p^H and p^OH       

Ion product of water

In the pure state, water is dissociated to a very small extent into hydrogen ion and hydroxyl ion, and behaves as a weak electrolyte. The equilibrium constant of the dissociation, is given by -----

                                H2O <=====> H+ + OH-

                        K =  [H+][OH-] / [H2O]

                        K X [H2O] = [H+][OH- ]

In any dilute aqueous solution, the concentration of the water molecules,(= 55.5 moles/litre) greatly exceeds that of any other ion, [H₂O] can be taken as a constant. Hence,

                           K X [H2O] = Kw = [H+][OH- ]

Where Kw, water dissociation constant (ionic product of water). The [H+] ion concentration in pure water is 1 x 10-7 . Since [H+] = [OH-] in pure water, therefore-

                                      Kw = [H+][OH-] 

                                  = [1x10-7 x1x10-7] 

                                  = [1 x 10-14]

A strong acid such as hydrochloric acid or nitric acid when added to water, the concentration of hydrogen ion increases very high and at that time the concentration of hydroxyl ion becomes very low, so that the product of concentration of hydrogen ion and hydroxyl ion remains constant, similarly when strong base such as sodium hydroxide or potassium hydroxide added to water the concentration of hydroxyl ion increases very high and at that time the concentration of hydrogen ion becomes very low, so that the product of concentration of hydrogen ion and hydroxyl ion remains constant.

                                       The pH and pOH

An aqueous solution whether it is in acidic condition, alkaline condition or in neutral condition it always contains hydrogen ion and hydroxyl ion. The condition of acidic and alkaline depends upon which ion concentration greater than other, If the concentration of hydrogen ion is greater then the solution is acidic condition and if the concentration of hydroxyl ion is greater then the solution is alkaline. Knowing the concentration of one ion other can be calculated, but it is conveinent to express acidity or alkalinity of a solution by reffering to the concentration of hydrogen ions only. Now hydrogen ion concentration can vary within wide limits, usually from about 1 mole per litre (as in 1 M HCl) to about 10-14 mole per litre (as in 1 M NaOH). Sorensen therefore introduced a term pH for indicating hydrogen ion concentration which is defined as :

The negative of the logarithm of [H+] ion concentration was defined as pH.

                                         pH = -log [H+] 

                               Or,[H+] = 10- pH 

Thus if a solution has hydrogen ion concentration   10^-1  M its p^H is 1, and if hydrogen ion concentration is  10^-14  M its p^H is 14. For such solution having [H⁺] ion concentration in the range 10^-1  M to10^-14  M it is more convenient and meaningful to express acidity in terms of p^H rather than ion concentration. As a result, the use of small fractions or negative exponents can thus be avoided. In the case of monobasic acid molarity and normality are the same but in the case of polybasic acid molarity and normality are different. Thus 0.1M H₂SO₄ is equivalent to 0.2 N H₂SO₄, so that :

                           p^H = - log [H⁺]

                                = - log (0.2)

                                = 0.699

The negative of the logarithm of [OH^-] ion concentration was defined as p^OH.

                               p^OH = - log [OH^-]

                              Or,[OH^-] = 10^-pOH 

 

From the above two relations, we know that the lower the p^H, the more acidic the solution is. If the acidity of the solution goes down to 10 fold its p^H goes up by 1 unit. For example, if a solution has p^H 1, its [H⁺] ion concentration is 10 times than for a solution whose p^H is 2. Taking the case of [OH^-] ion concentration, the p^OH will go down by 1 unit (from 13 to 12). Recalling that the product  of [H⁺] and [OH^-] is 10^-14 and, therefore we can write the equation as :

[H+][OH-] = 10-14

log[H+]+log[OH-]=log [10-14]= -14

pH + pOH  = 14 

On the basis of [H⁺] ion concentration and  [OH^-] ion concentration, we can differentiate between acidic, basic and neutral solution on one hand and on the basis of p^H on the other hand.

An acidic solution is one in which [H⁺] ion concentration exceeds that of  [OH^-] ion concentration.

[H+]>[OH-] 

[H+]> 10-7M 

[OH-]< 10-7 M

A basic solution is one in  which  [OH^-] ion concentration exceeds that of [H⁺] ion concentration.

[OH-]> [H+] 

[OH-]> 10-7M 

[H+]< 10-7 M

A neutral solution is one in which [H⁺] ion concentration and [OH^-] ion concentration are equal.

[H+] = [OH-] = (10-14)1/2 = 10-7M

In terms of p^H we have the following relations :

The scale of p^H :

The scale of pH

Carbene

 CARBENE

A reaction in which both the groups or atoms are lost from the same carbon is called an α elimination reaction and results in the formation of carbene.

Carbenes can be defined as neutral divalent carbon intermediates in which a carbon is covalently bonded to two atoms and has two non bonded orbitals containing two electrons between them.

Carbene

The simplest member of the class is methylene a non-isolable species of molecular formula H₂C:

Types of Carbenes

 The two nonbonded electrons of a carbene may be either paired or unpaired. If they are unpaired the carbene is said to be in a triplet state, if they are paired then the carbene is called a singlet. One physical property that the singlet carbene is diamagnetic while the triplet is paramagnetic.

In the singlet state, a carbon atom is presumed to be approximate sp² hybridization. Two of the three sp² hybrid orbitals are utilized in forming two covalent bonds whereas the third orbital contains the unshared pair of electrons. The remaining p-orbital remains vacant.

Singlet Carbene

The R₁—C—R₁angle would be expected to be contracted slightly from the normal 120⁰. The explanation comes from the valence bond electron pair repulsion theory, where l.p—l.p> l.p—b.p> b.p—b.p . Here the inter orbital repulsion will be greatest for the more diffuse lone pair orbital.

The carbon atom of a triplet carbene is sp hybridized. These two hybrid orbitals are involved in the bond formation with two groups and the remaining two electrons are placed, one each of the two unhybrid p-orbitals. These electrons have parallel spins.

Triplet Carbene

Triplet carbene is more stable than the singlet. A triplet carbene is lying at about 8 K.cal/mole lower in energy than the singlet state.

Generation of Carbene

1. Photolysis of diazo compound :

Carbene is usually formed by photolysis of diazo compound when photolysis occurs in the liquid phase singlet carbene generated, but when photolysis occurs in gas phase triplet carbene generated.

Generation of Carbene by Photolysis

2. From ketene : 

Carbene can be generated from ketene, the reaction occurs in the presence of light in the gas phase.

R₂C=C=O ---------> R₂C: + CO

3. From alkyl halide :

The three mixed alkyl halide, such as CHF₂Cl, CHF₂Br, CHF₂I undergo concerted elimination to carbenes.

OH^- + CHF₂Br --------> H₂O + F₂C: + Br^-

4. From the reaction of chloroform and base :

When chloroform reacted with a base like K⁺O^-CMe₃ dichloro carbene is generated.

HCCl₃ + K⁺O^-CMe₃ ------> Cl₃C^- + Me₃COH + KCl

Cl₃C^- ----> Cl₂C: + Cl^-

5. From esters of trichloroacetic acid :

When esters of trichloroacetic acid reacted with a base like MeO^- dichloro carbene is generated.

Cl₃CCOOEt +MeO^- -------> Cl₃C^- + CH₃OCOOEt

Cl₃C^- ----> Cl₂C: + Cl^-

6. From the reaction of carbon tetrachloride with alkyl lithium :

Butyl lithium and carbon tetrachloride react at low temperature (100⁰C) through halogen-metal interchange to give lithium trichloromethane. On warming (60⁰C) this lithium salts yield dichloro carbene.

CCl₄ + C₄H₉Li ------> LiCCl₃ + C₄H₉Cl

LiCCl₃ -------> Cl₂C: + LiCl 

Reactions of Carbene

1.Cycloaddition reaction :

Singlet carbenes add to alkenes in a stereospecific manner i.e stereochemistry of the alkene is retained in the cyclopropane.

Addition of Singlet Carbene

In contrast, the addition of triplet carbenes to alkenes takes place with non stereospecificity.

Addition of Triplet Carbene

The stereochemistry of these cycloaddition is so specific that it may be used as a diagnostic test for the identification of singlet and triplet carbenes.

The difference in behaviour between these two electronic states of a carbene has been explained in the following way. The addition of a singlet carbene to an alkene is a concerted process as there is no spin restriction on the simultaneous formation of two new sigma bonds of the cyclopropane, and hence it is a stereospecific process.

Addition of Singlet Carbene - a concerted process

In the case of triplet carbene, a cyclic transition state is not formed, the addition occurring stepwise as a radical fashion. This is represented as follows, the arrows indicating the direction of spin of each unpaired electron, and the assumption is made that the rotation about the single bond is more rapid than spin inversion.

Addition of Triplet Carbene - stepwise process

2. Insertion reaction :

Frequently carbenes can be inserted into a C—H bond.

Insertion Reaction of Carbene

The mechanism for insertion are recognized, it may be one step process or it may be two steps process.

Mechanism of Insertion Reaction of Carbene

3.Simon-smith reaction :

Difficulty for the preparation of cyclopropane derivative using :CH₂ and the solution is by using Simons-Smith reagent.

The addition of methylene, derived from diazomethane, ketene etc, to olifins is synthetically inefficient since insertion is a competing reaction.

Reaction of cyclohexene with carbene

When an alkene is treated with methylene diiodide CH₂I₂,in presence of Zn-Cu couple we get a cyclopropane derivative.

Simon-Smith Reaction of Carbene

This is known as Simon-Smith reaction. 

 Boron Nitride (Inorganic Graphite)

Much of B—N chemistry relates that a BN unit isoelectronic with the CC unit. The electronegativity and atomic radius of carbon are intermediate between boron and nitrogen. Therefore there are many azoborane analogues of hydrocarbon in which a pair of carbon atoms replace B and N unit. Boron Nitride an important ceramic material that is isoelectronic with graphite. Boron Nitride has a similar sheet-like structure except that rings are aligned in an eclipsed fashion rather than staggered in graphite. Hexagonal Boron Nitride is colourless, electrically nonconducting, and is more resistant to chemical attack than graphite.

Preparation of Boron Nitride 

Boron reacts with N or NH₃ on heating to form a binary nitride BN which is a white refractory solid. This compound is also obtained by fusing borax with NH₄Cl.

Na₂B₄O₅(OH)₄ + 2NH₄Cl -----> 2NaCl + 2BN + 2B₂O₃ + 6H₂O

Pure Boron Nitride is best obtained by heating boron amide. This decomposes first to boron imide and finally into Boron Nitride.

2B(NH₂)₃ -----> B₂(NH)₃ + 3NH₃

                 B₂(NH)₃ ------> 2BN + NH₃

Boron Nitride is also prepared by heating borazine--

B₃N₃H₆ ------> 3BN + 3H₂

Property of Boron Nitride

Boron Nitride is a white powder of density 2.34. It melts under pressure at 3000 ⁰C. It is a high melting refractory solid, very stable, and unreactive. It is unchanged by aqueous acids or alkalis, Cl₂, H₂, O_2, etc.

It is decomposed by steam --

2BN + 3H₂O = B₂O₃ + 2NH₃

It reacts with F₂ and HF at a lower temperature --

2BN + 3F₂ = 2BF₃ + N₂

BN + 4HF = NH₄BF₄

It is decomposed by alkali on fusion --

BN + KOH + H₂O = KBO₂ + NH₃

Structure of Boron Nitride

One B atom and one N atom together have the same no of valence electron as two carbon atoms. Thus Boron Nitride has a graphite-like layer structure. The layers are made up of hexagonal rings of alternate B and N atoms joined together. The B—N distance (1.45 A) in Boron Nitride is comparable to the C—C distance (1.42 A) in graphite. The layer spacing in Boron Nitride and graphite is also comparable. Both have the same density. This form of Boron Nitride is often called Inorganic Graphite. Each B and N is sp² hybridized as each six C-atom in graphite. The three sp² hybrid orbitals of each B overlaps with hybrid orbitals of three neighboring N atoms. The unhybridized p-orbital then accepts a lone pair forming a π-bond. Through resonance, all the B—N bonds become equivalent in Boron Nitride.

Structure of Boron Nitride and Graphite

Uses of Boron Nitride 

Boron Nitride possesses the same hardness as diamond and can withstand a temperature of more than 3000 ⁰C. Due to this property Boron Nitride is used for coating crucible linings, it is also used as a lubricant.

ABOUT HELIUM

 HELIUM

Symbol --- He

Abundance --- in the universe (23%), in the earth crust (5.5 x 10^-7%)

Physical state --- gas

Elemental Category --- noble gas

Colour --- colourless

Discovery --- Pierre Janssen, Norman Lockyer (1868)

Atomic no --- 2

Atomic weight --- 4.0026

Period --- 1

Group --- 18

Block --- s-block

Known Isotopes--- ₂He² ₂He³ ₂He⁴ ₂He⁵ ₂He⁶ ₂He⁷ ₂He⁸ ₂He⁹ ₂He¹⁰   

Stable Isotopes --- ₂He³ ₂He⁴

Isotopic abundance ---

[₂He³(0.0002%),₂He⁴(99.9998%)]

Melting Point --- 0.95 K or -272.20 ⁰C

Boiling Point --- 4.22 K or -268.93 ⁰C

Density (at STP) --- 0.1786 g/L

Electron Configuration --- 1s²

Oxidation States --- 0

Valence --- 0

Ionisation Energy --- 2372.3 KJ/mol (1st), 

5250.5 KJ/mol (2 nd)

Covalent Radius --- 28 pm

Van der Waals radius --- 140 pm

Crystal Structure --- Hexagonal closed packed (hcp)

Heat of fusion --- 0.0138 KJ/mol

Heat of vaporisation --- 0.0829 KJ/mol

Triple Point --- 2.177 K, 5.043 KPa

Critical Point --- 5.195 K, 0.227 MPa (2.24 atm)

Molar heat capacity --- 20.78 J/mol-K

Specific heat --- 5193.1 J/(Kg-K)

Thermal conductivity --- 0.1513 W/(m k)

Adiabatic index --- 5/3

Molar volume --- 0.022424

Refractive index --- 1.000035

Speed of sound --- 972 m/s

Magnetic type --- diamagnetic

Mass magnetic susceptibility ---  - 5.9 x10^-9 m³/kg

Molar magnetic susceptibility --- - 2.36 x10^-11 m³/mol 

Lattice angles --- π/2, π/2, π/2

Lattice constants --- 424.2 pm,424.2 pm,424.2 pm 

Quantum numbers --- ¹S₀

Neutron cross section --- 0.007

Neutron mass absorption --- 0.00001

About Helium

SYNTHESIS OF CARBON NANOTUBES

CARBON NANOTUBES

Carbon nanotubes have seamless cylindrical structure contains one or more graphene layers, there are single wall carbon nanotube (SWCNT) and multi wall carbon nanotube (MWCNT), with open or closed ends. For perfect structure of carbon nanotubes the bonding of all carbons in carbon nanotubes are in hexagonal lattice except at their ends, other bonding patterns are pentagons, heptagons.The fundamental carbon nanotube is a single wall structure and best described as a rolled-up tubular shell of graphene sheet, the body of the tubular shell is made up of hexagonal rings (in a sheet) of carbon atoms, where as the ends are capped by a dome-shaped half fullerene molecules. Diameter of single wall carbon nanotube is 0.8 - 2 nm.The arrangement of the carbon atoms in the hexagonal network of the multi wall carbon nanotube is often helicoidal, resulting in the formation of chiral tubes. Multi wall carbon nanotube will typically be composed of a mixture of cylindrical tubes having different helicity or no helicity, thereby resembling turbostratic graphite. Diameter of multi wall carbon nanotube is 2 - 20 nm.

SYNTHESIS OF CARBON NANOTUBES

Carbon nanotubes can be prepared by varius ways, such as arc discharge, laser ablation, chemical vapor  deposition (CVD), electrolysis, flame synthesis etc.

1. Arc Discharge ---

For the synthesis of carbon nanotubes this is one of the oldest method . 4-30 nm in diameter and 1 mm in length carbon needles were grown on the negative electrode used for the direct current (DC) arc discharge. A gas mixture of 10 Torr methane and 40 Torr argon filled in a pressurised chamber used during the process. Two thin electrodes installed vertically in the center of the chamber. The cathode, that is the lower electrode had a shallow dip to hold a small piece of iron during the evaporation. A DC current of 200 A and 20 V was used between the electrodes for the generation of arc. For the synthesis of single wall carbon nanotube (SWCNT) the use of three components such as methane, argon and iron was essential. As a result of arc discharge carbon soot was produced and carbon nanotubes grew in the negative cathode that contained a iron catalyst. The diameter of the nanotubes distributed between 0.7 nm to 1.65 nm.

2. Laser Ablation ---

A pulsed laser is made to strike at graphite target in the laser ablation process, in the presence of a inert gas such as helium in a high temperature reactor for vaporizes a graphite target. As the vaporized carbon condenses the nanotubes were developed on the cooler surfaces of the reactor. For the vaporization of target more rapidly a second pulse was used, that is in this process two step laser ablation was used. The benefit of two step laser process for minimised the carbon deposited as soot. In this method tubes grow on catalysts atoms and grows continued until to many catalysts atoms aggregate at the end of the tube. The produced carbon nanotubes diameter was 10 - 20 nm and length was 100 micron or more. By varying the reaction condition such as temperature, catalyst composition the average diameter and length of the produced carbon nanotubes could ve varied.

3. Chemical vapor deposition (CVD) ---

For the production of carbon nanotubes in large scale chemical vapor deposition (CVD) is a useful method. This method is very useful for controlling the growth of carbon nanotubes. In this process in the reaction chamber at a temperature of (700 ⁰C – 900 ⁰C) and at atmospheric pressure a mixture of hydrocarbon gases such as methane, ethylene, acetylene and process gases such as hydrogen, nitrogen, ammonia is made to react on heated metal substrate. Since hydrocarbon gas deposit and grows on metal catalysts (substrate), so carbon nanotubes was formed. On growing carbon nanotubes catalyst particles can stay at the bottom or on the top. The choice of metal catalysts and substrate were very important because they controlled the nature and type of carbon nanotubes. Generally silicon used as a substrate, sometimes aluminium even glass used as a substrate. Fe, Co, Ni metal nanoparticles were used as a catalyst. The diameter of the nanotube depends on the catalyst and substrate.