# Ionic Equlibrium

Introduction:

This type of equilibrium is observed in substances that undergo ionization easily, or in polar substances in which ionization can be induced. Ionic and polar substances are more easily soluble in polar solvents because of the ease of ionization taking place in the solvent medium. With the dissolution of ionic and polar substances in the solvent, these solutions become rich in mobile charge carriers (ions) and thus can conduct electricity. Substances, which are capable of conducting electricity, are called as electrolytes while those substances which are non-conducting are called as non-electrolytes.

Ionization in weak electrolyte (Ostwald’s dilution law):

The degree of dissociation of a weak electrolyte is proportional to the square root of dilution i.e. on increasing dilution the degree of dissociation of weak electrolyteswill be increased is called ostwald’sdilution law.

For weak electrolytes,

Or, kc = $\frac{{{\alpha ^2}}}{{\rm{v}}}$. Where, kc = dissociation constant.

α = degree of dissociation

v = volume of solution.

Or, α = $\sqrt {\frac{{{{\rm{k}}_{\rm{c}}}}}{{\rm{v}}}}$

So, α $\propto$$\frac{1}{{\sqrt {\rm{v}} }}$

Degree of ionization and ionization constant:

The fraction of the total number of molecules present as free ions in the solution is known as degree of ionization of electrolyte (α):

Or, α = $\frac{{{\rm{No}}.{\rm{of\: molecules\: of\: ionized\: as\: ions}}}}{{{\rm{Total\: no}}.{\rm{of\:moleucles\: dissolved}}}}$

The thus formed ions try to recombine to form unionized molecules, forming a dynamic equilibrium, described by a constant known as ionization constant.

Or, K = $\frac{{\left[ {{{\rm{A}}^ + }} \right]\left[ {{{\rm{B}}^ - }} \right]}}{{\left[ {{\rm{AB}}} \right]}}$

Arrhenius concept of acids and bases:

According to the Arrhenius concept, hydrogen chloride, acetic acid, and sulphuric acid, are

acids because all these compounds give free H+ ions in aqueous solutions.

##### Compounds such as NaOH and NH4OH are bases, because these compounds give free OH- ions in aqueous solutions.

NaOH + H2O(excess) à Na +(aq) +OH-(aq)

NH4 OH+ H2 O(excess) àNH4+(aq) + OH-

Thus, According to Arrhenius concept of acids and bases, the neutralization of an acid with a base involves the reaction between H+(aq) and OH-(aq) i.e.,

H+ (aq) + OH-(aq) $\mathop \to \limits^{{\rm{Neutralization\: }}}$ H2O (l)

From acid from base

However, the Arrhenius concept is applicable to the acid-base behavior only in the aqueous medium. It does not provide any explanation to the acid-base behavior in the absence of water.

This concept defines acids and bases as compounds-containing hydrogen and hydroxyl group respectively. There are however, many compounds, which act as acid even when there is no hydrogen in their molecule. Similarly, there are many bases, which do not contain hydroxyl group.

BronstedLowry concept of acids and bases:

According to the Bronsted-Lowry concept, an acid is a proton-donor, and a base is a proton-acceptor.

The reaction of an acid with a base involves transfer of a proton from the acid to the base. So, an acid and a base should be present simultaneously in any system. The extent of an acid-base reaction is governed not only by the proton-donating ability of the acid, but also by the proton-accepting tendency of the base. Acids and bases classified on the basis of this concept are termed as Bronsted acids and bases.

HCl(aq)+ H2O(l)↔H3O+ (aq)+ CL- (aq)

In this reaction, HCl donates its one proton to become Cl-, and H2O accepts one proton to become H3O+. Thus, HCl is Bronsted acid and H2O is a Bronsted base. For the reverse reaction, H3O+is able to transfer its proton to Cl-. So, H3O+is a Bronsted acid and Cl- is a Bronsted base.

Every acid must form a base on donating its proton, and every base must form an acid on accepting a proton. The base that is produced when an acid donates its proton is called the conjugate base of the acid. The acid that is produced when a base accepts a proton is called the conjugate acid of the base. The above reaction can be written as,

HCl+H2OH3O++CL-

Acid1 base2acid2base1

In this Cl- is the conjugate base of the acid HCl and H2O is the conjugate base of the acid H3O+. The conjugate acid differs from conjugate base by one proton. A pair of an acid and a base which differ from one another by a proton constitute a conjugate acid base pair. Thus,

Although the Bronsted-Lowry concept of acids and bases is better than the Arrhenius concept, it cannot account for the acidic and basic character of compound not containing hydrogen. For example, acidic nature of oxides such as CO2, SO2 etc., and the basic nature of the compounds of the type CaO, Na2O etc

## Relative Strengths of Conjugate Acid-Base Pairs:

A stronger Bronsted acid will have a higher tendency for donating a proton to the base, hence would tend to exist as its conjugate base. The conjugate base so formed will have very little tendency to pick up a proton, hence would act as a weak base. Thus, there exists an interdependent relationship between the strengths of an acid and its conjugate base.

'The stronger an acid, weaker is its conjugate base, and stronger a base, weaker is its conjugateacid.'

In water, HCl acts as a strong acid. As the reverse reaction occurs to a very small extent Cl- ion acts as a weak base. So, the anion of a strong acid is a weak base. Similarly, the cations of a weak base acts as a strong acid, e.g., NH4+ ion in water is a strong acid.

Lewis concept of acid and bases:

Lewis proposed broader and more general definitions of acids and bases which do not require presence of protons to explain the acid base behavior. According to Lewis concept ,An acid is a substance which can accept a pair of electrons.

#### A base is a substance which can donate a pair of electron.

Acid-base reactions according to this concept involve donation of electron pair by a base to an acid to form a co-ordinate bond..

Lewis acids are the species having vacant orbitals in the valence shell of one of its atoms. The following species can act as Lewis acids.

a) Molecules having an atom with incomplete octet e.g., BF3, AlCl3 etc.

b) Simple cations for e.g., H+, Ag+ etc.

### Ionization of water, pH and pH scale:

Pure water being a weak electrolyte under goes self ionization to a small extent as follows:

H2O(l)+H2O(l)↔H3O+ (aq)+OH- (aq)

${\rm{K}} = \frac{{\left[ {{{\rm{H}}_3}{{\rm{O}}^ + }} \right]\left[ {{\rm{O}}{{\rm{H}}^ - }} \right]}}{{{{\left[ {{{\rm{H}}_{2{\rm{O}}}}} \right]}^2}}}$

${\rm{\: }}$

The equilibrium constant for this reaction is:

The concentration of unionized water is taken as constant because the degree on ionization of water is very small. So we can write this equation as:

${\rm{K*}}{\left[ {{{\rm{H}}_2}{\rm{O\: }}} \right]^2} = \left[ {{{\rm{H}}_3}{{\rm{O}}^ + }} \right]\left[ {{\rm{O}}{{\rm{H}}^ - }} \right]$

Or, K*a constant = $\left[ {{{\rm{H}}_3}{{\rm{O}}^ + }} \right]\left[ {{\rm{O}}{{\rm{H}}^ - }} \right]$

${{\rm{K}}_{\rm{w}}} = \left[ {{{\rm{H}}_3}{{\rm{O}}^ + }} \right]\left[ {{\rm{O}}{{\rm{H}}^ - }} \right]$

where Kw is a constant and is known as the ionic product of water whose value is 1.008 x 10-14 mol2 L-2at 298 K. In pure water the concentration of H3O+ and OH- are equal and so we can write,

[H3O+] = [OH-]

If, Kw = [H3O+] [OH-] = 1.008 x 10-14 mol2 L-2 then,

[H3O+] [OH-] = 1.008 x 10-14

[H3O+]2 = 1.008 x 10-14

${\rm{or\: }}\left[ {{{\rm{H}}_3}{{\rm{O}}^ + }} \right] = {\rm{\: }}\sqrt {1.008{\rm{*}}{{10}^{ - 14}}} = 1.0{\rm{*}}{10^{ - 7}}{\rm{mol\: }}{{\rm{L}}^{ - 1}}$

Thus in pure water [H3O+] = [OH-] = 1.0 x 10-7 mol L-1 at 298 K

### Effect of temperature on K:

The value of Kw varies with the change in temperature. The values of [H3O+] and [OH-] are always equal to each other at all temperatures but the values of Kw are different at different temperatures. The value of Kw increases with the rise in temperature. This is because increase in temperature will shift the equilibrium in the forward direction producing large concentrations of [H3O+] and [OH-] ions (Le Chatelier's principle).

H2O(l)+H2O(l)↔H3O+ (aq)+OH- (aq)

Hence, Kw increases with rise in temperature.

Hydrolysis of salts:

The process of dissolving salt in water to make its aqueous solution which may be acidic, basic or neutral is called hydrolysis of salt.

It is divided into four categories they are:

a.Salts of strong acid and strong base do not go hydrolysis. E.g: NaCl, NaNO3, etc.

Here, let us consider NaCl as an example. It is strong electrolyte, when dissolved in water; it goes complete dissociation to give Na+ and Cl- ions. But these ions do not have tendency to react with H+ or OH-. So, there is no change in concentration of H+ or OH- ions and hence the solution remains neutral.

b.Salts of weak acid and strong base:

Sodium acetate, CH3COONa, NaCN, KCN are examples of this type of salts. Here let us consider sodium cyanide (NaCN) it is the salt of weak acid, HCN and NaOH. It ionizes to form CN- anions. Being conjugate base of a weak acid. CN- is relatively strong base. Thus, the anion CN- accepts a H+ ion from water and undergoes hydrolysis.So, the solution becomes basic due to the generation of OH- ions.

c. Salts of weak bases and strong acids:

Some salts of weak bases and strong acids undergo cationic hydrolysis and yield slightly acidic solution.

Ammonium chloride is a typical e.g. of this salts. It is the salt of a weak base NH4OH and strong acid HCl. It ionizes in aqueous solution to form the cation NH4+.

Here, NH4OH+ is a relatively strong acid. It accepts OH- ion from water (H2O) and forms the unionized NH4OH and H+ ion.

So, the accumulation of H+ ions in solution makes it acidic.

d. Salts of weak acids and weak bases:

The e.g. of this type of salts are ammonium acetate, ammonium cyanide etc. The resulting solution is neutral, basic or acidic depending on the relative hydrolysis of the anions and the cations.

Solubility product principle and its application:

When a sparingly soluble ionic solid is dissolved in water it undergoes ionization and the ions forming from solid phase pass into the solution till the solution becomes saturated and a dynamic equilibrium us established between the ions present in the saturated solution and the ions present in the solid phase at a constant temperature.

Consider a sparingly soluble substance AB which ionized as A+B-

At equilibrium,K = $\frac{{\left[ {{{\rm{A}}^ + }} \right]\left[ {{{\rm{B}}^ - }} \right]}}{{\left[ {{\rm{AB}}} \right]}}$

Where, Ksp = solubility product. The solubility is the product of concentration of ions of sparingly soluble salts in its saturated solution to a particular temperature. It is represented as Ksp.

The value of Ksp changes with the change in temperature. The value of Ksp give the idea of precipitation of an electrolyte at a given temperature.

To precipitate in a chemical reaction, the ionic product must exceed the solubility product of sparingly soluble salt at particular temperature.

For precipitation.

IP spà Unsaturated à No ppt.

IP = Kspà saturated à No. ppt.

IP >Kspà Super saturated à ppt.

Solubility product principle is very applicable in analytical chemistry. In salt analysis i.e. (qualitative analyisis) the solubility product principle is more applicable. The group separation of metal ions in salt analysis is done on the basis of solubility product principle.

Qualitative analysis of solubility product:

The common ion effect is generally employed in qualitative analysis.

The cations of group II (Hg2+, Pb2+, Bi3+, Cu2+, As3+, Sb3+, Sn2+) are precipitated as their sulphides (such as CuS, PbS) by passing H2S gas in the presence hydrochloric acid (Common H+ ions).

The cations of group III are precipitated as their hydroxides by NH4OH in the presence of NH4Cl.

The cations of group V are precipitated as their carbonates by the addition (NH4)2CO3, in the presence of HCl.

Common ion effect and its application:

When a soluble salt, say, A+C- is added to a solution of another salt (A+B-) containing a common ion (A+), the dissociation of AB is suppressed

AB⇔A+ + B-

By the addition of the salt, AC, the concentration of A+ increases. Therefore, according to Le Chatelier's principle, the equillibrium will shift to the left, thereby decreasing the concentration of A+ ions. Of that, the degree of dissociation of AB will be reduced.

a salt of a weak acid is added to a solution of the acid itself, the dissociation of the acid is diminished further. For example, the addition of sodium acetate to a solution of acetic acid suppresses the dissociation of acetic acid which is already very small.

Consider the equilibrium,

CH3COOH ⇔ H+ + CH3COO-

The addition of one of the products of dissociation (example:acetate ion), supplied by the largely dissociated salt (example:sodium acetate) pushes the equilibrium to the left. In other words, the dissociation of acetic acid is suppressed. Similarly, the addition of hydrogen ions furnished by the addition of a largely dissociated acid such as hydrochloric acid , also suppresses the dissociation of acetic acid.

Thus, the common ion effect is the "suppression of the dissociation of a weak acid or a weak base on the addition of its own ions.

Applications:

Precipitation of sulphides of group II and IIIB basic radicals

Precipitationof hydroxides of group IIIA basic radicals

Precipitation of group IV basic radicals

## Buffer Solution:

A solution which resists any change of pH when a small amount of a strong acid or a strong base is added to it, is called a buffer solution or simply as a buffer.

Alternatively, a buffer solution may be defined as a solution whose pH value does not change appreciably upon the addition of small amounts of a strong acid, base and/or water from outside.

Thus, buffers have reserve acidity and reserve alkalinity.

Buffer solutions usually consist of a mixture of a weak acid and its salt with a strong base e.g., CH3COOH and CH3COONa, or that of a weak base and its salt with a strong acid e.g., NH4OH and NH4Cl. The solution of any salt of a weak acid and a weak base e.g., ammonium acetate, also shows buffering property.

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