CONDUCTOMETRIC TITRATIONS

Conductometric titration of strong acid with strong base

Consider the conductometric titration of a strong acid, HCl with a strong base, NaOH. Since both the acid HCl and the base NaOH are strong, so complete dissociation occurred. Here neutralization mean replacement of H⁺ ions by an equal number of Na⁺ ions.

H⁺ + Cl^- + [Na⁺ + OH^-] -----> Na⁺ + Cl^- + H₂O

H⁺ ion has much higher ionic conductance than that of Na⁺ ion. So, the conductance of the solution will decrease as more and more NaOH is added. When all the H⁺ ions replaced by the Na⁺ ions, conductance will reach the lowest limit. Any subsequent addition of NaOH means increase in the numbers of both Na⁺ ions and fast moving OH^- ions. These are no longer removed, the conductance therefore increases linearly with addition of NaOH. On plotting the conductance against the volume of alkali added, the point of intersection of two lines, that is the lowest point, corresponds to the minimum conductance, which is the exact neutralization point of this conductometric titration between HCl and NaOH.

Strong acid with strong base

Conductometric titration of weak acid with strong base

Consider the conductometric titration of a weak acid, CH₃COOH with a strong base NaOH. Since the acid is weak, the conductance of the acid will be low on account of its poor dissociation. As NaOH is added the OH^- ion removed the H⁺ ion by producing H₂O. Undissociated CH₃COOH molecules produce fresh H⁺ ions. The conductivity of the solution rises due to presence of some Na⁺ ions. At the starting stage, due to common ion effect, there may be a little fall in conductivity, but later on this fall will be insignificant compared to rise in the conductivity of the solution due to the added new Na⁺ ions.

CH₃COOH+[Na⁺ + OH^-] ----> CH₃COO^- + Na⁺ + H₂O

The total volume of CH₃COOH dissociates slowly in this way and is neutralized. When the acid is completely neutralized, further addition of NaOH will increase the conductivity of the solution, because OH^- ions have large ion-conductance. On plotting the conductance against the volume of alkali added, the point of intersection is obtained by extending the lines, which gives the end point.

Weak acid with strong base

Conductometric titration of mixture of strong and weak acids with strong base

Suppose of a mixture of strong acid HCl and weak acid CH₃COOH, is to be titrated with a strong base NaOH. Since HCl is much stronger acid than CH₃COOH, HCl will get titrated first. When HCl is completely neutralized by NaOH, then titration of CH₃COOH will start. On plotting the conductance against the volume of alkali added, the following type of curve is obtained.

Mixture of strong and weak acids with strong base

Conductometric titration of strong acid with weak base

Consider the conductometric titration of a strong acid, HCl by a weak base, NH₄OH. The conductance of the solution will decrease due to the replacement of fast-moving H⁺ ions by slow moving NH₄⁺ ions. When all the H⁺ ions replaced by the NH₄⁺ ions, conductance will reach the lowest limit and neutralization point comes.

H⁺ + Cl^- + NH₄OH -----> NH₄⁺ + Cl^- + H₂O

Due to weakly ionized nature of NH₄OH, further addition of NH₄OH will not cause any appreciable change in the conductance. On plotting the conductance against the volume of alkali added, the following type of curve is obtained.

Strong acid with weak base

Conductometric titration of weak acid with weak base

Consider the conductometric titration of a weak acid, CH₃COOH by a weak base NH₄OH. Since the acid is weak, the conductance of the acid will be low on account of its poor dissociation. As NH₄OH is added, the OH^- ions removed the H⁺ ions. Undissociated CH₃COOH molecules produced fresh H⁺ ions. Besides the solution has some NH₄⁺ ions.  At the starting stage, due to common ion effect there may be little fall in conductivity. But later on, the conductivity of the solution increases slowly due to the presence of slow moving NH₄⁺.

CH₃COOH + NH₄OH ----> CH₃COO^- + NH₄⁺ + H₂O

The total volume of CH₃COOH dissociates slowly in this way and neutralized. Due to weakly ionized nature of NH₄OH, further addition of NH₄OH will not cause any appreciable change in the conductance. On plotting the conductance against the volume of alkali added, the following type of curve is obtained.

Weak acid with weak base

 COLLISION THEORY

The first theory to explain the mechanism of chemical reaction was the collision theory. According to this theory the reactant molecules collide and due to this collision, some structural rearrangement occurs which is responsible for chemical reaction.

However, if each collision leads to reaction then number of molecules reacting per c.c. per second should be equal to frequency. But the number of molecules reacting per c.c. per second much less than the collision frequency. Further more while rate of a reaction increases by 100% to 200% for 10⁰C rise in temperature, collision frequency increases by only 2% to 3% for the same change in temperature. Hence all collision may not lead to reaction. It was at this time; Arrhenius introduced the concept of activation energy. According to which for a molecule to react, it must have energy equal to or greater than activation energy (E). These molecules are called active molecules. Collision between active molecules are fruitful and lead to reaction where as collision between passive molecules are fruitless.

Now, according to Boltzmann’s distribution law, if n₀ is the total number of molecules, out of which n_E molecules have energy greater or equal to E, then—

n_E = n₀ e^{- E/RT}

Hence, if Z is the total number of collisions per c.c. per second, out of which Z_E is the number of collisions between activated molecules, then---

Z_E = Z e^{- E/RT}

Hence number of molecules reacting per c.c. per second is proportional to Z_E. This is collision theory.

Test of this theory was made from kinetic study of the decomposition of HI.

2HI <========> H₂ + I₂

If, Z is the collision frequency, then since each collision involves two molecules, number of molecules reacting per c.c. per second is---

 – dn/dt = 2 Z e^{- E/RT}

Now from kinetic theory----

Z = (1/√2) Π σ² C_a n²

Where,

σ = Collision diameter

C_a = Average velocity

n = Number of molecules per c.c.

So,

 – dn/dt = 2 (1/√2) Π σ² C_a n² e^{- E/RT} ----- (1)

Now, we calculate the rate in another way.

For the above reaction rate----

 – dc/dt = K₂C²

Where,

K₂ = 2 nd order rate constant

C = Molar concentration

N = Avogadro number

But, C = (n x 10³)/N

Or, – dc/dt = - (10³/N) dn/dt

Hence, - (10³/N) dn/dt = K₂ [(n x 10³)/N]²

Or, - dn/dt = K₂ (10³/N) n² ----- (2)

Comparing (1) and (2), we get---

K₂ (10³/N) n² = √2 Π σ² C_a n² e^{- E/RT}

Or, K₂ = √2 Π (N/10³) σ² C_a e^{- E/RT}

Or, K₂ = A e^{- E/RT}

[Where, A = √2 Π (N/10³) σ² C_a and it is known as frequency factor.]

LIMITATIONS OF THE THEORY

Though collision theory explains many reactions very well, it fails to explain many other cases. Thus, in many cases, the observed rate constant is much different from A e^{- E/RT}. The cases where it is greater than A e^{- E/RT} are chain reaction. However, the cases where it is less than A e^{- E/RT} are explained on the basis of orientation of molecules during collisions. If the collisions are not perfect oriented than collisions between active molecules also may not lead to reaction. In these aspects the expression for rate constant K is now written as—

K = P A e^{- E/RT}

Where P is known as steric factor or probability factor, generally its value is less than 1 (excepting chain reaction).

Another defect of collision theory is that it does not consider the entropy change for the reaction. Actually, probability factor is related with entropy change, which can be shown below.

For reversible reaction, the forward and backward rate constant K₁ and K₂ can be written as---

K₁ = P₁ A₁ e^{- E}₁^/RT

K₂ = P₂ A₂ e^{- E}₂^/RT

Or, K₁/K₂ = [(P₁ A₁) / (P₂ A₂)] e^{- (E}₁^{- E}₂^)/RT

But, K₁/K₂ = Equilibrium constant (K)

So, K = [(P₁A₁) / (P₂A₂)] e^{- (E}₁^{- E}₂^)/RT ----- (3)

Again, from Vant Hoff’s isotherm----

ΔG = - RT ln K

Or, K = e^{- ΔG/RT}

Putting, ΔG = ΔH – TΔS

K = e^{- ΔH/RT} e^ΔS/R ----- (4)

Comparing (3) and (4), we get---

[(P₁A₁)/(P₂A₂)] = e^ΔS/R

Thus, probability factor is related with entropy change of the reaction. This factor has not been maintained in collision theory.

 EFFECT OF CATALYST ON SUBSTITUTION REACTION

Catalytic effect on S_N¹ reaction---

The rate of S_N¹ reaction increases by the addition of Lewis acids such as AlX₃, Ag⁺ ion and the Bronsted acids. The more acidic the nucleophilic solvent, the faster is the rate of S_N¹ reaction. Ag⁺ or Al³⁺ has a stronger affinity for X^- than has a solvent molecule. The formation of AgX or AlX₄^- accelerates the dissociation of X^-, thus increases the S_N¹rate. This is an example of electrophilic catalysis. The effectiveness of the H bonding, a factor that accelerates the dissociation of X^-, increases with the acidity of the H of H―A, the Bronsted acid.

Catalytic effect on S_N² reaction---

Crown ethers and phase transfer catalyst accelerate the rate of S_N² reaction.

Crown Ethers

The crown ethers contains at least four oxygen (O) atoms, they are the heterocyclic poly ether. The naming of crown ethers is done by the following way x-crown-y, where ‘x’ represents the total number of atoms in the ring, and ‘y’ represents the number of oxygen atoms (O). The structure of crown ethers are:

Crown Ethers

Crown ethers strongly complex with metallic cation in the cavity of the ring by forming ion-dipole bonds. 18-crown-6 strongly complexes and traps K⁺ as shown in the figure.

18-crown-6 traps potassium cation

There are a host-guest relationship between the crown ether and the ion that is transports. There host is crown ether, and guest is the coordinated cation. Similarly, 12-crown-4 forms complex with Li⁺ and 15-crown-5 forms complex with Na⁺ ion.

Ion pairing diminishes the reactivity of the anion which is intended to act as a nucleophile in substitution reaction. By complexing the cation, the crown ethers leave a ‘bare’ anion with a greatly enhanced reactivity. Since the nucleophile comes after the rate determining step in an S_N¹ reaction, enhancement of nucleophilic character of an anion does not influence the rate of an S_N¹ reaction, but it increases the rate of S_N² reaction. For example, the rate of the reaction---

CH₃―CH₂―Br + KF -------> CH₃―CH₂―F

Increases several times by the addition of 18-crown-6.

Phase Transfer Catalyst

A difficulty that occasionally arises when carrying out nucleophilic substitution reaction is that the reactants do not mix. For a reaction to take place the reacting molecule is usually insoluble in water and other polar solvents, while the nucleophile is often an anion which is soluble in water, but the nucleophile is insoluble in the substrate or other organic solvents. To overcome this problem is to use a solvent that will dissolve both species. A dipolar aprotic solvent may serve this purpose. Another way, which is used may often is phase transfer catalysts.

An example of phase transfer catalyst (Q⁺X^-) is usually a quaternary ammonium halide (R₄N⁺X^-), such as tetra butyl ammonium chloride (Bu₄N⁺Cl^-), benzyl triethyl ammonium chloride [Ph-CH₂-N⁺ (CH₂CH₃)₃Cl^-]. These are soluble in organic phase because of the four hydrocarbons substituents on nitrogen as well as these are soluble in aqueous phase due to the ionic in nature. The transfer of the nucleophile (for example CN^-) as an ion pair (Q⁺CN^-) into the organic phase, is causes by the phase transfer catalyst. The reaction between the nucleophile of the ion pair (CN^-) and the organic substrate RX, occur in the organic phase. The cation (Q⁺) then migrates back into the aqueous phase to complete the cycle. Until all of the nucleophile or the organic substrate has reacted, the process goes continues.

Phase transfer catalyst

An example of a nucleophilic substitution reaction carried out with phase transfer catalysis is the reaction of 1-chlorooctane (in decane) and sodium cyanide (in water). The reaction (at 105⁰C) is complete in less than 2 hours and gives a 95% yield of the substitution product.

Another example of phase transfer catalyst is crown ethers. They render many salt soluble in non-polar solvents. Salts such as KF, KCN and CH₃COOK for example can be transferred into aprotic solvents by using 18-crown-6. A nucleophilic substitution reaction carry out by the relatively unsolvated anions of these salts on an organic substrate in the organic phase.