QUESTION NO. 1

(a) What is Solubility product? Discuss its applications in salt analysis

Solubility Product (Ksp)

The solubility product constant (Ksp) is a measure of the solubility of a sparingly soluble ionic compound in water. It is the product of the molar concentrations of the ions, each raised to the power of their respective coefficients in the balanced chemical equation. For a generic salt ( AB ) that dissociates into ( A^+ ) and ( B^- ):

[ AB(s) \rightleftharpoons A^+(aq) + B^-(aq) ]

The solubility product expression is:

[ K_{sp} = [A^+][B^-] ]

For salts that dissociate into more complex ions, such as ( A_2B_3 ) dissociating into ( 2A^{3+} ) and ( 3B^{2-} ):

[ A_2B_3(s) \rightleftharpoons 2A^{3+}(aq) + 3B^{2-}(aq) ]

The solubility product expression is:

[ K_{sp} = [A^{3+}]^2[B^{2-}]^3 ]

Applications in Salt Analysis

1. Qualitative Analysis (Group Separation):

• The solubility product helps in the qualitative analysis of cations in a mixture by separating them into groups based on their differing solubility products. For example, in the qualitative analysis of cations, specific reagents are added to precipitate groups of cations as insoluble salts. The selective precipitation is based on differences in Ksp values.

1. Precipitation Reactions:

• The Ksp is used to predict whether a precipitation reaction will occur when two ionic solutions are mixed. If the product of the ionic concentrations in the mixture exceeds the Ksp of the salt, a precipitate will form.

1. Determination of Ion Concentrations:

• The solubility product can be used to calculate the concentration of ions in a saturated solution of a sparingly soluble salt. This is important in determining the extent of solubility of the salt under various conditions.

1. Common Ion Effect:

• The presence of a common ion reduces the solubility of a salt. This principle is applied in qualitative analysis to prevent the precipitation of certain salts by adding a solution containing a common ion. The solubility product helps predict the extent of this effect.

1. Purification of Salts:

• Ksp is used in the recrystallization process to purify salts. By manipulating temperature and concentration, impurities with different solubility products can be separated from the desired product.

1. Environmental Chemistry:

• Understanding the solubility products of various salts helps in predicting the behavior of minerals and pollutants in natural water bodies. This is crucial for environmental monitoring and remediation efforts.

In summary, the solubility product is a fundamental concept in chemistry that is widely used in salt analysis, both for qualitative and quantitative purposes. It aids in understanding and predicting the behavior of ionic compounds in solution.

(b) Distinguish order and molecularity of reaction.

Order of Reaction vs. Molecularity of Reaction

Order of Reaction:

1. Definition:

• The order of a reaction refers to the sum of the powers of the concentration terms in the rate law expression of the reaction.

1. Determination:

• It is determined experimentally by observing how changes in reactant concentrations affect the reaction rate.

1. Dependence:

• The order of reaction can be zero, fractional, integer, or even negative and does not necessarily relate to the stoichiometric coefficients of the reactants in the balanced chemical equation.

1. Example:

• For the reaction ( A + 2B \rightarrow C ) with a rate law ( \text{rate} = k[A][B]^2 ), the reaction is first-order with respect to ( A ) and second-order with respect to ( B ). The overall order of the reaction is ( 1 + 2 = 3 ).

1. Types:

• There are various types of reaction orders: zero-order, first-order, second-order, and mixed-order (fractional).

1. Significance:

• The order of a reaction is important for understanding the kinetics of a reaction and for determining the reaction mechanism.

Molecularity of Reaction:

1. Definition:

• Molecularity refers to the number of reactant molecules, atoms, or ions that come together in a single step to form the products.

1. Determination:

• It is a theoretical concept based on the reaction mechanism and can only be an integer (1, 2, or 3).

1. Dependence:

• Molecularity is related to the reaction mechanism and is always a positive integer. It represents the number of species involved in the elementary step of the reaction.

1. Example:

• For the elementary reaction ( A_2 \rightarrow 2A ), the molecularity is 1 (unimolecular). For the reaction ( A + B \rightarrow C ), the molecularity is 2 (bimolecular).

1. Types:

• The molecularity of a reaction can be unimolecular, bimolecular, or trimolecular.

1. Significance:

• Molecularity helps in understanding the mechanism of an elementary reaction, describing how reactant molecules collide and react in a single step.

Key Differences:

1. Nature:

• Order is an empirical value determined by experiments, whereas molecularity is a theoretical value based on the reaction mechanism.

1. Values:

• Order can be zero, fractional, integer, or negative, while molecularity is always a positive integer (1, 2, or 3).

1. Application:

• Order applies to the overall reaction or complex reactions, whereas molecularity applies only to elementary reactions.

1. Dependence on Mechanism:

• Order does not necessarily depend on the reaction mechanism, but molecularity directly relates to the mechanism of the elementary step.

In summary, while both the order and molecularity of a reaction provide insight into reaction kinetics, they are distinct concepts with different definitions, values, and applications. The order of reaction is determined experimentally and applies to the overall reaction, whereas molecularity is a theoretical concept that applies to individual elementary steps in a reaction mechanism.

(c) Show that half life period of first order reaction is independent of initial concentration.

To show that the half-life period of a first-order reaction is independent of the initial concentration, we can derive the half-life expression from the integrated rate law of a first-order reaction.

For a first-order reaction, the rate law is:

[ \text{rate} = k[A] ]

where ( k ) is the rate constant and ([A]) is the concentration of the reactant ( A ).

The integrated rate law for a first-order reaction is:

[ \ln [A] = -kt + \ln [A_0] ]

where ([A_0]) is the initial concentration of the reactant at ( t = 0 ).

To find the half-life (( t_{1/2} )), we set ([A] = \frac{[A_0]}{2} ), the concentration of ( A ) at half-life. Substituting this into the integrated rate law gives:

[ \ln \left( \frac{[A_0]}{2} \right) = -kt_{1/2} + \ln [A_0] ]

Using the properties of logarithms, we can simplify the left side of the equation:

[ \ln [A_0] – \ln 2 = -kt_{1/2} + \ln [A_0] ]

Next, we subtract (\ln [A_0]) from both sides of the equation:

[ -\ln 2 = -kt_{1/2} ]

Solving for ( t_{1/2} ) gives:

[ t_{1/2} = \frac{\ln 2}{k} ]

Since ( \ln 2 ) is a constant (approximately 0.693) and ( k ) is the rate constant, it is evident that the half-life ( t_{1/2} ) for a first-order reaction is:

[ t_{1/2} = \frac{0.693}{k} ]

This expression shows that the half-life of a first-order reaction is independent of the initial concentration ([A_0]). It depends only on the rate constant ( k ).