Ionic Equilibrium for intermediate and B.Sc

Ionic Equilibrium

Equilibrium established between the ions and the undissociated electrolyte in a solution is called the ionic equilibrium. In other words, Ionic equilibrium is the study of solutions of electrolyte.

Electrolyte: Substances which furnish ions in aqueous solution or in fused state is called the electrolytes. These substances conduct electricity in their aqueous solutions or in their fused state.

Degree of dissociation (α): The number of molecules dissociated out of total number of molecules originally taken is called the degree of dissociation.

Mathematically,

It is expressed in percentage or as fraction or decimals. If 40 molecules are dissociated out of 100 molecules than the degree of dissociation is expressed as 40% or 0.4.

Strong Electrolytes: These substances dissociate almost completely into ions in aqueous solutions and hence are good conductor of electricity. Ex: KCl, NaCl, KOH, NaOH etc.

Weak Electrolytes: These substances dissociate to a small extent in aqueous solutions and accordingly conduct electricity to a small extent. Ex: NH₄OH, CH₃COOH etc.

            A strong electrolyte dissociates completely in aqueous solution, therefore their ionization is represented by single right handed arrow which suggests that the solution contains almost ions.

HCl +H₂O →  H₃O⁺ + Cl ^—                   

Here the H⁺ ion from HCl is received by water to form H₃O⁺. Thus here we may consider H⁺ and  H₃O⁺ the same.

Similarly, NaOH (aq.) →  Na⁺ (aq)  +  OH^— (aq.)

            But a weak electrolyte dissociates to a small extent. Some of the ions formed react back to give undissociated electrolyte and hence equilibrium is established in this process. Such an equilibrium is called the ionic equilibrium. The equilibrium constant in this case is called the ionisation constant. Thus the ionisation of a weak electrolyte AB can be represented as:

 AB ⇌ A⁺ + B^—

The equilibrium or ionisation constant for this equilibrium is represented as:

K_i   = [A⁺] . [ B^—]  /  [AB], where [AB] represents concentration of AB in mol/ltr and so on

Ionisation of weak Acid - Ostwald’s Dilution Law:

Consider the dissociation of a weak acid such as CH₃COOH. Let its degree of dissociation is α. It means α mole of the acid will dissociate out of each 1 mole initially taken. Thus if C mole of the acid is initially taken then Cα moles of the acid will be dissociated. In the following dissociation, the concentration of water is in excess and hence can be considered as constatnt. Accordingly,

Applying law of chemical equilibrium and considering H⁺ and  H₃O⁺ the same, 

K = {[CH₃COO^—] . [H⁺]} / {[CH₃COOH] . [H₂O]}

But  K . [H₂O] = Constant = K_a 

Where K_a = Acid constant or dissociation constant of acid 

=> K_a  =  [CH₃COO^—] . [H⁺] / [CH₃COOH]

=>  K_a  = (Cα . Cα) / {C (1 — α)} 

= Cα² / {1 — α}

In case of weak electrolyte, the value of α is very small and can be neglected as compared to 1.

i.e., 1 — α = 1        

=> K_a = Cα² ............... eq. 1

 => α = (K_a /C)^1/2

Hence, Ostwald’s dilution Law states that the degree of dissociation of weak electrolyte is inversely proportional to the square root of its concentration.

We know, C = n/V.

If n = 1 mole then, C = 1/V        

=> α = (K_{a .}V)^1/2

The [H⁺] = C α = (K_aC)^1/2

In a similar way the degree of dissociation of a weak base, NH₄OH (a weak electrolyte) can be written as,

=> α = (K_b / C)^1/2 

= (K_b .V)^1/2,

where K_b = Disociation constant of base

=> [OH^—] = C α = (K_bC)^1/2

Relative strength of weak acids:

Note:  Form eq. 1, it is clear that, higher is the value of acid constant of an acid higher is the value of α (degree of dissociation) and thus its relative strength to furnish H⁺ ion is stronger. Thus an acid with higher acid constant is relatively a stronger acid.

Similar conclusion can be drawn between two bases.

Concept of Acids and Bases:

Arrhenius Concept:

This concept proposed by Swedish chemist Svante Arrhenius in 1884, is one of the earliest theories explaining the behavior of acids and bases in aqueous solutions. According to this concept:

Arrhenius Acid:

An acid is defined as a substance that, when dissolved in water, increases the concentration of hydrogen or hydronium ions (H₃O⁺).

The typical chemical equation for the dissociation of an Arrhenius acid in water is: 

Acid → H⁺ + Anion

For example, hydrochloric acid (HCl) dissociates in water as follows:

HCl → H⁺ + Cl⁻

Arrhenius Base:

A base is defined as a substance that, when dissolved in water, increases the concentration of hydroxide ions (OH⁻).

The typical chemical equation for the dissociation of an Arrhenius base in water is:

Base → OH⁻ + Cation

For example, sodium hydroxide (NaOH) dissociates in water as follows:

NaOH → Na⁺ + OH⁻

Neutralization Reaction:

When an Arrhenius acid reacts with an Arrhenius base, a neutralization reaction occurs, giving rise to the formation of water and a salt.

The general form of the neutralization reaction is:

Acid + Base → Salt + Water

For example, the reaction between hydrochloric acid (HCl) and sodium hydroxide (NaOH) is a neutralization reaction:

HCl + NaOH → NaCl + H₂O

While the Arrhenius concept is useful for understanding acid-base behavior in aqueous solutions, it has limitations. It is primarily applicable to substances that ionize or dissociate in water, and it does not account for the behavior of acids and bases in non-aqueous solvents. Later theories, such as the Brønsted-Lowry and Lewis concepts, provide broader and more versatile definitions of acids and bases.

Bronsted – Lowry Concept:

This concept was formulated independently by Danish chemist Johannes Brønsted and English chemist Thomas Lowry in 1923, is a more general and versatile theory compared to the Arrhenius concept. According to the Brønsted-Lowry definition:

Brønsted-Lowry Acid:

An acid is a substance that can donate a proton (H⁺ ion) to another substance.

The acid is often referred to as a proton donor.

Brønsted-Lowry Base:

A base is a substance that can accept a proton (H⁺ ion) from another substance.

The base is often referred to as a proton acceptor.

In the Brønsted-Lowry theory, the acid-base reaction involves the transfer of protons from the acid to the base. This concept extends the understanding of acids and bases beyond aqueous solutions and allows for the characterization of acid-base reactions in various solvents.

General Reactions:

An acid (HA) donates a proton to a base (B):

HA→A⁻+H⁺

A base (B) accepts a proton from an acid (HA):

HA+B→A⁻+HB⁺

Examples:

Acid-Base Reaction in Water:

HCl+H₂O→Cl⁻+H₃O⁺

In this reaction, HCl (hydrochloric acid) donates a proton to water, forming chloride ion (Cl⁻) and hydronium ion (H₃O⁺).

Ammonia Acting as a Base:

NH₃+H₂O→NH₄⁺+OH⁻

In this reaction, ammonia (NH₃) accepts a proton from water, forming ammonium ion (NH₄⁺) and hydroxide ion (OH⁻).

Conjugate Acid – Base Pair:

In this concept, a conjugate acid-base pair consists of two substances related to each other by the transfer of a proton (H⁺ ion) during an acid-base reaction. Specifically:

Conjugate Acid is the species formed when a base accepts a proton (H⁺).

Example: In the reaction NH₃+H₂O→NH₄⁺+OH⁻, NH₄⁺ is the conjugate acid of NH₃.

Conjugate Base is the species formed when an acid donates a proton (H⁺).

Example: In the reaction HCl+H₂O→Cl⁻+H₃O⁺, Cl⁻ is the conjugate base of HCl.

The relationship between a conjugate acid-base pair can be represented using the following general reaction:

Acid+Base⇌Conjugate Base+Conjugate Acid

For example, considering the reaction of acetic acid (CH₃COOH) with water:

CH₃COOH+H₂O⇌CH₃COO⁻+H₃O⁺

Here, CH₃COOH is the acid, H₂O is the base, CH₃COO⁻ is the conjugate base, and H₃O⁺ is the conjugate acid.

Note: If an acid is strong its conjugate base must be weak so that it does not react back with the H⁺ ion to give rise to the same acid again. Similarly if a base is strong then its conjugate acid should be weak and vice versa.

The Brønsted-Lowry concept is more inclusive than the Arrhenius theory because it applies to a wider range of solvents and allows for a more comprehensive understanding of acid-base reactions. 

Lewis Concept:

This concept was proposed by American chemist Gilbert N. Lewis in 1923. Unlike the Brønsted-Lowry and Arrhenius theories, which focus on proton transfer, the Lewis theory defines acids and bases based on electron pair interactions. According to the Lewis definition:

Lewis Acid:

A Lewis acid is a substance that can accept an electron pair.

Lewis acids are electron pair acceptors.

All cations (such as Na⁺) and electron deficient species (molecules having incomplete octate such as BF₃) are Lewis acids.

Lewis Base:

A Lewis base is a substance that can donate an electron pair.

Lewis bases are electron pair donors.

All anions (such as Cl^-) and molecules having lone pairs of electrons (such as NH₃, H₂O) are Lewis bases.

In this theory, the acid-base interaction is characterized by the sharing or transfer of electron pairs. Lewis acids and bases can form coordinate covalent bonds, where both electrons in the bond come from the Lewis base.

General Reactions:

Formation of a Coordinate Covalent Bond: The Lewis acid accepts an electron pair from the Lewis base to form a complex.

Examples:

Reaction between Boron Trifluoride (BF₃) and Ammonia (NH₃):

BF₃+NH₃→BF₃NH₃     (i.e., H₃N: --->BF₃)

In this reaction, BF₃ acts as a Lewis acid by accepting a lone pair of electrons from NH₃, which acts as a Lewis base.

Formation of Hydronium Ion (H₃O⁺):

H₂O+H⁺→H₃O⁺

In this reaction, H⁺ acts as a Lewis acid by accepting a lone pair of electrons from H₂O, which acts as a Lewis base.

The Lewis acid-base theory is more inclusive than the Brønsted-Lowry and Arrhenius theories because it doesn't rely on the presence of protons or the requirement of aqueous solutions.

Ionisation constant or Ionic Product (K_W) of water:

Water undergoes a process of self-ionization, where a small fraction of water molecules dissociate into hydronium ions (H₃O⁺) and hydroxide ions (OH⁻). The ionization constant of water is expressed by the following equilibrium reaction:

H₂O⇌H⁺+OH⁻

Applying law of chemical equilibrium,

K={[H⁺].[OH⁻]}/[ H₂O]

Since water is a very weak electrolyte, the concentration of undissociated water [H₂O] is almost constant.

Thus K[ H₂O] = Constant = K_W = [H⁺].[OH⁻]

K_W is called the ionic product of water or Ionisation constant of water.

The equilibrium constant (Kw) for this reaction is defined as the product of the concentrations of hydronium ions ([H₃O⁺] or [H⁺]) and hydroxide ions in water at a given temperature:

At 25 degrees Celsius, the ionization constant of water (Kw) is approximately 1.0×10⁻¹⁴ mol²/L²

The expression for Kw at any temperature is given by the product of the concentrations of H⁺ and OH⁻ ions, and it can be used to calculate one of the concentrations if the other is known.

The value of Kw changes with change in temperature.

pH :

The term "pH" stands for ‘’power of hydrogen’’ or "potential of hydrogen" which is a measure of the acidity or basicity of a solution or to quantify the concentration of hydrogen ions (H⁺) in a solution.

. Mathematically, it is defined as the negative logarithm of hydrogen ion concentration in moles per litre.

p^H = - log [H⁺]

pH scale:

The pH scale is a measure used to specify the acidity or basicity (alkalinity) of a solution. It is a logarithmic scale that ranges from 0 to 14, with 7 considered neutral. The pH scale is based on the concentration of hydrogen ions (H⁺) in a solution. Here's an overview of the pH scale:

For a neutral solution, [H⁺] = [OH^-]

and we know [H⁺] X [OH^-] = 10 ^-14

Thus [H⁺] = [OH^-] = 10 ^-7

Thus p^H = - log [H⁺] = - log 10 ^-7 = 7 for Neutral solution

For Acidic solution, [H⁺] > 10 ^-7

That means, [H⁺] = 10 ^-6, 10 ^-5, 10 ^-4 and so on

Thus for acidic solution, p^H is less than 7

Similarly, for basic solution, p^H is greater than 7

A solution with a pH of 1 is highly acidic.

A solution with a pH of 7 is neutral.

A solution with a pH of 14 is highly basic.

Accordingly, we can write p^OH = -log [OH^-]

Also p^H + p^OH = 14