find f(x) and g(x)

Electrochemical or Galvanic or Voltaic Cells

An Electrochemical Cell is a device used to convert chemical energy (produced in a redox reaction) into electrical energy.

Electrochemical Cells are also known as Galvanic or Voltaic Cells.

If we take a zinc rod and place it in a container filled with copper sulphate solution heat will be produced. This happens due a spontaneous redox reaction given below:

Zn(Solid) + CuSO₄(Aqueous) ZnSO₄(Aqueous) + Cu (Solid) deposited

As the reaction would proceed the zinc rod would get eroded ,copper particles would get deposited and solution would becom warm

.

It would be useful to be able to convert this chemical energy to electrical energy instead of heat energy. This is done by an electrochemical cell.

Construction of an Electrochemical Cell

Let us use the redox reaction given below to explain the construction of an Electrochemical Cell.

Zn(Solid) + CuSO₄(Aqueous) ZnSO₄(Aqueous) + Cu (Solid)

The ionic form of the reaction is:

Zn + Cu²⁺ Zn²⁺ + Cu

This reaction can be split into the following two half reactions.

1. Oxidation half reaction

Zn Zn²⁺ + 2e^-

2. Reduction half reaction

Cu²⁺ + 2e^- Cu

An Electrochemical Cell

The oxidation reaction in the zinc rod releases two electrons.These two electrons are taken by the Copper ion in the copper sulphate solution.

If these two half reactions can be separated then the electrons can be made to move through a wire.

In this manner we can produce electical energy from chemical energy.

The salt bridge is a concentrated solution of inert electrolytes. It is required for completing the circuit. It allows the movement of ions from one solution to the other.

kanika

Electrolysis

It is the process of decomposition of an electrolyte by the passage of electricity through its aqueous solution or molten state.

Mechanism of electrolysis

When ever an electrolyte is dissolved in water or taken in the molten state it dissociates into positive and negative ions. The positive ions are known as cations and the negative ions are known as anions.

On passing electric current through the electrolyte cations move towards the cathode and anions move towards the anode.

On reaching their respective electrodes these ions loose their charge. On loosing their charge they get deposited on the electrode or discharged as a gas.

Let us take an example of electrolysis of aqueous copper sulphate solution using inert electrodes such as platinum electrodes.

In the aqueous solution copper sulphate dissociates into its respective ions.

CuSO₄ Cu²⁺ + SO₄ ^2-

On passing electric current the copper ions(cations) move towards the cathode and get deposited as copper. Simultaneously the sulphate ions(anions) move towards the anode.

Faraday's Laws of Electrolysis

Faraday's First Law of Electrolysis

The mass of a substance deposited or liberated at any electrode is directly proportional to quantity of electric current passed.

If W grams of a substance is deposited or liberated on passing Q Coulomb of charge then :

W Q

and W = Z x Q

where Z is the proportionality constant and is called the Electrochemical Equivalent

Faraday's Second Law of Electrolysis

When the same amount of charge is made to pass through any number of electrolytes, the mass of the substance liberated or deposited at the electrodes are directly proportional to their chemical equivalents.

Chemical equivalent = atomic mass / valence

m₁/m₂ = E₁/E₂

where m₁ and m₂ are the respective masses liberated or deposited on the electrodes

and E₁ and E₂ are the chemical equivalents of the substances liberated or deposited.

ELECTROCHEMISTRY

Electrolysis , Faraday's Laws of Electrolysis , Electrochemical or Galvanic or Voltaic cells

Electrochemical or Galvanic or Voltaic Cells

An Electrochemical Cell is a device used to convert chemical energy (produced in a redox reaction) into electrical energy.

Electrochemical Cells are also known as Galvanic or Voltaic Cells.

If we take a zinc rod and place it in a container filled with copper sulphate solution heat will be produced. This happens due a spontaneous redox reaction given below:

Zn(Solid) + CuSO₄(Aqueous) ZnSO₄(Aqueous) + Cu (Solid) deposited

As the reaction would proceed the zinc rod would get eroded ,copper particles would get deposited and solution would becom warm

.

It would be useful to be able to convert this chemical energy to electrical energy instead of heat energy. This is done by an electrochemical cell.

Construction of an Electrochemical Cell

Let us use the redox reaction given below to explain the construction of an Electrochemical Cell.

Zn(Solid) + CuSO₄(Aqueous) ZnSO₄(Aqueous) + Cu (Solid)

The ionic form of the reaction is:

Zn + Cu²⁺ Zn²⁺ + Cu

This reaction can be split into the following two half reactions.

1. Oxidation half reaction

Zn Zn²⁺ + 2e^-

2. Reduction half reaction

Cu²⁺ + 2e^- Cu

An Electrochemical Cell

The oxidation reaction in the zinc rod releases two electrons.These two electrons are taken by the Copper ion in the copper sulphate solution.

If these two half reactions can be separated then the electrons can be made to move through a wire.

In this manner we can produce electical energy from chemical energy.

The salt bridge is a concentrated solution of inert electrolytes. It is required for completing the circuit. It allows the movement of ions from one solution to the other.

kanika

Here is a short summary of chemical bonding , very imp for iit
Chemical Bonding and Molecular Structure

Chemical Bond: It is the force which keeps atoms together in a molecule. The causes of formation of a chemical bond are:

• 
  

  Tendency of atoms to complete their octets or duplets by rearrangement of their valence electrons (octed theory).
  

• 
  

  The system acquires minimum energy when atoms are at some equilibrium distance where attractive forces dominate over repulsive forces.
  

Types of Chemical Bonds:

• 
  

  Ionic bond
  

• 
  

  Covalent bond
  

• 
  

  Metallic bond
  

• 
  

  Co-ordinate bond
  

Ionic Bond:

a) Favourable conditions to form Ionic Bond:

• 
  

  Formed between electro positive element (group 1,2,13) and electro negative element (group 15,16,17)
  

• 
  

  E.N >=2
  

• 
  

  Lower I.E of one atom and high E.A of second atom
  

• 
  

  Higher lattice energy
  

• 
  

  Larger cations, smaller anions
  

b) Properties: Crystaline, stronger force of attraction, thermally stable, low volatality, high density, high melting point and boiling point, highly soluble in polar solvent, good conductor of electricity in molten or solution state, nondirectional bond.

Covalent Bond:

a) Favourable conditions to form Covalent Bond:

• 
  

  Formed between two electronegative elements (group 14,15,16,17)
  

• 
  

  E.N < 1.9
  

• 
  

  Small cations, larger anions (Fajan's Rule)
  

• 
  

  High charges on cation and anion (Fajan's Rule)
  

• 
  

  Covalent bond is formed by sharing of electrons by two atoms to complete their octet or duplet
  

b) Properties:

• 
  

  Compounds containing covalent bonds under normal condition of pressure and temperature exist as gases or liquids of low boiling point due to weak Vander Wall's force
  

• 
  

  Relatively low melting point and boiling point, generally non-conductor, and soluble in non-polar solvent
  

• 
  

  As the bond is rigid and directional, compounds with covalent bond show isomerism
  

• 
  

  Covalency of the atom is equal to the number of covalent bonds formed by the atom
  

Bond Length: It is the average distance between the nuclei of two bonded atoms. It depends upon:

• 
  

  Size of the atom: Bond length increases with increase in the size of atom (HI > HBr > HCl > HF)
  

• 
  

  Multiplicity of bond: Bond length decreases with multiplicity of bond (C-C > C=C )
  

• 
  

  Type of hybridisation: More s-character, shorter is the bond length, greater is the acidity with comparable compound
  

Bond Energy: It is the energy required to break one mole of bonds of a particular type of substance in gaseous state.

Bond Angle: It is the internal angle between the orbitals containing electron pairs in the valence shell of the central atom in a molecule:

• 
  

  More the lone pairs on the central atom, smaller is the bond angle due to bp repulsion
  

• 
  

  More electronegative the central atom, more is the bond angle
  

• 
  

  More electronegative the surrounding atoms, lesser is the bond angle
  

VBT: Proposed by Heitler and London and extended by Pauling and State. The postulates are:

• 
  

  Overlapping of atomic orbitals of valence shells of two atoms leads to the formation of a covalent bond
  

• 
  

  Half filled orbital and opposite spin electrons are used
  

• 
  

  - bond is formed by head on overlapping, - bond is formed by lateral overlapping
  

• 
  

  Greater the overlapping, stronger is the bond
  

• 
  

  - bond is stronger than - bond and - bond is directional while - bond is non-directional
  

• 
  

  The directon of the bond is the same as the direction of overlapping of orbitals
  

• 
  

  The strength of - bond follows the order s -s < s - p < p - p
  

• 
  

  Paired electrons are shifted to higher energy levels while forming a bond
  

• 
  

  VBT cannot explain paramagnetic behaviour of O₂
  

Hybridization:

• 
  

  Number of hybrid orbitals = number of atomic orbitals intermixed
  

• 
  

  Hybrid orbitals form -bond on overlapping
  

• 
  

  It does not take place in and isolated atom. It occurs only during bond formation
  

• 
  

  Hybrid orbitals tend to remain far apart therefore repulsion order is lp-lp>lp-bp>bp-bp
  

• 
  

  Total number of hybrid orbitals of central atom = Number of its - bond pairs + Number of lone pair of electrons around the central atom
  

• 
  

  Different types of hybridization are sp, sp² , sp³ , sp³d ,sp³ d² ,sp³ d³
  

MOT: The theory was developed by Hund & Mulliken. The basic postulates are:

• 
  

  All atomic orbitals are mixed up to form molecular orbitals
  

• 
  

  Total M.O = Total A.O
  

• 
  

  Two A.O. combine to form tow M.Os. One is anti bonding M.O. and the other is bonding M.O.
  

• 
  

  The filling up of electrons must follow Aufbau's principle., Pauli exclusion principle and Hund's rule.
  

• 
  

  Bond order = (N_b - N_a )/2 where N_b = Number of electrons in bonding M.O and N_b = Number of electrons in antibonding M.O
  

• 
  

  Bond order Bond energy 1/Bond length
  

Dipole Moment(µ):

• 
  

  Common in covalent compounds when formed between two dissimilar atoms
  

• 
  

  Used to predict the extent of polarity in a molecule
  

• 
  

  A vector quantity so follows vector addition or subtraction rule in predicting net dipole moment of a molecule
  

• 
  

  Can predict the shape of molecules, H₂ O - bent, BeF₂ - linear
  

Metallic Bond:

a) Favourable conditions to form Metallic Bond:

• 
  

  Formed between Electro positive ions packed in one of the 3 arrangements (1.CCP(or FCC), 2.HCP, 3 BCC)
  

b) Properties:

• 
  

  Negatively charged electrons hold the ion together
  

• 
  

  Highly conducting becauls the mobility of these electrons through the lattice
  

• 
  

  High m.p and b.p
  

• 
  

  If soluble, then soluble only in polar solvents of high dielectric constant
  

Co-ordinate Bond:

a) Favourable conditions to form Metallic Bond:

• 
  

  One of the group or or atom must have a lone pair of electrons whereas the other must have the incomplete octet or duplet.
  

• 
  

  Also known as dative bond
  

b) Properties:

• 
  

  Intermediate between ionic and covalent compounds
  

• 
  

  Sparingly soluble in water, not forming ions, largely soluble in non-polar solvents
  

• 
  

  Melting and boiling points are higher than purely covalent compounds but less than purely ionic compounds
  

• 
  

  Stable as covalent compounds, addition compounds are very stable
  

• 
  

  Non conductor
  

• 
  

  Bond is rigid and directional
  

• 
  

  High value of dielectric constant
  

Other Bonds:

a) H-bonding: When H is attached to N, O, F

• 
  

  It's strength is about one tenth of a covalent bond
  

• 
  

  Small size and high electronegativity of atoms forms a strong H-bond
  

• 
  

  They are of twor types; intermolecular (between two molecules) and intramolecular (within a molecule)
  

• 
  

  Used to predict boiling point and density of water, solubility of alcohols and carboxylic acids in water.
  

b) Dipole-dipole interactions:

• 
  

  These exist between molecules having permanent dipoles e.g. H-Cl, I-F etc
  

c) Ion-dipole interactions:

• 
  

  Between and ion and a polar molecule eg hydration of ions like Na⁺ , Mg²⁺ etc
  

• 
  

  Smaller the ion, more the dipole moment, stronger will be these interactions
  

d) Ion-induced dipole interactions:

• 
  

  Between an Ion and a dipole induced by the ion in a nonpolar molecule
  

e) Dipole-induced dipole interactions:

• 
  

  Between a dipole and and induced dipole in a non polar molecule
  

f) Dispersion forces:

• 
  

  Between two nonpolar substances. The forces are between an instantaneous dipole and and induced dipole eg in O₂ , N₂ , He, Ne, Ar etc
  

Note: Dipole-dipole, dipole-induced dipole and dispersion forces are called Van der Wall's forces

if a point is not in the domain of the function will it be a point of discontinuity?

for eg in    1/x-2 will 2 be considered a pt of discontinuity as we dont include 2 in the domain of the function?

what is the difference between sin x and sinh x ?

please solve for the same

ammonium carbamate when heated to 473 K, gives mixture of ammonia and carbon dioxide with density of 16. what is the degree of dissociation of ammonium carbamate?

General statement:

• The effect of the induced emf is such as to oppose the change in magnetic flux that causes the induced emf.

Appling Lenz' Law: Method One - Determining the Direction of Secondary B-Field

• The induced emf creates a current that itself creates a secondary magnetic field. This secondary magnetic field also changes with time and thus creates a changing secondary magnetic flux. The secondary flux changes in such a way to opposes the change in flux creating the emf.

Normally this means that the secondary magnetic field increases or decreases in such a way as to oppose the change in the magnetic field creating the induced emf.

Permanent Magnet Example: The magnetic field of a permanent magnet emanates out of its north pole and enters its south pole. The B-field is also stronger closer to its poles.

When the north pole of a permanent magnet is pushed into a loop (Fig b) the flux increases. An upwards secondary magnetic field is created that opposes the downward B-field of the magnet. As viewed from above, the current in loop must flow counterclockwise in order to create this secondary B-field. Don't be mislead, it is the changing flux created by the changing secondary B-field which opposes the changing flux created by the permanent magnetic being pushed down and not just the creation of secondary B-field in the opposite driection.
When the magnet is removed from the loop (Fig c), the decreaing B-field in the loop creates a decreasing flux. To oppose this decrease, the current in the loop flows in such a way that tries to sustain the magnetic field. The current now has to flow clockwise in order to create a positive secondary flux that tries to counter acts the decreasing flux due to the with drawl of the permanent maget. This means that the secondary magnetic field has to be in the same direction as the magnets B-field.

Applying Len'z Law: Method Two - Determining the Sign of the various Terms

• Choose a positive direction for area of the loop A. The direction of A is normal to the surface - either up or down in the example below.
  
  
  
  


• The right hand rule: With your thumb pointing along the direction chosen for A , the curl of your fingers gives the positive direction for e.

1) a+b=c+d . the reaction quotient q during initial stages of reaction is

a) 0    b) increases with time

2) ammonium carbamate when heated to 473 K, gives mixture of ammonia and carbon dioxide with density of 16. what is the degree of dissociation of ammonium carbamate?

Q1. in a vessel containing SO₂, O₂, SO₃ at eq. some he gas is introduced so that total pressure increases while temp and vol remain constant. so, dissociation of SO_{3 will}

_a)  increase

b.decrease

c. remain unaffected

Q2, For 4NH₃+5O₂ = 4NO+6H₂0

Kc HAS THE DIMENSIONS OF

a> conc⁺¹           b) it is dimensionless

p, q, r are real nos with p+q+r=0, then roots of 3px are

1) positive 2)negative 3)real and distinct 4)imaginary