Pinacol Pinacolone rearrangement

The conversion Vic. diols to ketones or aldehydes in the presence of mineral acids, acid chloride or ZnCl₂ or other electrophilic reagent is known as Pinacol Pinacolone rearrangement. The reaction involves the elimination of water. The name was given from the classical example of the conversion of Pinacol (Vic. diol) to Pinacolone (ketone).

Mechanism: - The reaction involves the carbocation rearrangement in which the driving force is the stabilization of the resulting carbocation. The reaction starts with the protonation of the hydroxyl group followed by elimination of water and formation of carbocation. The carbocation is then stabilized by 1-2 shifts to give stabilized carbonium ion, which is followed by loss of proton to give product. Following steps involves in the mechanism.

Step I: - Protonation of hydroxyl group

Step II: - Loss of water molecule to form carbonium ion

Step III: - 1-2shift to form rearranged carbonium ion

Step IV: - Elimination of proton to form carbonyl compounds. (The elimination of proton may fascinate by conjugate base)

Similar mechanism can be preformed in the following reaction. (Note: - hydride shift)

The reaction proceeds via "Path-b" as it produces more stable tertiary carbocation.

Schrödinger fundamental wave equation

In order to provide sense and meaning to the probability approach, Schrödinger in1926 derived on equation known after his name as Schrödinger's wave equation. This equation is the basic of wave mechanics and is based upon the idea of the electron as standing wave around the nucleus. If the electron has wave like nature, it should obey the same equation of motion as all other known type of wave. On the basis of simple idea Schrödinger derived an equation which describes the wave motion of an electron wave along of the three axis x, y, z called Schrödinger wave equation.

Schrödinger's wave equation correlates the wave property of the electron with its energy. During the derivation of this equation, he took the following under consideration.

1. de-Broglie's wave particle duality equation

2. Heisenberg's uncertainty principle

3. Bohr's concept of quantized energy levels.

The equation for the standing wave comparable with that of a stretched string is

Where,. (sigh) = amplitude at displacement x and is wave function

A = constant

x = displacement direction

l = wavelength.

Differentiating eq (i) twice with respect to x we get,

As total energy (E) = KE + PE

or [P.E. = U]

Again

According to de-Broglie's equation

Putting the value of v² from eq (iii) on eq (iv) we get,

Putting the value of eq (v) on eq (ii) we get

or

or

Equation (vi) is a Schrödinger wave equation for the wave motion in one dimension only ie x-axis. For electron moving in a three dimension space it is modified as:

Where Ѳ (del-square)[Laplacian operator] =

Equation (vii) and (viii) are Schrödinger wave equation expressions.

The valid values of are called Eigen functions, and the values of E corresponding to this Eigen functions are called Eigen values. The Eigen values are found to be more or less the same energy values given by Bohr's in different orbit.

For to be valid it should satisfy following conditions:

i. must be finite and continuous

ii. It should be single valued

iii. must be continuous functions of x, y, and z coordinates respectively.

Significance of and ²

represent the three dimensional amplitude of electron wave at various points surrounding the nucleus, and is called orbital. However, ², gives the probability of finding electron of certain energy at a space inside the atom.

The value of may be real or imaginary. If is real, ² also is real. Thus ² gives the probability of finding electron.

But if is imaginary * gives the probability of finding electron wave

let = a + ib (imaginary quantity)

* = (a+ib) (a–ib) = a²+b² (real)

Note: The probability should always be real and positive.

Physical concept of uncertainty principle

The physical concept of uncertainty principle become illustrated by considering an attempt to measure the position and momentum of electron moving in Boh'r orbit. To locate the position of the electron, we should devise an instrument 'super microscope' to see the electron. A substance is said to be seen only it could reflect light or any other radiation from its surface. Because the size of the electron is too small, its position at any instant may determined by super microscope employing light of very small wavelength (such as x-rays). A photon of such a radiation of small l, has great energy and therefore has quite large momentum. As one such photon strikes the electron and is reflected, it instantly changes the momentum of electron. Now the momentum gets changed and becomes more uncertain as the position of the electron being determined.

Application of Uncertainty principle: Several phenomenons in the case of particles of atomic dimensions can be understood in terms of the uncertainty principle. Few of them are as below:

1. It easily follows from the uncertainty principle that electrons cannot exist with in the nuclei of the atom.

2. The principle helps us to know that limit to the accuracy with which we can measure the frequency of the radiation emitted by an atom.

Numerical work out:

An electron has a velocity of 600 m/s² with an accuracy of 0.005%. Calculate the certainty with which the position of the electron can be determined. ( h = 6.6 x10-34Js, m = 9.1x10-31 kg)

Solution:

Given Δv = 

Now, Dx = ?

Again: we know

A microscope using photons is employed to locate an electron in an atom to with in a distance of 0.2ºA. What is the uncertainty in the momentum of the electron located in this way?

Solution:

Δp = ?

Δx = 0.2ºA = 0.2x10^-10m

According to Heisenberg principle

electromagnetic waves and matter wave:

S.N	Electromagnetic wave	Matter wave
1	These wave are associated with electrical and magnetic fields, which are perpendicular to each other and to the direction of propagation	These waves are not associated with electrical and magnetic fields.
2	These can be pass through vacuum	These wave cannot pass through vacuum
3	These are actually emitted by their source	These are not emitted by material particle. They are simply associated with the particle.
4	These waves always travel with the constant speed of light.	These waves always travel with the different speeds depending upon the mass of the moving bodies. Their speed is always less than that of light.
5	These waves have always sufficient wavelength and are practically significant.	Only the matter waves associated with extremely small particles have sufficient wavelength and hence significant. Those associated with large objects are insignificant.

Work out example: de-Broglie's equation

What is the wave length of α particle having a mass of 6.6 x 10^-27 kg and kinetic energy of 7.42 x 10-¹² J?

Solution:

We know from de-Broglie's equation

Again we have given:

now

 

Atomic theory(Basic Concept and History)

From the early history of time people were inquisitive about their surrounding, especially the matter. The ancient Greek thinker Damocritus (about 400 BC) began making predictions about the structures of matter. The Roman Lecretius (about 350 years later) took up the same question who predicted that when a piece of gold is cut into several times, a time would come when the piece could not be cut further and they called that invisible small particle of matter as "atom" and following these two ancient philosophers. There appeared a succession of thinkers. European and Arabian whose prediction was end at the beginning of the nineteenth century after around 2000 years in the ideas of John Dalton.

Dalton's Atomic Theory

Dalton introduced his theory as Atomic Theory in 1808 and his theory includes the following points.

1. Mater is made up of small individual particles called atoms.

2. Atoms are indestructible and they cannot be created.

3. The atoms of a particular element are all exactly alike in every way and are different from the atoms of all other elements.

4. Chemical combination takes place between small whole number of atoms.

It seems fairly certain that for most of the nineteenth century, atoms were regarded as very small spherical particles like a every minute lead ball. It was believed atoms are indivisible. This idea was greatly changed in the first half century, mainly by the work of Rutherford.

Atomic Structure:

Less than a century ago, scientist believed that atoms were solid indestructible particles like minute snooker ball, since then they have built up a great deal of evidence concerning the detailed structure of atoms. Experiments involving electrolysis (Faraday's work) suggested that certain compounds contained charged particles called ions; formation of these ions from atoms could be explained only in terms of loss or gain of negative charged particles. This led to the idea that atoms consisted of some other subatomic particles.

Evidence for the existence of subatomic particles:

1897 J.J. Thomson discharge tube experiment with electrons:

In 1897 G.J. Stoney suggested the name electron for the tiny negative particles which made up an electric current. Stoney realized that the experiments involving electrolysis, which Faraday had carried out earlier in the nineteenth century, could be explained in terms of electrons.

However the firm evidence of the existence of electrons was not found until 1897. In that year. J.J. Thomson was investigating the conductivity by gasses at very low pressure.

When Thomson applied 1500 volts across the electrodes of a tube containing a trace of gas, a bright green glow appeared on the glass. The green glow results from the bombardment of the glass by rays traveling in straight line from the cathode when they strike the anode or the glass wall of the tube. Thompson called these rays "cathode rays".

When the rays were deflected by an electric field across a pair of charged plates. The rays moved away from the negative plate attracted towards the positive plate. This suggested that cathode rays were negative. Thompson studied the bending of a thin beam of cathode rays by magnetic and magnetic electric fields and concluded that they consist of electrons tiny negatively charged particles.

By studying the degree of deflection of cathode rays in different magnetic field and electric field. Thompson determined the charge to mass ratio for the electron. He found that the ratio to be e/m = –1.76×10⁸ coulomb/gram

It was further observed by Thompson that the particles present in cathode rays are always same and their e/m value are also the same irrespective of the nature of metal electrode and the nature of the gas used. Therefore it was concluded that cathode rays are up of fundamental particles which were named electrons. Later Robert Milliken, (1909) from his oil drop determined the charge the electron. Which is found to be.

From Thompson e/m Value Millikan's e charge value. The mass of the cathode particle electrons was found to be

This mass is nearly equal to the 1/1837 the mass of one hydrogen atom.

Electron:

Electron is a subatomic particle with unit negative charge and mass equal to 1/1837^th of hydrogen atom in amu and its mass is 9.10910^-28 gram.

1886 Goldstein discharge tube experiment. Anode rays (positive rays) protons:

Godstein was able to show the presence of positive particles in the discharge tube experiment. The presence of negatively charged particle in an atom suggested that there most be some positively charge particle because the atom on the whole is electrically neutral Goldstein repeated the discharge tube experiment using a perforated cathode tube. It was found that in addition to cathode rays new kinds of rays streaming behind the cathode were found these rays were found to travel in opposite direction to the cathode rays and passed through the holes of cathode. These positively charged particles believed to be formed by collisions between electrons in cathode rays and residual gas. The positive particles move towards cathode where they get electron to form neutral atom or molecules and some of the +ve particle passed through the holes in perforated cathode and straight strike on the glass wall.

Fig: Gold stein discharge tubes

These rays seemed to be emitting from anode and consist of positively charged particle and were named positive rays or anode rays. It was found that the value e/m of particle rays depends upon the nature of the gas taken in the discharge tube.

The lightest positively charged particle in such rays when hydrogen gas is used in the discharge tube Each of the particle has the mass of hydrogen atoms carrying unit positive charge. No positively charged particle of matter, which is smaller than hydrogen yet discovered The masses of other simple ions are found to be approximately integral multiple of masses of these +ve particle of hydrogen which are now called protons. Protons are now considered to be the fundamental particle and a constituent of all atoms. Cont……..

Fundamentals of Organic chemistry

Factors influencing electron availability: - (electron displacement effect or electronic effect)

Those effects, which are produced due to the movement of electron from one position to other, so that polarities are developed on the atoms, are known as electron displacement effects. The covalent bond, which has been considered as an ideal covalent bond, may attack by an attacking reagent, which may be negatively or positively charged. For reaction to take place on the covalent bond, it should posses oppositely charged centers. The reactant molecules although as a whole is electrically neutral, it must develop polarity on its carbon. Thus any factor that influence the relative availability of electrons in particular bonds or at particular atoms, in a compound might be expected to affect very considerably its reactivity towards a particular reagent. It is well known that a positive species always tends to attack the electron rich center and vice versa.

The electron displacement in molecule in turn may be due to certain effects some of which are permanent and other may be temporary (time variable effects). Such important effects are discussed in this chapter.

Permanent effect: -

Inductive effect: -

When the carbon atom is joined to a more electronegative atom (like Cl, O or N) by single covalent sigma bond than sigma electrons moves slightly towards more electronegative atom so that more electron rich acquire partial negative charge while carbon atom having electron deficiency acquires partial positive charge. Such type of electron displacement, which takes place due to the different in electro negativity of atoms, is called inductive effect.

Inductive effect may be defined as a type of electronic effect in which partial polarities are developed on the atoms joined by single covalent bond due to the slight displacement of sigma electron caused by different  in electronegativity of atoms.

 

 Characteristic of inductive effects: -

i)      It is represented by symbol I and indicated by arrow (®), pointing towards the more electronegative atom i.e. towards the direction of displacement of electron.

ii)   It is generally occurs in single covalent bond and it involves the displacement of electrons.

iii) Since it is always occurs in single covalent bond. It is permanent effect.

iv)  Due to inductive effect partial polarities are developed on the atoms due to slight displacement of sigma electrons.

v) The inductive effect can be transmitted along with carbon chain. Inductive effect decreases with increase in distance from the sources (i.e. more electronegative atom). The inductive effect may also be defined as type of electronic effects, which involves the successive polarization of one bond by another polar bond.

vi) For the measuring of inductive effect, hydrogen is taken as standard element and is supposed to be having zero effect i.e. neither repels nor withdraws the electrons.

vii) Atoms or groups having higher electron attracting power then hydrogen are called electron withdrawing or –I groups.

              E.g. –CN. –COOH, - CN, -NO₂, -C₆H₅ etc.

viii) Atoms or groups of having lower electron attracting power then hydrogen is called electron releasing groups or + I group for eg . –CH₃, -C₂H₅, -OR, etc.

Inductive effect may be negative or positive, It is –I when electronic displacement take place toward an atom or away from the carbon. It is +I when electronic displacement takes places away from the atom or towards the carbon atom. 

Effect of inductive effect:-

As it is permanent effect in organic compounds plays great role in its reactivity and other properties.

a)      Strength of acid and base:--I effect increases the strength of acid and vice versa.

e.g. Chloroacetic acid is stronger then acetic acid.

The chlorine atom is electron-withdrawing constituent. i.e. it has a –I effect. If it is substituted for one of the hydrogen atom of the CH₃— radical in Ethanoic acid, it brings about the electron displacements as shown

Similar displacements occur in the chloroethanoate anion. In this case the inductive effect of the chlorine atom increases the partial positive charge on the hydrogen atom of the —OH group. While it decreases the partial negative charges on the oxygen atoms of the chloroethanoate anion. The ionization of the acid is thus made easier and the recombination of ions more difficult. Hence Chloroacetic acid is a stronger acid than acetic acid.

 

Here H has fewer electrons deficient due to the present of +I group (-CH₃). The proton is difficult to abstract by base. So that lower tendency to donate proton thus weak acid.

+I effect increases the strength of base.

E.g. alkyl amine is stronger base than ammonia.

All amines are basic; they are stronger bases than ammonia. The basic character of amines is due to the availability of lone pair of electrons, on nitrogen atom, for protonation. Since the alkyl groups are electron releasing (+I effect) compared to hydrogen, It increases the availability of electrons for protonation. The greater the number of electrons releasing alkyl groups (+I effect) the one pair will became more available for protonation. The basicity of the amines wills therefore increases. The introduction of one methyl group into ammonia strengthens the base the second methyl group further strengthens the base. How ever the introduction of third methyl group decreases the strength of the base. E.g.

                (CH₃)₂NH > CH₃ NH₂> (CH₃)₃NH >NH₃

The introduction of third methyl group increases crowding (steric effect). This steric effect retards the protonation of nitrogen and weakens the base.

                                   

The alkyl group is electron-releasing groups. So alkyl group releases electron towards nitrogen. Thus nitrogen acquires higher tendencies to donate electron and exhibits more basic nature.

The hydrogen doesn't releases the electron towards nitrogen atom so that nitrogen became comparatively less electron rich. Thus it acquires lower tendencies to donate electrons pair, which is weak base.

b) Reactivity of alkyl halides: - More reactivity of alkyl halide than alkanes can be explained on the basis of inductive effect. More the number of alkyl group attached with the halide carbon more will be the polarity of C-Cl bond in alkyl halide thus more reactive.

Among three types of alkyl halides, tertiary alkyl halides consist of three alkyl groups (+I effect) attached with the halide carbon. Thus the carbon chlorine bond in tertiary alkyl halides is more polar than other alkyl halides.

The reactivity order of three types of alkyl halides is as follows.

	H3C—Cl < (H3C)2CHCl  < (H3C)3CCl

 

While the primary and secondary alkyl halides undergo hydrolysis by alkali through SN₂ mechanism, the hydrolysis of tertiary halides proceeds through SN₁ mechanism. The ionization of tertiary halides is facilitated due to the +I effect of the three-alkyl groups attached to the carbon carrying the halogen atom.

 

Mesomeric effect, conjugative effect or Resonance effect: -

The effect takes palace in unsaturated and conjugated system via their Pi- orbital. It is a permanent effect. Consider an example of carbonyl group whose all of the properties can neither satisfactorily be represented by the classical formula (I) not by polar structure (II).

 

The actual structure   is somewhat in between the two forms I and II, known as the resonance hybrid III.

                                                      

Hence the carbonyl group is present in compound with the conjugated system the polarization of electrons is further transmitted through pi- electrons. This type of displacement of electrons may also be caused by the presence of an atom having at least one lone pair of electron in the conjugation with a conjugated system.

This type of resonance may occur in between lone pair of electron and pi-bond.

     Or between positive charge and pi-bond.

 

The mesomeric effects like inductive effects are permanent polarizations and always operate in non-reacting molecules like inductive effect. It also affects the physical properties of the molecules.

Characteristic of mesomeric effects: -

1)                  It is represented by symbol M and indicated by (→) arrow pointing towards the direction of movement of electrons.

2)                  It is generally occurs in conjugated system

3)                  It is permanent effects.

4)                  In this the electron pairs is transferred completely with the result full positive and negative charges   are created.

5)                  It can also me transmitted from one end to the other of quite large molecules provided the conjugation

Mesomeric effect may be +ve M or –ve M. It is +M when the transference of electron pair is away from the atom and –M when transference of electron pair towards the atom.

                           

+M effect is the shown by the atoms or groups of atoms containing lone pair of electrons pair attached with conjugated system. e.g. Halogen, —OR, —OH, —NH₂, —NR₂, —SR and -M effect is shown by groups such as:- >C=O, —NO₂, —CN, —SO₃H etc. when attached to conjugated system.

There are several compounds, which cannot be represented by a single structure. Such compounds are represented by a set of hypothetical structures. The real structure of such compounds is represented by an intermediate of all such hypothetical structures. The true structure is known as resonance hybrid. The other hypothetical structures are known as resonating or canonical or contributing structures and the phenomenon is mesomerism or resonance. Thus resonance may be defined on the phenomenon in which two or more structures involving indicial position of atoms but different by the position of electrons and canonical structures of a system may be defined as any set of hypothetical structure which are sufficient to define all the possible electron distribution. Similarly resonance hybrid can be defined as the actual structure of all different possible structures that can be written for the molecules with out violation the rules of covalence maxima for the atom.

e.g. Benzene can not be represented by a single structures but is said to be a resonance hybrid of following resonating structures or canonical structure.  

 

The resonance defines the stability of molecules. It is found that greater the number of canonical or contributing or resonating structures greater will be its contribution in the formation of resonance hybrid, more will be the stability of resonance hybrid.