effect.
• The encounters of the reactant molecules dissolved in a
solvent are considerably less frequent than in a gas.
• This lingering of one molecule near another on account of
the hindering presence of solvent molecule is called the
cage effect.
• There is an average of four collision in each encounter, but
the intervals between successive encounters would tend to be
about four times the interval between collisions in gas phase.
• The overall collision frequency is therefore the same in both
phase.
• This tendancy for collision to occur in sets has no effect on
ordinary reactions, which involve activation energy , since
reaction may occur at any collisions within the set.
• Here pre-exponential factor is the reciprocal of the average
time elapsing between successive encounters.
CAGE EFFECT
• In photochemical reactions in solution a pair of
free radicals produced initially may recombine
before they can separate from each other.This
phenomenon is known as primary recombination
as opposed to secondary recombination which
occurs after the free radicals have separated.

COMPARISON BETWEEN GAS PHASE AND SOLUTION REACTIONS
• Reactions that occur in gas phase as well as in solution
often show similar behaviour in solution as in the gas
phase and are affected little by a change of solvent.
• Eg : - Thermal decomposition of nitrogen pentoxide.
• The rate constant , pre-exponential factors and activation
energies are much the same in most of the solvents as they
are in gas phase.
• An exception is nitric acid which plays a more active role
in the reaction than the other solvents.
• So generally when a reaction occurs in the gas phase as
well as in solution , the solvent usually plays a relatively
subsidiary role ; it seems to act merely as a space filler
and has only a minor influence on the kinetics.

COMPARISONS BETWEEN DIFFERENT SOLVENTS
• When reactions that do not occur in gas phase are
studied , rates usually vary much more widely from
solvent to solvent.
• A good example is given by the reaction between
triethyl amine and ethyl iodide , studied by
Menschutkin in 22 different solvents.
• The rate of this reaction is quite sensitive to the
solvent.
• From the least polar solvent (hexane) to the most
(nitrobenzene), the rate constant increases 2700 times.
• Hence, if the reaction is faster the more polar the
solvent.

CLASSES OF REACTION
• Let us consider a bimolecular ionic reaction proceeding via
transition state mechanism as,
𝐴 + 𝐵 ⇌ [𝐴𝐵] ∗ → 𝑃 …(1)
Step I: 𝐴 + 𝐵 → [𝐴𝐵] ∗
𝑘𝑑
where [𝐴𝐵] ∗ is the encounter pair which is formed when ions A and
B approach each other (diffuse towards each other) in solution phase.
And 𝑘𝑑 is the diffusion controlled constant.
• Once the encounter pair is formed, there are two possibilities –
either it may diffuse back to give ions in solution phase (step II) or
it may lead to product formation (step III).
Step II: [𝐴𝐵] ∗ 𝑘−𝑑 → 𝐴 + 𝐵 [𝐴𝐵] ∗
is highly unstable and diffuse back in the medium to ions A and B.
Step III: [𝐴𝐵] ∗ → 𝑃
Over here, the encounter pair leads to product formation. And 𝑘𝑎 is
the activation controlled constant.
The overall rate of the reaction can be expressed as,
𝑅𝑎𝑡𝑒 = 𝑑[𝑃] /𝑑𝑡 = 𝑘𝑎 [𝐴𝐵] ∗ …(2)
Applying Steady State Approximation to the reactive encounter pair [
𝐴𝐵] ∗ gives,
𝑑[𝐴𝐵] ∗/𝑑𝑡 = 0 …(3)
Using Steps I, II and III, we can rewrite the above equation as,
𝑑[𝐴𝐵] ∗ /𝑑𝑡 = 𝑘𝑑 [𝐴][𝐵] − 𝑘−𝑑 [𝐴𝐵] ∗ − 𝑘𝑎 [𝐴𝐵] ∗ = 0 …(4)
The above equation can be rewritten as,
[𝐴𝐵] ∗ = 𝑘𝑑[𝐴][𝐵] 𝑘−𝑑+𝑘𝑎 …(5)
Substituting equation (5) in equation (2) gives,
𝑅𝑎𝑡𝑒 = 𝑑[𝑃] /𝑑𝑡 = 𝑘𝑎 𝑘𝑑[𝐴][𝐵] /𝑘−𝑑+𝑘𝑎 …(6)

Case I: 𝑘𝑎 ≫ 𝑘−𝑑
Under this condition, the rate expression (6) becomes,
𝑅𝑎𝑡𝑒 = 𝑑[𝑃]/ 𝑑𝑡 = 𝑘𝑑 [𝐴][𝐵] …(7)
The rate of the reaction is dependent on rate constant kd. Therefore, this reaction is called
diffusion controlled ionic reaction.
• In this, activation energy is assumed to be approximately zero and rate of diffusion of the reactions
towards each other determines the overall rate of reaction.
Case II: 𝑘−𝑑 ≫ 𝑘𝑎
𝑅𝑎𝑡𝑒 = 𝑑[𝑃]/ 𝑑𝑡 = 𝑘𝑎 𝑘𝑑[𝐴][𝐵] /𝑘−𝑑
Since 𝑘𝑑 = 𝑘−𝑑
𝑅𝑎𝑡𝑒 = 𝑑[𝑃] /𝑑𝑡 = 𝑘𝑎 [𝐴][𝐵] ...(8)
Hence rate depends on 𝑘𝑎 [𝐴][𝐵], i.e. this in an activation controlled ionic reaction.
SIGNIFICANCE OF DIFFUSION CONTROLLED AND ACTIVATION
CONTROLLED PROCESSES

Factors determining the reaction rates in solution
1) POLARITY OF SOLVENT
• A change from a polar solvent to a non – polar solvent has been
suggested to increase or decrease reaction rates depending on the type
of reactions.
• If the reaction is one in which the products are more polar than the
reactants , then a polar solvent accelerates the reaction.
• If the reactants are more polar than the products , then a polar solvent
decreases the reaction rate.
• When both reactants and products are non – polar , polarity of
solvents will have no influence on the rate of the reaction .
• In general, a polar solvent accelerates the reaction in the direction
of increase in polarity.

2) INFLUENCE OF SOLVATION
• If either the reactant or the product or the activated complex interacts with the solvent , there may be
considerable influence on the rate of the reaction.
Consider , for example , the reaction between a tertiaryamine such as pyridine and an alkyl iodide such as methyl
iodide :
The products are two separated ions , and in the activated complex there is partial ionization , as represented above .
In a polar solvent such as nitrobenzene there is more solvation of the activated complex than of the reactants. The
effect of solvation is to lower the activity coefficient and as a result the rate is high.
On the other hand , in a reaction of the type ,
There is a decrease in polarity as the activated complex is formed . A polar solvent therefore solvates the activated
complex less than the reactants, now the activity coefficients are smaller for the reactants than for the solvent and
such a solvent reduces the rate.

EFFECT OF DIELECTRIC CONSTANT ON THE REACTION RATE
[Application of absolute theory to a reaction between ions]
In the double sphere model , the ions are considered to remain
intact as they approach one another and form an activated
complex in which the centres of the ions are separated by a
distance dAB .
When the ions are separated by a distance x , the force acting
between them is , according to Coulomb’s law ,
Where ℇ is the dielectric constant and ε0 is the permitivity of
vacuum [8.854 ×10⁻¹² C²/Nm²] .
The workdone on the system in moving them together by a
distance dx is ,
[Here negative sign appears because x decreases by dx]

The work done on the system in moving the ions from x = α to x = dAB is therefore ,
This work is positive if the ionic charge are of the same sign and if they are different , it is negative .
This work ‘w’ is the electrostatic contribution to the Gibbs energy of activation when two ions form an
activated complex .
Multiplying by the Avogadro constant‘L’ gives the molar quantity ,
There is also a non – electrostatic contribution
Thus , the total molar Gibbs energy of activation is ,

According to the theory of absolute reaction rates, the rate constant is related to the free energy of the activation by
the reaction ,
Since R/L = K .
Taking natural logarithms,
This may be written as ,
Where k0 is the value of k in a medium of infinite dielectric constant , in which the electrostatic forces have
become zero.
According to this equation , it follows that the logarithm of the rate constant of a reaction between ions should vary
linearly with the reciprocal of the dielectric constant.

VOLUME OF ACTIVATION
A quantity derived from the pressure dependence of the rate constant of a reaction (mainly used for
reactions in solution), defined by the equation:
Δ‡V=−R T (∂(lnk)∂p)T
The volume of activation is interpreted, according to transition state theory, as the difference
between the partial molar volumes of the transition state(V) and the sums of the partial
volumes of the reactants at the same temperature and pressure, i.e.
Δ‡V=‡V−∑(r VR)
where r is the order in the reactant R and VR its partial molar volume.

 Polanyi and Evans pointed out that two distinct effects must be considered in the explanation of the
volume of activation.
1. There must be a change due to structural factors in the volume of the reactant molecules as they
pass into the activated state. This always leads to a volume decrease for a bimolecular process, while
for a unimolecular process, there is a volume increase.
2. There may be a volume change resulting from reorganization of the solvent molecules.
Studies of various reactions have showed that the solvent effects are generally more important than the
structural ones for reactions in which ions or strong dipoles are concerned.
There is a general correlation between entropy of activation and volume of activation for reactions in
aqueous solutions.
The activation entropy depends on the strength of the chemical bonds whereas ΔV# depends on
electrostriction which is the electrostatic action of the reacting ions on the solvent molecules leading to a
decrease of their degrees of freedom.

QUESTIONS
1) Write a note on the effect of dielectric constant of the solvent on the
rate of an ionic reaction.
2) Explain the significance of solvent cage in chemistry .

Reactions in solution [ solution kinetics]

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Reactions in solution [ solution kinetics]