Ionic Equilibrium

Vijay Ratna

Ionic equilibria is about the ionising behaviour of acids and bases. The study of this chapter assumes significance in the light of points such as (1) Most drugs are weak acids and bases and their ionising behaviour in aqueous solutions should be understood for formulating them properly (2) absorption of drugs across biological membranes depends on ionisation, which depends on the pH of the surroundings. In this chapter we study how various substances ionise and how it is related to the pH of the medium. We will also learn to calculate the pH of different solutions from their concentrations. This chapter is divided into (1) Basic definitions (2) Acid-base theroies (3) Ionisation of water, acids and bases (4) pH, H₃O+ and pKa

I. Basic definitions :

(1) A protophilic or basic solvent is one that is capable of accepting protons from the solute.

Ex : acetone, ether, liquid ammonia

(2) A protogenic solvent is a proton donating compound.

Ex : formic acid, acetic acid, sulfuric acid, liquid Hcl and liquid HF.

(3) Amphiprotic solvents act as both proton acceptors and proton donors.

Ex : Water, alcohol

(4) Aprotic solvents, neither accept nor donate protons.

Ex : hydrocarbons

(5) Equilibrium is a balance between two opposing forces or actions. This is a dynamic equality between the two velocities. Chemical equilibirium maintains the concentrations of the reactants and products constant.

II. Acid – Base Theories :

Arrhenius :

Acid is a substance that liberates hydrogen ions.

Base is a substance that supplies hydroxyl ions on dissociation.

The oppositeness of acids and bases is emphasized.

Demerits :

1.No complimentary reationship between acids and bases is suggested.

2.Behaviour of acids and bases in non aqeous solvents not explaned.

3.Concept of base much more complex than that of acid.

4.Compounds like Ammonia (NH3) and Calcium Oxide (CaO) that are bases contain no OH ions in their original formulation.

Bronsted and Lowry :

This theory is more satisfactory and more general, i.e., it can explain the character of many more substances.

1.An acid is a substance that is capable of donating a proton or hydrogen ion.

2.A base is a substance capable of accepting a proton.

3.This complementary relationship is expressed as A ↔ H⁺ + B

acid base

The pair of susbtances thus related by gain or loss of proton are called conjugat acid – base pair.

4. Not only molecules but also cations and anions may function as acids and bases.

5. This proton transferring reaction is known as protolysis or protolytic reaction.

6. The ionic specis H₃O⁺ (hydronium ion) is always formed when an acid is dissolved in water.

7. Examples of protolytic equations :

NH₃ + H₂O ↔ NH₄⁺ + OH^-

base1 acid2 acid1 base2

CH₃COO^- + H₂O ↔ CH₃COOH + OH^-

base1 acid2 acid1 base2

NH₄⁺ + H₂O ↔ NH₃ + H₃O⁺

base1 acid2 acid1 base2

8. Water can act as a base as well as an acid. It is amphoteric and is called an amphiprotic substance.

9.Not limited to aqueous solutions. Can be extended to gas phase. Gaseous ammonia (base) can react with hydrogen chloride gas (acid) to give ammonium chloride gas.

10.Demerits:

a.Does not indicate the basic reason for proton transfer.

b.Cannot explain how substances not containing proton can be acids ex: Sulfer trioxide, boron trichloride, stannic chloride or carbon dioxide.

Lewis Theory: More inclusive than the previous two theories.

Theory: An acid is a substance capable of sharing a pair of electrons made available by another substance called a base, thereby forming a coordinate covalent bond.

Examples :

Boron trichloride

(1)Compounds such as Boron trichloride and aluminium chloride, though they do not contain hydrogen (hence are not acids under the Brownstead Lowry scheme) are acids as per Lewis theory.

(2)Compunds that do not contain hydroxyl ions, such as amines, ethers and carboxylic acid anhydrides are lewis bases.

(3)Lewis model is more general than Bronsted – Lowry model, which is more general than Arrhenius model. All Bronsted – Lowry acids base reactions are covered by Lewis model.

(4)Many reactions which do not involve transfer of a proton are also covered by Lewis theory.

(5)Lewis theory is used in describing many organisc and inorganic reactions, which are used in explaining the concpets in solubility and complexation.

(6)Bronsted – Lowry nomenclature is used in explaninig ionic equilibira.

Levelling effect of solvent

When strong acids such as HClO₄, H₂SO₄, HCl and HNO₃ are dissolved in water, the solutions – if they are of identical normality and are not too concentrated – all have about the same hydrogen – ion concentration, indicating the acids to be of the same strength. Reason is that these acids undergo practically complete protolysis in water. This is called the leveling effect of water. This occurs when the added acid is stronger than the hydronium ion. The tendency of proton – transfer equations is to proceed spontaneously in the direction of forming a weaker acid or weaker base.

When the strong bases, such as sodium hydride, sodium amide or sodium ethoxide are dissolved in water, each reacts with water to form sodium hydroxide – Levelling effect of water on bases.

Since the hydroxide ion is the strongest base which can exist in water, any base stronger than the hydroxide ion undergoes protolysis to hydroxide.

Differences in the acidity of acids become clear if they are dissolved in a relatively poor proton acceptor – such as anhydrous acetic acid.

HclO₄ + CH₃COOH → ClO₄^- + CH₃COOH₂

[Perchloric acid, base₂ base₁ acid₂

Strong acid] (strong) (weak) (weak)

acid₁ (acetonium ion)

But sulfuric acid and hydrochloric acid behave as weak acids when dissolved in anhydrous acetic acid.

Because perchloric acid is strong in the presence of acetic acid, it is used as a titrant for a variety of substances which behave as bases in acetic acid.

So perchloric acid is a differentating solvent for aids.

Liquid ammonia is a differentating solvent for bases.

Acid Base Equilibira

(1)Ionisation of a weak acid:

HAC + H₂O ↔ H₃O⁺+ AC^-

Acid₁ Base₂ Acid₂ Base1

Law of Mass Action : The rate of the forward reaction, R_f is proportional to the concentration of the reactatns.

R_f= K₁ x [HAc]¹ x [H₂O]₁

R_r= K₂ [H₃O⁺]¹ [AC^-]¹

Rate of forward reaction decreases with time as acetic acid is depleted,

Rate of reverse reaction begins at zero and increases as larger quantities of hydrogen ions and acetate ions are formed.

When R_f = R_r

The concentrations of products and reactants are not necessarily equal at equilibrium; the speeds of the forward and reverse reactions are what are the same.

K₁ x [HAc] x[H₂O] = K₂ [H₃O⁺] [ Ac^-]

K = K₁ [H₃O⁺][Ac-]

___ = ____________

K₂ [HAc] [H₂O]

Ka = 55.3K = [H₃O⁺][Ac^-]

-----------------

[HAc]

Ka – equilibrium constant, ionization constant, acidity constant.

In general,

HB + H₂O↔ H₃O⁺ + B^-

Ka= [H₃O⁺] [B^-]

---------------

[HB]

Let [HAc] = C, and [H₃O⁺] = x,

At equilibrium,

[HAc] = c-x

HAc + H₂O ↔ H₃O⁺ + Ac^-

(c-x) x x

Ka = X²

----

c-x

When C is large in comparison with x,

Ka ~ x²

----

C

And x² = kaC

x = [H₃O⁺]= √¯Kac

(ii) for charged acids BH+

Ka = [H₃O⁺][B]

---------------

[BH⁺]

(iii) for weak base [OH^-] = √¯KbC

(iv) for charged base B^-,

K_b= [OH^-] [HB]

--------------

[B^-]

(v) Ionisation of water :

One molecule of water reacts as a weak electrolyte with another molecule of water as solvent.

This is an autoprotolytic reaction

H₂O + H₂OH₃O⁺ +OH^-

K = [H₃O⁺][OH^-]

------------------

[H₂O]²

[H₂O]² is combined with K to give a new constant Kw – dissociation constant or autoprotolysis constant or the ion product of water.

Kw = K [H₂O]² = 1 x 10^-14at 25^oC

In pure water, [H₃O⁺] = [OH^-] ~ V¯¯1x10^-14

= 1x10^-7

K_aK_b= k_w

V. Ionisation of polyprotic Electrolytes :

1. H₃PO₄ + H₂O ↔ H₃O⁺+ H₂PO₄^-

2. H₂PO₄^- + H₂O ↔ H₃O₊+HPO₄^—

3. HPO₄^-- + H₂O ↔ H₃O⁺+ PO₄^—

In general for a polyprotic acid system for which the parent acid is H_nA, there are n+1 possible species in solution.

VI. A spcies that can function either as an acid or as a base is called an ampholyte and is said to be amphoteric in nature.

⁺NH₃CH₂COO^- is called a Zwitterion and differs from the amphoteric species in that it carries both a positive and a negative charge and the whole molecule is electrically neutral. The pH at which the zwitterion concentration is a maximum is the isoelectric point. Here net movement of solute molecules in an electric field is negligible.

Sorensen’s pH “

pH = log 1 = - log [H₃O⁺]

-----

[H₃O⁺]

0 – 7 – acid

7 – 14 – alkaline

Neutral pH at 0^OC is 7.47, at 100^OC is 6.15.

More exact definition :

pH = -log a_H⁺

Hydronium ion concentration x Activity coefficient

=Hydronium ion activity

pH = -log (γ±c)

pH + pOH = pK_w

pK_a + pK_b= pK_w

Species Concentration as a function of pH:

Polyprotic acids, H_nA, can ionize in successive stages to yield n+1 possible species in solution. In research it is important to be able to calculate the concentration of all acidic and basic species in solution.

[H_nA] = [H₃O⁺]ⁿCa

---------------

D

H₂A : D = [H₃O⁺]² + K₁[H₃O⁺] + K₁K₂

[H₂A] = [H₃O⁺]² Ca

------------------------------------------

[H₃O⁺]² + K₁[H₃O⁺] + K₁K₂

Calculation of pH:

Proton Balance Equation :

The PBE for the system of HCl in water is

[H₃O⁺]= [OH^-] + [Cl^-]

General Method :

(a)Always start with the species added to water.

(b)On the left side of the equation, place all species that can form when protons are consumed by the starting species.

(c)On the right side of the equation, place all species that can form when protons are released from the starting species.

(d)Each species in the PBE should be multiplied by the number of protons lost or gained when it is formed from the starting species.

(e)Add [H₃O⁺] to the left side of the equation and [OH^-] to the right side of the equation.

This is Proton Balance Equation.

Ex : 1. H₃PO₄ : [H₃O⁺]= [OH^-] + [H₂PO₄^-] + 2[HPO₄^--] + 3[PO₄^---]

2. Na₂HPO₄ : [H₃O⁺][H₂PO₄^-] + 2[H₃PO₄] = [OH_-] + [PO₄^---]

Exact equation :

[H3O+]= Ca + √¯Ca2+4Kw

----------------------

2

[OH-]= Cb + √¯Cb2 + 4Kw

-------------------------

2

Graphical solution to pH problems :

1.Half – reutralisation point is pKa.

2.pka is the pH where exactly half the substance is ionised and half is unionised.