Ionic Equilibrium in Solution

Ionic Equilibrium in Solution: A solution containing ions that are formed by dissolving ionic compounds in a solvent is known as an ionic solution. Common salt (sodium chloride, \(\text {NaCl}\)) dissolved in water is an example of an ionic solution. When these ionic compounds are dissolved in water, they dissociate into cations and anions. In Ionic equilibrium, the ionic substance gets dissociated into their ions in the polar solvents.

During equilibrium, the reactants and products coexist so that the conversion of reactant to product is always less than \(100\%\). Substances in ionic solutions that dissociate into their constituent ions, and conducts electricity are known as electrolytes and substances that do not dissociate into their constituent ions in an aqueous solution are known as non-electrolytes. For calculating the degree of dissociation of these electrolytes, Ostwald’s dilution law is applicable. In this article, we will learn about the ionic equilibrium in solutions in detail.

Ionic Equilibrium Definition

In the case of weak electrolytes, ions are partially ionised, and because of this ionisation, weak electrolytes exist in dynamic equilibrium with the unionised molecules. This type of equilibrium is called ionic equilibrium. Thus, we can say that the equilibrium which is established by the unionised molecules and the ion in the weak electrolytic solution is known as the ionic equilibrium. 

Based on the electrical conductivity of the ions in the solutions, the substances present in them are classified into two types:

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Electrolytes

The substances that dissociate into their constituent ions in their aqueous solution and conduct electricity are known as electrolytes. For example, salt solution, acid solution, base solution etc., are electrolytes.

Further, Electrolytes can be further classified into strong and weak electrolytes.

• Strong Electrolytes – The substances that ionise completely upon dissociation in their ionic solution are known as strong electrolytes. For example, sodium chloride, \(\text {NaCl}\) is a strong electrolyte as it undergoes complete ionisation in its aqueous solution to release sodium ions \(\left(\text {Na}^{+}\right)\) and chloride ions \(\left(\text {Cl}^{-}\right)\).
• Weak Electrolytes – The substances that undergo partial dissociation in their ionic solution are known as weak electrolytes. Such as, acetic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) undergoes partial ionisation to release some amount of acetate ions \(\left(\mathrm{CH}_{3} \mathrm{COO}^{-}\right)\) and hydrogen \(\left(\text {H}^{+}\right)\) ions.
• Non-Electrolytes – Apart from these two types of electrolytes, some substances bear no charge and do not dissociate into ions in an aqueous solution or in a molten state and do not conduct electricity are known as non-electrolytes. Like sugar in a water solution.

Ostwald’s Dilution Law: Degree of Dissociation

On applying the law of mass action to weak electrolytes in solution, Ostwald’s dilution law was derived. It is a relationship between the dissociation constant \(\text {K}_{\text {d}}\) and the degree of dissociation \((\alpha)\) of a weak electrolyte. According to this law:
A binary electrolyte \({\text{AB}}\) that dissociates into \(\text {A}^{+}\) and \(\text {B}^{-}\) ions, is represented by the chemical equilibrium:

On applying the law of chemical equilibrium:

\({\text{Equilibrium constant}}\;({\text{K}}) = \frac{{[{{\text{A}}^ + }][{{\text{B}}^ – }]}}{{[{\text{AB}}]}}\;{\text{or}}\;{\text{K}} = \frac{{{\text{C}}\alpha  \times {\text{c}}\alpha }}{{{\text{C}}(1 – \alpha )}} = \frac{{{\text{C}}{\alpha ^2}}}{{1 – \alpha }}\)

In case of weak electrolytes, \(\alpha\) is very small when compared to unity, and hence we can consider \((1-\alpha)\) as \(1\). Hence,

Or, \(\mathrm{K}=\mathrm{C} \alpha^{2}\)

Or, \(\alpha^{2}=\frac{\mathrm{K}}{\mathrm{C}}\)

Or, \(\alpha=\sqrt{\frac{\mathrm{K}}{\mathrm{C}}}\)

Hence, \(\alpha \propto \frac{1}{\sqrt{\text {C}}}\)

Thus, according to the above formula, it can be inferred that the degree of ionisation of weak electrolyte is inversely proportional to the square root of its molar concentration.
For \(1\) mole of electrolyte, Concentration \((\text {C})=1 /(\text {V})\) dilution, thus:

\(\alpha \propto \sqrt{\text {V}}\)

Thus, from the above equation, the degree of ionisation is directly proportional to the square root of the dilution, i.e., volume.

Acid-Base Equilibrium

Acids and bases exist in chemical equilibrium in the solution. At chemical equilibrium, the products and reactants have reached a state of chemical balance. At equilibrium, though reactions may still be taking place within the sample, the forward and reverse reactions take place at the same rate, so the concentrations of the products and reactants do not change with time.

According to Arrhenius concept, strong acid completely dissociates releasing \(\text {H}^{+}\) ions and strong bases completely dissociate releasing \(\mathrm{OH}^{-}\) ions in an aqueous solution.

At equilibrium, the relative strengths of the compounds can be determined using the equilibrium constants of acids \(\left(\text {K}_{\text {a}}\right)\) and bases \(\left(\text {K}_{\text {b}}\right)\). The percent ionisation of an aqueous solution can be calculated using these constant values which are also called dissociation constants or ionisation constants. Additionally, the equilibrium constant for an acid-base reaction can be calculated from \(\left(\text {K}_{\text {a}}\right)\) and \(\left(\text {K}_{\text {b}}\right)\) values.

For acid, the equilibrium reaction of acid dissociation is:

\(\mathrm{HA}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{A}^{-}\)

Equilibrium constant is given below:

\(\text {K}_{a}=\frac{\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\left[\mathrm{A}^{-}\right]}{[\mathrm{HA}]}\)

In this equation, \([\text {HA}]\) is the concentration of acid, \(\left[\text {A}^{-}\right]\) is the concentration of conjugate base, and \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) is the concentration of hydronium.

For base, the equilibrium reaction of base dissociation is:

\(\text {B}+\text {H}_{2} \text {O} \rightleftharpoons \text {B H}^{+}+\text {O H}^{-}\)

Equilibrium constant is given below:

\(\text {K}_{\text {b}}=\frac{\left[\mathrm{BH}^{+}\right]\left[\mathrm{OH}^{-}\right]}{[\mathrm{B}]}\)

In this equation, \([\text {B}]\) is the concentration of base \(\left[\text {BH}^{+}\right]\) is the concentration of conjugate acid, and \(\left[\mathrm{\text {OH}}^{-}\right]\) is the concentration of hydroxide ion.

Solubility Equilibrium and Solubility Product

Solubility Equilibrium – The total amount of the solute that can be dissolved in the solvent at equilibrium is known as the solubility of the solvent. An equilibrium constant that provides insight into the equilibrium between the solid solute and its constituent ions that are dissociated in the solution is known as the solubility equilibrium. 

Solubility Product

The property by which a solute gets dissolved in a solvent for the formation of a solution is known as solubility. Ionic compounds get disassociated into cations and anions, and their solubility in water vary to a great extent.

Solubility Product Constant

The type of equilibrium constant whose value depends on temperature is called the solubility product, denoted as Ksp. It usually increases with the increase in temperature due of the increased solubility.

As an exception, there are some ionic compounds that are believed to be insoluble but will still dissolve in water to some extent. Such ‘substantially insoluble’ compounds are considered as strong electrolytes since whatever portion of electrolytes that get dissolved in water will dissociate. For example, silver chloride when added to water dissociates to a small extent in the silver ions and chloride ions.

\(\text {AgCl}(\text {s}) \leftrightarrow \text {Ag}^{+}(\text {aq})+\text {Cl}^{-}(\text {aq})\)

The solubility product:

\(\text {K}_{\text {sp}}=\left[\mathrm{Ag}^{+}\right]\left[\mathrm{Cl}^{-}\right]\)

Solubility Product Formula

To describe the saturated solutions of ionic compounds having relatively low solubility, the solubility product formula is used.  A saturated solution is assumed to be in a state of dynamic equilibrium between the ionic compound and the undissolved solid.

The solubility product formula \(\left(\text {K}_{\text {sp}}\right)\) is given in the form of the following equation:

\(\text {A}_{\text {x}} \text {B}_{\text {y}}(\text {s}) \rightarrow \text {xA}^{\text {y}+}(\text {aq})+\text {yB}^{\text {x}-}(\text {aq})\)

The general equilibrium constant of the above equation can be written as:

\(\text {K}_{\text {c}}=\left[\text {A}^{\text {y}+}\right]^{\text {x}}\left[\text {B}^{\text {x}-}\right]^{\text {y}}\)

Significance of the Solubility Product

The solubility depends on the most important factors like the lattice enthalpy of salt and the solvation enthalpy of ions in the solution. The significance of the solubility product is:

1. When a salt is dissolved in a solvent, the strong forces of attraction of solute that are the lattice enthalpy of its ions should be overcome by the interactions between the ions and the solvent.
2. During solvation, energy is released, and this is signified by the negative solvation enthalpy of ions.
3. The solvation enthalpy depends upon the nature of the solvent.
4. The lower value of solvation enthalpy means that this energy is not sufficient for overcoming the lattice enthalpy.
5. Due to this reason, the salts are not dissolved in the non-polar solvents. Therefore, for a salt to be dissolved in a solvent, its solvation enthalpy needs to be greater than its lattice enthalpy.
6. The solubility depends on the temperature, and it varies for every salt.

Based on the solubility, Salts are classified accordingly:

Summary

Equilibrium can be established for both physical as well as chemical processes and at this stage rate of forward and reverse reactions are equal. The equilibrium constant, \(\text {K}_{\text {c}}\) is expressed as the concentration of products divided by reactants, where each term is raised to their stoichiometric coefficients. The substances that conduct electricity in aqueous solutions are known as electrolytes. Acids, bases, and salts are electrolytes, and the electricity is conducted by their aqueous solutions due to anions and cations produced by the dissociation or ionisation of electrolytes in the aqueous solution. The type of equilibrium constant whose value depends on temperature is called the solubility product denoted as \(\text {K}_{\text {sp}}\). It usually increases with the increase in temperature due to the increased solubility. 

FAQs

Q.1. What is ionic equilibrium?
Ans: In the case of weak electrolytes, ions are partially ionised and because of this ionisation, weak electrolytes exist in dynamic equilibrium with the unionised molecules. This type of equilibrium is called ionic equilibrium. Thus, we can say that the equilibrium which is established by the unionised molecules and the ion in the weak electrolytic solution is known as the ionic equilibrium. 

Q.2. What is the difference between chemical and ionic equilibrium?
Ans: The key difference between chemical and ionic equilibrium is that in chemical equilibrium the equilibrium occurs between the chemical reactants and the products while in the case of ionic equilibrium the equilibrium remains between the unionised molecules and ions in an electrolyte.

Q.3. What is an ionic equilibrium example?
Ans: The equilibrium gets established between ions of a molecule after dissociation is known as ionic equilibrium. For example, sodium chloride, \(\text {NaCl}\) is an electrolyte as it undergoes complete ionisation in its aqueous solution to release sodium ions \(\left(\text {Na}^{+}\right)\) and chloride \(\left(\mathrm{Cl}^{-}\right)\) ions, \({\text{NaCl}} \leftrightarrow {\text{N}}{{\text{a}}^ + } + {\text{C}}{{\text{l}}^ – }\)

Q.4. How important is ionic equilibrium?
Ans: Ionic equilibrium is very important as it is established between the unionised molecules and the ions in the solution of weak electrolytes. With the help of ionic equilibrium, we can calculate the fraction of the initial amount of the reactant that gets converted into the product at equilibrium. The fraction of molecules that get dissociated can be represented by using the degree of dissociation.

Q.5. What is the principle of ionic solubility?
Ans: The principal of ionic solubility states that for a sparingly soluble electrolyte, the product of the concentrations of the constituent ions (raised to the powers equal to the numbers of ions in solution) is constant at a given temperature. For an ionic equilibrium equation, \(\text {A}_{\text {x}} \text {B}_{\text {y}}(\text {s}) \rightarrow \text {xA}^{\text {y}+}(\text {aq})+\text {yB}^{\text {x}-}(\text {aq})\), the equilibrium constant is \(\text {K}_{\text {c}}=\left[\text {A}^{\text {y}+}\right]^{\text {x}}\left[\text {B}^{\text {x}-}\right]^{\text {y}}\). 

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