Electro Chemistry

Making rolled gold ornaments, electroplating, extraction of metals, purification of metals, alloys, car battery, dry cells, preparation of chemical substances like NaOH, redox reactions, electrolysis and production of electrical energy by electrochemical cells are some of the applications of electrochemistry. The branch of chemistry that explains the relation between electrical energy and chemical energy. Flow of electrons is considered as electric current. If the flow of current takes place through metals it is called electronic conduction, if takes place through fused or aqueous, acidic, alkaline, salt solutions is called electrolytic conduction. Electrolytic conductors are electrolytes. Strong acids, bases, salt solutions are strong electrolytes whereas weak acids, bases are weak electrolytes. If the substances are unable to pass electricity either in molten state or in aqueous state are called non electrolytes.
* Electrolytic solutions offer resistance (R) to the flow of current, which is directly proportional to 'l' (distance between the two parallel electrodes of the cell) and inversely proportional to a (area of cross-section of the electrode).
 

       
 

Specific conductance (K): The conductance of an electrolytic solution enclosed between two parallel electrodes of Unit area of cross-section (a) and separated by a Unit distance (l).
            K = C. l/a           Units of K: ohm^-1 m^-1
 

Equivalent conductance (Λ): The conductance of a solution containing 1 gram equivalent of electrolyte present between two parallel electrodes, separated by Unit distance (1 m or 1 cm).
                          Λ = K × 1000/N  ohm^-1 m² equivalent^-1
 

^{Molar conductance (µ): The conductance of a solution containing 1 gram mole of electrolyte present between two parallel electrodes, separated by Unit distance.}
                             ohm^-1 m² mole^-1
 

Conductance ratio (α): The ratio of equivalent conductance at any concentration (Λ _c) to that at infinite dilution (Λ₀).

 For weak electrolytes 'α' is called degree of ionization. Debye - Huckel - Onsagar equation explains the relation between Λ _c and Λ _∞ as below.

D = Dielectric constant of water                C = Concentration
 T = Temperature in Kelvin scale               η = Viscosity of water.
 

Kohlrausch's law: The equivalent conductance of an electrolyte at infinite dilution (Λ_∞ ) is equal to the algebraic sum of equivalent conductance of cation (λ⁺_∞ ) and anion (λ^-_∞ ).
                          (Λ_∞^Electrolyte )  =  λ⁺_∞  + λ^-_∞.
Applications: 1) In the calculation of ''Λ_∞'' of weak electrolyte.
                             2) To calculate "α" of weak electrolytes.

3) To calculate solubilities of sparingly soluble salts like BaSO₄.
^{Degree of dissociation (α): α =}  

 λ⁺_∞, λ^-_∞ are ionic conductances at infinite dilution. These are directly proportional to ionic mobilities (u⁺, U ^-).

λ⁺_∞ =  K. u⁺_∞ , λ^-_∞ = K. U^-_∞
^{K =  Proportionality constant.} 

The process of decomposition of a chemical compound (either in molten state or in aqueous state) into its constituent elements under the influence of EMF is called "electrolysis". Anions move towards anode and oxidised and cations move towards cathode and reduced. Two Faradays electricity is required to electrolyse 1 mole of water (acidified/ alkaline). Mg, Na (Castner, Down methods) can be extracted by electrolysis. NaOH (Nelson cell) or Cl₂ also obtained during electrolysis. To carry out electrolysis, inert electrodes (Pt) or metallic rods of same salt solution (active electrodes) are used.

 

Chemical Kinetics

Some chemical reactions occur slowly and some reactions that occurs rapidly. The branch of Chemistry that deals with rates of reactions and influencing factors of the rates is called Chemical Kinetics. Reactants are consumed to form the products with time. Meanwhile the concentration of the reactants decreases, products increases with time.

The change (decrease) in molar concentration of reactants or the increase in molar concentration of products in Unit time is known as the rate of a reaction.

Units of reaction rate: Moles lit⁻¹ sec⁻¹.

             Rate = 

           The relation between the rates of the reactants P, Q and the products R, S for the reaction

           x P + y Q → mR + nS is 

      

Factors effecting reaction rates:

1. The chemical nature of the reactants: Rate of a reaction mainly depends upon the chemical nature of the reactants. A reaction taking place between ionic compounds is faster than the reaction taking place between covalent compounds. For example the reaction between
Ag⁺ (aq.) and Cl ^- (aq.) occurs very fast to give AgCl (white precipitate).

          NaCl (aq.) + AgNO₃ (aq.) →  AgCl ↓ + NaNO₃ (aq.)

The reactions taking place between covalent compounds involve breaking of existing bonds and making of new bonds. Hence such reactions take much time. Formation of NH₃ from N₂ and H₂

           N₂ (g) + 3 H₂ (g)     2 NH₃ (g)

2. Concentration of reactants: The rate of a reaction increases with the concentration of reactants. If the concentration increases, number of molecules, collisions among them increases to increase the rate. It was well explained by Guld Berg and Waage by the Law of Mass Action. According to this law "The rate of a reaction is directly proportional to the product of active mass of reacting substances".

             cⁿ  or     =  k. cⁿ

Where  k = rate constant            

              c = concentration of reactants         

             N = order of the reaction.

3. Effect of temperature: According to Arrhenius equation, the rate of a reaction increases with increase in the temperature of the reaction. For every 10°C rise of temperature, specific rate or rate constant gets doubled.

Temperature coefficient = 

Arrhenius equation 

                        

where  A = Arrhenius frequency factor

             R = Gas constant

           E_a = Activation energy

     k₁, k₂ = Rate constants at = T₁K,  T₂K

According to collision theory of reaction rates, with the rise of temperature, the number of activated collisions increases to increase the rate of a reaction.

4. Effect of catalyst: Reactions take place slowly at room temperature. But in presence of a positive catalyst (the substance that increases the rate of a reaction without being consumed during the course of the reaction), the path of the reaction changes in which activation energy is low and the rate of the reaction is more.

e.g.: 2 KClO₃  2 KCl + 3 O₂    

         Sun light, surface area of the reactants are other influencing factors of rate.

Rate Law or Rate equation: The mathematical equation that explains the dependence of the rate of a reaction on the concentration of the reactants.

         Rate equation for the reaction

          2 NO + Cl₂→ 2NOCl  is Rate (v) = k [NO]^₂ [Cl₂]

 This is possible only in elementary reactions but not in all reactions. It is not possible to write rate equation for every balanced reaction. It is to be written according to experimental results.

       Units of Rate constant (k) =   

For nth order, Units of k: (lit.) (n ^-1) moles ^{1 - n} sec^-1.

Order of reaction: "The sum of the powers of the concentration terms in the rate equation of the reaction". Order is experimentally determined. This can have values including zero, negative, positive, fractional values.

1st order reaction: N₂O₅ (g) → N₂O₄ (g) +  ½ O₂ (g)              Rate = k [N₂O₅]¹

2nd order reaction: 2 N₂O (g) → 2 N₂ (g) + O₂ (g)                   Rate = k [N₂O]²

3rd order reaction: 2 NO (g) + O₂ (g) → 2 NO₂ (g)                   Rate = k [NO]² [O₂]¹

Zero order reaction: H₂ (g) + Cl₂ (g)     2 HCl (g)      Rate = k [H2]⁰ [Cl2]⁰

Molecularity of reaction: Number of atoms or ions or molecules participating in rate determining step. This is known theoretically from the reaction mechanism. This can have values 1 or 2 or 3, but not fractional or negative or zero. Order of a reaction can be determined from trial and error method, Half-life method, Van't Hoff differential method and Ostwald isolation method.

INTEGRATED RATE EQUATIONS

Zero Order Reactions:

If the rate of the reaction is proportional to zero power of the concentration of reactants, the reaction is called Zero Order Reaction.

R (Reactants) →P (Products)

Rate = k [Reactants]⁰

 d(R) = −k.dt

Integrating both sides

R = −kt + I  (1)

I = Constant of  integration

At t = 0, R = [R]₀

[R]₀ = initial concentration of the reactant

[R]₀ = −k × 0 + I

 I = [R]₀  (2)

Substituting (2) in (1)

R = −kt + [R]₀

−kt = [R] − [R]₀

kt = [R]₀ − [R]

FIRST ORDER REACTIONS

If the rate of the reaction is proportional to first power of the concentration of the reactants, the reaction is called First Order Reaction.

   Rate of the reaction = k [Reactants]¹

   R = Reactnts, P = Products

   R →P

Integrating both sides

   ln R = −kt + I  (1)

I = Integration Constant

When t = 0, R = [R]₀

R0 = initial concetration of the reactant

  ln [R]0 = −k × O + I

  I = ln [R]₀ (2)

By substituting (2) in (1)

  ln R = −kt + log [R]₀

HALF LIFE OF A REACTION

The time in which the concetration of a reactant is reduced to half of its initial concentration.

For Zero Order Reaction: 

 

FOR FIRST ORDER REACTION:

PSEUDO FIRST ORDER REACTION

If a bimolecular (molecularity = 2) reaction behaves like first order reaction, then that reaction is called as 'Pseudo First Order Reaction'.

As the concentration of water does not change during the course of the reaction, it behaves as first order reaction.
 

COLLISION THEORY OF CHEMICAL REACTION RATES
¤ This theory was proposed by Arrhenius and developed by Max Trautz & William Lewis to explain the rates of gaseous reactions.
¤ It is based on kinetic theory of gases.
¤ According to this theory the reactant molecules are assumed to be hard spheres.
¤ Collisions must takes place between reactants (molecules) to occur a reaction.
¤ Collisions are possible if 2 or more molecules are present.
¤ The minimum energy must be possessed by the reactant molecules to give products is called threshold energy (E_T).
¤ Molecules having other than threshold energy are called "normal molecules".
¤ Collisions between normal molecules are called "normal collisions", which do not lead the chemical reaction, hence products are not formed.
¤ In addition to the normal molecules, the molecules must aquire some extra amount of energy, called "activation energy" (E_a).
    Ea = E_T − E_R
¤ The molecules possesing threshold energy are called activated molecules.
¤ Proper orientation of reactant molecules lead to bond formation and products are formed.
¤ Collisions occuring between activated molecules with proper orientation are called "effective collisions".
¤ Effective collisions are less in number, when compared to normal collisions.
¤ The number of collisions per second per unit volume of the reaction mixture is known as collision frequency (Z). Activation energy also affects the rate of a reaction.

or a bimolecular elementary reaction
A + B →Products
Rate = P.ZAB. e−Ea/RT
ZAB = Collision frequency of reactants A & B
P = Probability (Steric) factor
E_a = Activation energy
R = Universal gas constant.
¤ Rate of a reaction is determined by Ea & proper orientation of the molecules.
e.g.: Formation of CH₃OH from CH₃Br
 

Drawbacks:

¤ It considers atoms or molecules as hard spheres.
¤ It ignores structural aspect of molecules.