13. SOLUBILITY EQUILIBRIA OF SPARINGLY SOLUBLE SALTS

SOLUBILITY EQUILIBRIA OF SPARINGLY SOLUBLE SALTS

The solubility of a particular salt in a solvent is always a very significant fact to be taken into consideration when studying its properties and the properties of the solution it forms with a particular solvent. While salts like NaCl,KCl and others such as potassium dichromate are completely soluble in water, there are some salts that do not dissolve at all or dissolve only to a very minimal extent. These salts form a special case when defining the solubility equilibria and are called sparingly soluble salts.

Such sparingly soluble salts present solubility equilibria which are measured using an entity called a solubility product. This article will discuss the solubility product and how it can be applied to the solubility equilibria of sparingly soluble salts.

Salts are classified on the basis of their solubility in the following table.

• Solubility Products
A sparingly soluble salt is so-called because when it is stirred into water or mixed with water, only a very small amount of the salt goes into the solution, and most of it remains undissolved. The solution becomes saturated with that little amount of salt dissolved, and the salt immediately dissociates into its ions. For example, when a sparingly soluble salt like AgCl goes into the solution, it dissociates as Ag+ and Cl− ions immediately. So, a dynamic equilibrium exists between the two entities: the undissolved salt and the dissolved ions which are in the solution.

At equilibrium, the dissolving of solid AgCl and precipitation of undissolved AgCl will take place at the same rate. Hence, the equilibrium between the two opposite processes can be given by a reversible equation:

AgCl_(s) Dissolution/Precipitation ⇔ AgCl_(aq) ↔ Ag⁺_(aq) + Cl^-_(aq)

The equation can also be written as: AgCl_(aq) ↔ Ag⁺_(aq) + Cl^–_(aq)

When the law of chemical equilibrium is applied to the above equation, it can be written as: K = [Ag⁺][Cl^–][AgCl]

The concentration of the undissolved solid AgCl usually remains constant, and hence, the above equation can be written as: [Ag⁺][Cl⁻]= K∗[AgCl] = Ksp

The Ksp is the solubility product and is equal to the ionic product: [Ag⁺][Cl⁻] in the saturated solution.

So, for any sparingly soluble salt solution, AxBy the equilibrium of the reaction can be represented as: AxBy ↔ xAy⁺ + yBx^–

The solubility product for AxBy can be written as: Ksp = [Ay⁺]x ∗ [Bx^–]y

The x and y represent the number of ions present in the formula of the sparingly soluble salt.

Hence, the solubility product at a specified temperature for an electrolyte can be defined as the product of the molar concentrations of the ions present in its saturated solution, with each concentration raised to the power equal to the number of ions produced on the dissociation of one molecule of the electrolyte.

Difference between Solubility Product and Ionic Product

As we know, the solubility product and the ionic product of an electrolyte is represented by the product of their concentrations, raised to a power that is equal to the number of ions present on its dissociation. So, how do we differentiate between the two of them? Here is how:

a. Ionic product is used for all types of solutions, both saturated and unsaturated. However, the solubility product is only used for saturated solutions, where a dynamic equilibrium exists between the undissolved salt and the dissolved ions present in the solution. So, one can call the solubility product the ionic product in saturated solutions.

b. For any salt, its solubility product is constant at a constant temperature. The ionic product, however, will depend upon the number of ions present at that particular time.

Solubility products of any sparingly soluble salt can be determined using the value of its solubility product in water at that temperature.

Significance of Solubility Product

The solubility product value can be applied in various aspects and, therefore, is very useful. Below are some of the applications of the solubility product of salts.

a. To Calculate the Solubility of Sparingly Soluble Salt: The solubility of a sparingly soluble salt is very difficult to measure. However, the knowledge of its solubility product can help in determining its solubility at any temperature.

The relationship between solubility (inmol/L) and solubility product (Ksp) depends upon the nature of the salt.

(i) Salts of type AB: (Example: PbSO₄,AgCl,AgBr etc.)

AB ↔ A⁺ + B^–

Ksp = [A⁺][B^–] = s ∗ s = s₂

(ii) Salts of type AB₂:(PbCl₂,SrF₂)

AB₂ ↔ A⁺ +  2B^–

Ksp = [A+][B−] = s ∗ (2s)₂ = s∗4 s₂ = 4 s₃

Similarly, it can be calculated for all other salts with different types to determine the relationship between solubility and solubility product.

b. To Predict Precipitation Reactions: We know that the solubility product of salt is its maximum saturation point at a particular temperature. So, it represents the upper limit in the ionic product of a sparingly soluble salt.

What that means is that if the ionic product is equal to Ksp then no more solute can go into that solution at that particular temperature. This can help in predicting the precipitation.

When the ionic product or the product of the concentration of ions in any solution is more than that of the value of its solubility product of that sparingly soluble salt, then the excess ions will result as a precipitate or precipitation will occur.

So, when two solutions containing known concentrations of ions are mixed together, the knowledge of their solubility product can help predict whether the precipitation will occur or not.

c. In Qualitative Analysis: The separation and identification of basic radicals are made based upon the principles of common ion effect and solubility product principle in qualitative analysis.

d. Precipitation of Soluble Salts: The use of solubility product and common ion effect explains the phenomenon of precipitation when a saturated solution is mixed with a suitable electrolyte containing a common ion. The increase in the ionic product over the solubility product results in precipitation. This phenomenon is used in the purification of common salt, salting out of soap and also in the manufacture of baking soda or sodium bicarbonate.

It is applicable to sparingly soluble salt. There is equilibrium between ions and unionised solid substance.

AgCl ↔ Ag⁺ + Cl^-

K_sp = [Ag⁺] [Cl^-]

K_sp is called solubility product

In pure water,

K_sp = [Ag⁺] [Cl^-]

K_sp = S² { ∵ S = [Ag⁺] = [Cl^-] }

S = √K_sp

• Equilibrium: It can be established for both physical and chemical processes. At the state of equilibrium rate of forward and backward reactions are equal.
• Equilibrium constant: Kc is expressed as the concentration of products divided by reactants each term raised to the stoichiometric coefficients. For reactions,

aA + bB ↔ cC + dD

K_c = [C]^c_eq [D]^d_eq

 [A]^a_eq [B]^b_eq

K_c >> 1 : Mixture contains mostly product

K_c << 1 : Mixture contains mostly reactants

• Le Chatelier’s principle: It states that the change in any factor such as temperature, pressure, concentration etc., will cause the equilibrium to shift in such a direction so as to reduce the effect of the change.
• Electrolytes: Substances that conduct electricity in aqueous solutions are called electrolytes.
• Arrhenius Concept: According to Arrhenius, acids give hydrogeneous while bases produce hydroxyl ions in their aqueous solution.
• Bronsted-Lowry concept: Bronsted-Lowry defined acid as proton donor and a base as a proton acceptor.
• Conjugate base and Conjugate acid: When a Bronsted-Lowry acid reacts with a base it produces its conjugate base and conjugate acid.
• Conjugate pair of acid and base: Conjugate pair of acid and base differs only by one proton.
• Lewis acids: Define acid as an electron pair acceptor and a base as an electron pair donor.
• pH Scale: Hydronium ion concentration in molarity is more conveniently expressed on a logarithmic scale known as the pH scale. The pH of pure water is 7.
• Buffer solution: It is the solution whose pH does not change by addition of small amount of strong acid or base.
For example: CH₃COOH + CH₃COONa.
• Solubility product (K_sp): For a sparingly soluble salt, it is defined as the product of molar concentration of the ions raised to the power equal to the number of times each ion occurs in the equation for solubilities.

BaSO₄ ↔ Ba²⁺_(aq) + SO₄^2-_(aq)

This equilibrium system may be described by the mass action expression