Free Radical

Free Radicals



Structure and Geometry of Free Radicals: A free radical is a species which has one or more unpaired electrons. In the species where all electrons are paired the total magnetic moment is zero. In radicals, however, since there are one or more unpaired electrons, there is a net magnetic moment and the radicals as a result are paramagnetic. Free radicals are usually detected by electron spin resonance, which is also termed electron paramagnetic resonance. Simple alkyl radicals have a planar (trigonal) structure, i.e., these have sp2 bonding with the odd electron in a p orbital. The pyramidal structure is another possibility when the bonding may be sp3 and the odd electron is in an sp3 orbital. The planar structure is in keeping with loss of activity when a free radical is generated at a chiral center. Thus, a planar radical will be attacked at either face after its formation with equal probability to give enantiomers. Unlike carbocations, the free radicals can be generated at bridgehead shows that pyramidal geometry for radicals is also possible and that free radicals need to be planar.



Stability of Free Radicals: A As in the case of carbocation, the stability of free radicals is tertiary > secondary > primary and is explained on the basis of hyperconjugation. The stabilizing effects in allylic radicals and benzyl radicals is due to vinyl and phenyl groups in terms of resonance structures. Bond  dissociation energies shown that 19 kcal / mol  less energy is needed  to form the benzyl radical from toluene than the formation of methyl radical from methane. The triphenyl methyl type radicals are no doubt stabilized by resonance, however, the major cause of their stability is the steric  hindrance to dimerization. 






Carbenes



Carbenes are neutral intermediates having bivalent carbon, in which a carbon atom is covalently bonded to two other groups and has two valency electrons distributed between two non bonding orbitals. When the two electrons are spin paired the carbene is a singlet, if the spins of the electrons are parallel it is a triplet.

Structure of Carbenes : A singlet carbene is thought to possess a bent sp2 hybrid structure in which the paired electrons occupy the vacant sp2 orbital. A triplet carbene can be either bent sp2 hybrid with an electron in each unoccupied orbital, or a linear sp hybrid with an electron in each of the unoccupied p-orbital. It has however, been shown that several carbenes are in a non-linear triplet ground state. However, the dihalogenocarbenes and carbenes with oxygen, nitrogen and sulphur atoms attached to the bivalent carbon, exist probably as singlets. The singlet and triplet state of a carbene display different chemical behaviour. Thus addition of singlet carbenes to olefinic double bond to form cyclopropane derivatives is much more stereoselective than addition of triplet carbenes.

Generation of Carbenes: Carbenes are obtained by thermal or photochemical decomposition of diazoalkanes. These can also be obtained by a-elimination of a hydrogen halide from a haloform with base, or of a halogen from a gem dihalide with a metal.

Reactions of Carbenes: These add to carbon double bonds and also to aromatic systems and in the later case the initial product rearranges to give ring enlargement products (a car-benoids –oranometallic or complexed intermediates which, while not free carbenes afford  products expected from carbenes are usually called carbenoids).

When a carbene is generated  in a three membered ring allenes are formed by rearrangement. However, a similar formation at a cyclopropylmethyl carbon gives ring expansion. Carbenes are also involved in Reimer —Tiemann reaction.




Arenium Ions



A considerable amount of experimental evidence indicates that electrophiles attack the p system of benzene to form a delocalized non-aromatic carbocation known as arenium ion or sometimes a s complex CMR spectroscopic evidence is available in favour of  s complex.


Benzynes



It is a reactive intermediate in some nucleophilic aromatic substitutions. It is a benzene with two hydrogen atoms removed. It is usually drawn with a highly strained triple bond in the six membered ring. Benzyne intermediate has been observed spectroscopically and trapped.

By:- NKGupta

Rate Law and order of reaction

Rate Law

We know that the rate law is the expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some power, which may or may not be equal to the stoichiometric coefficient of the reacting species in a balanced chemical equation.

Consider a general reaction, aA + bB → cC + dD where a, b, c, d are the stoichiometric coefficients of the reactants and products. Therefore, the rate law for this reaction is,

Rate ∝ [A]x [B]y

where x and y may or may not be equal to the stoichiometric coefficients of the reactants. Therefore, the rate of the reaction is equal to k [A]x [B]y, where k is the rate constant.

∴ -d[R]/dt = k [A]x [B]y 

Order of Reaction

Order of a reaction is the sum of the powers of the concentrations of the reactants in the rate law expression. In the above general reaction, x and y are the powers. The sum of them will give the order of the reaction. Order of a reaction can be 0, 1, 2, 3 and even a fraction. A zero-order reaction means that the rate of the reaction is independent of the concentration of reactants.

Zero Order Reaction

So we already know that in a zero order reaction, the rate is independent of the concentration of the reactants. Thus, it means the sum of the powers of concentrations is zero. It can only be zero when the all the powers are zero. Consider a reaction, R → P. Therefore, the rate law of this reaction is,

Rate ∝  [R]0

∴ Rate = -d[R]/dt = k[R]0 = k × 1

∴ Rate = -d[R]/dt = k

∴ d[R] = -kdt

Integrating both sides, [R] = -kt + I……………….(I)

where I is the constant if integration. At t = 0, the concentration of the reactant R = [R]0.where [R]0 is the initial concentration of the reactant. Substituting this value in the equation I,

[R]0 = -k ×0 + I = I

Substituting this value of I in the equation (I), we get

[R] = -kt + [R]0 ………………(II)

Comparing equation II with the equation of a straight line y= mx +c, if we plot [R] against t, we get a straight line with slope = -k and intercept = [R]0 

(Source: askiitians.com)

Therefore, on simplifying equation II, we get

k ={ [R]0 – [R]}/t……………..(III)

Example of Zero Order Reaction

Zero-order reactions are very uncommon but they occur under certain condition. An example of a zero-order reaction is decomposition of ammonia, 2NH3 → N2 + 3H2 

Rate = k[NH3]0 = k

First Order Reaction

In this type of reaction, the sum of the powers of concentrations of reactants in rate law is equal to 1, that is the rate of the reaction is proportional to the first power of the concentration of the reactant. Consider the reaction R → P again. Therefore, the rate law for this reaction is,

Rate ∝ [R]

We know that [R] = -kt + [R]0 ( from equation II). Taking log of both sides, we get

ln[R] = -kt + ln[R]0 ………………………….(IV)

∴ ln[R]/[R]0 = -kt …………………………….(V)

∴ k = (1/t) ln [R]0 /[R] ………………………(VI)

Now, consider equation II again. At time t1 and time t2, the equation II will be [R]1 = -kt1 + [R]0 and [R]2 = -kt2 + [R]0 respectively, where [R]1 and  [R]2 are concentrations of the reactants at time t1 and t2 respectively. Subtracting second equation from first one, we get

ln [R]1– ln[R]2 = -kt1 – (- kt2 )

∴ ln[R]1 /[R]2 = k (t2 – t1)

∴ k = [1/(t2 – t1)] ln[R]1 /[R]2

Now, taking antilog of both sides of equation V, we get [R] = [R]0e-kt

Comparing this equation with equation of a straight line y = mx + c, if we plot ln [R] against t, we get a straight line with slope = -k and intercept = ln[R]0

(Source: nonsibihighschool.org)

On removing natural logarithm from equation VI, the first-order reaction can also be written as,

k = 2.303/t log[R]0 /[R] …………..(VII)

If we plot a graph of log[R]0 /[R] against t, we get slope = k/2.303

Example of First Order Reaction

An example of a first-order reaction is hydrogenation of ethene.

C2H4 + H2 → C2H6

Therefore the rate of reaction = k [C2H4]. Hence, equations III and VII are the equations of rate constants of zero and first order reactions respectively. We can find rate constants, initial and final concentrations and the time taken for the reaction to occur using these reactions.

A Solved Question for You

Q: The order of a reaction is:

a) can never be zero                                   b) can never be a fraction

c) must be a whole number only             d) can be a whole number or a fraction or zero

Solution: d) can be a whole number or a fraction or zero. It depends on the dependency of the rate of reaction on the reactants. If the rate is independent of the reactants, then the order of reaction is zero. Therefore, the rate law of a zero order reaction would be rate α [R]0 where [R] is the concentration of the reactant.

By : NKGupta

Collision Theory For Chemical reaction

Collision Theory

Collision theory basically explains how reactions occur and why different reactions have different reactions rates. It states that:

• Molecules must collide in order to react.
• In order to effectively initiate a reaction, the molecules in the collisions must have sufficient energy to bring about disruptions in the bonds of molecules.
• A rise in temperature will cause the molecules to move faster and collide more vigorously, increasing the likelihood of bond cleavages and rearrangements greatly.
• The reactions containing neutral molecules cannot take place at all until they have acquired the activation energy needed to stretch, bend or distort one or more bonds.

Activation Energy

Activation energy is the energy that must be overcome in order for a reaction to occur. It is the minimum energy that is required to start a chemical reaction.

Explanation of Collision Theory

As we discussed, collision theory qualitatively explains how chemical reactions occur and why different reactions have different rates. Consider a simple biomolecular step:

• Clearly, if two molecules A and B are to react, they must approach closely enough to disrupt some of their existing bonds and to permit the creation of new bonds that are required to form products. We call this a collision. The frequency of collision between A and B in a gas will be proportionate to the concentration of each. If we double the concentration of A, the frequency of A-B collision will double. Doubling the concentration of B will have the same effect.
• It is not enough that the molecules just collide. They need to be oriented in a specific manner that is appropriate for the process to occur. The molecules must collide with one another from the correct side. If they do not do so, the collision will not lead to the reaction.
• The molecules must collide with energies greater than or equal to the activation energy of the reaction. If this does not happen the reaction will not take place. The molecules need the energy to break their existing bonds and form new bonds. This is the kinetic energy that the molecules possess. If this energy is not equal to or greater than the activation energy, the reaction will not proceed.

Temperature dependence of Collison theory

Thermal energy relates direction to motion at the molecular level. As the temperature rises, the molecules move faster and collide more vigorously, therefore causing more collisions and increasing the likelihood of bond cleavages. In most cases, the activation energy is supplied in the form of thermal energy.

As the reaction is completing and products are being formed, the activation energy is returned in the form of vibrational energy which is quickly released as heat. Therefore, it very important for the molecules to collide with energies greater than or equal to the activation energy of the reaction.

Rate of Reaction according to Collison theory

For a bimolecular elementary reaction, A + B → Products, the rate of reaction is,

Rate = ZAB e -Ea/RT  

where ZAB represents the collision frequency of reactants A and B and e –Ea/RT represents the fraction of molecules with energies equal to or greater than the activation energy of the reaction. This is why different reactions have different reactions rates. Different reactions have different frequencies of reactants and different activation energies.

A collision that satisfies all the conditions in the collision theory and succeeds in forming a new product is known as an effective collision. Thus, the two important criteria in collision theory are the activation energy and proper orientation of molecules.

A Solved Question for You

Q: Mention the important criteria in order for a reaction to occur.

Solution:

• The molecules must collide.
• The molecules must have correct orientation, that is, they must collide from the correct side.
• The colliding molecules must collide with energies greater than or equal to the activation energy of the reaction.
• The molecules can be given kinetic energy in the form of thermal energy in order to increase the chance of bond cleavages.

Therefore, if all the criteria are fulfilled, the collision will lead to fruition

By : NK GUPTA 

Temperature and Rate – the Relationship

Temperature and Rate – the Relationship

By now, we know that temperature influences the rate of a reaction. As the temperature increases, the rate of a reaction increases. For example, the time taken to melt a metal will be much higher at a lower temperature but it will decrease as soon as we increase the temperature. It has been found that the rate constant is nearly doubled for a chemical reaction with a rise in temperature by 10°.

We can explain the dependence of the rate of a chemical reaction on temperature by Arrhenius equation.

Arrhenius Equation

The equation was first proposed by Dutch chemist, J.H. Van’t Hoff but Swedish chemist, Arrhenius provided its physical justification and interpretation. The Arrhenius equation is based on the Collision theory. It is not an equation that is born out of pure math that we can derive. It is an empirical equation that fits experimental data in most of the situations. The Arrhenius equation looks like this,

k = A e -Ea/RT……………(I)

(Source: chemguide.co.uk)

where A is the Arrhenius factor or the frequency factor. It is also known as the pre-exponential factor. This constant is specific to a particular reaction. R is the gas constant and Ea is the activation energy which we measure in joules/mole.

According to the Arrhenius equation, a reaction can only take place when a molecule of one substance collides with the molecule of another to form an unstable intermediate. This intermediate exists for a very short time and then breaks up to form two molecules of the product. The energy required to form this intermediate is known as activation energy (Ea).

(Source: en.wikipedia.org)

In a graph of potential energy vs reaction coordinate, the reaction coordinate represents the profile of energy change when reactants change into products.  Some of the energy releases when the complex decomposes to form products. Therefore, the final enthalpy of the reactions depends only on the nature of the reactants and products.

Obviously, all the molecules do not have the same energy. The distribution of kinetic energy can be described by plotting the fraction of molecules with given kinetic energy vs kinetic energy.  The peak of the curve in the graph corresponds to the most probable kinetic energy. When the temperature increases, the maximum of the curve moves to the higher energy value. Therefore, the curve broadens.

(Source: wps.prenhall.com)

Increasing the temperature increases the fraction of molecules, which collide with energies greater than the activation energy Ea.

Temperature dependence of Rate of Reaction in Arrhenius Equation

In Arrhenius equation, the factor e -Ea/RT  corresponds to the fraction of molecules colliding with activation energies more than Ea. Taking natural logarithms of both sides of the equation I, we get,

ln k = -Ea/RT + ln A …………..(II)

Therefore, from the Arrhenius equation, we can find that increasing the temperature or decreasing the activation energy will result in an increase in the rate of the reaction and an exponential increase in the rate constant. In a graph of activation energy vs rate of reaction, slope = -Ea/R and intercept = ln A.

At temperature T1, equation II will be

ln k1 = -Ea/RT1 + ln A …………………(III)

At temperature T2 , equation II will be

ln k2 = -Ea/RT2 + ln A …………………(IV) (k1 and k2 are the rate constants at temperature T1 and T2)

Subtracting equation III from equation IV, we get

ln k2 – ln k1 = Ea/RT1 – Ea/RT2

∴ ln k2 / k1 = (Ea /R)[1/T1 – 1/T2]

∴ log k2 / k1 = (Ea /2.303R)[(T2 – T1)/T1T2]

A Solved Question for You

Q: Why does the rate of a reaction increase when the temperature increases?

Solution: When the temperature increases, the fraction of molecules that have kinetic energies more than the activation energy of the reaction increases. Therefore, the total activation energy of the reaction decreases. Thus, the rate of the reaction increases

Rate of a Chemical Reaction Nkgupta

Rate of a Chemical Reaction

Some reactions happen very fast like the precipitation of silver chloride. It occurs immediately after mixing aqueous solutions of silver nitrate and sodium chloride. On the other hand, some reactions are very slow like the rusting of iron in the presence of air and moisture. Some chemical reactions are neither slow nor fast but take place at a moderate rate.

 The speed or rate of a chemical reaction is the change in concentration of a reactant or product per unit time. To be specific, it can be expressed in terms of:

• the rate of decrease in concentration of any of the reactants
• the rate of increase in the concentration of any of the products

Let’s understand the rate of a chemical reaction better. Consider a reaction in which the total volume of the system remains constant. Let R be the reactants and P be the products i.e. R → P

Thus, one mole of reactant R produces one mole of product P. Let the initial concentration of R be [R]1 and the concentration of P be [P]1 at time t1. Therefore at time t2, the concentrations of R and P are [R]2 and [P]2 respectively. Therefore,

Δt = t2 –  t1

Δ[R] = [R]2 – [R]1

Δ[P] =  [P]2 – [P]1

(The square brackets represent the molar concentrations)

Equation of Rate of a Chemical Reaction

Rate of disappearance of R = Decrease in concentration of R/time taken = -Δ[R]/Δt

and, rate of appearance of P = Increase in concentration of P/time taken = + Δ[P]/Δt

Δ[R] is a negative quantity because the concentration of the reactants is decreasing while Δ[P] is a positive quantity because the concentration of the products is increasing. While performing calculations on the rate of a chemical reaction, we multiply Δ[R] by -1 to make it a positive quantity. The above equations give the average rate of a chemical reaction which is, rav.

Therefore, the average rate of a reaction depends upon the change in concentrations of the reactants or products and the time taken for that change to occur.

Unit of Rate of a Chemical Reaction

It is clear from equations I and II that the unit of rate of a reaction is concentration time-1. But if the concentration is in mol L-1 and time is in second then the unit will be mol L–1 s–1 . In case of gases, the rate of a chemical reaction will be atm s-1  when the concentration of gases is expressed in their partial pressures.

Solved Questions For You

Q1: Define average rate of a chemical reaction.

Solution: The average rate of a chemical reaction is the change in the concentration of the reactant or product divided by the time taken for that reaction to occur.

Q2: Derive formula of the rate of reaction for the reaction given below:

2Na + Cl2 → 2NaCl

Solution: The rate of a reaction is the change in concentration of the reactant or product divided by the change in time.Therefore, the formula of rate of reaction for the above reaction would be:

Rate of reaction =  -(1/2)Δ[Na]/Δt = -Δ[Cl]/Δt = +(1/2)[NaCl]/Δt .

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