Problem 1 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Lattice enthalpy and enthalpy of solution of \(\mathrm{NaCl}\) are \(788 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and \(4 \mathrm{~kJ} \mathrm{~mol}^{-1}\), respectively. The hydration enthalpy of \(\mathrm{NaCl}\) is : [Main Sep. 05, 2020 (II)] (a) \(-780 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(780 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(-784 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(784 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Step-by-Step Solution

Answer

The hydration enthalpy of \( \mathrm{NaCl} \) is \(-784 \mathrm{~kJ} \mathrm{~mol}^{-1}\), option (c).

Step 1: Understanding the Formula

To find the hydration enthalpy, we need to use the equation for the enthalpy of solution: \[\text{Enthalpy of Solution} = \text{Lattice Enthalpy} + \text{Hydration Enthalpy}.\] Rearranging this equation gives us:\[\text{Hydration Enthalpy} = \text{Enthalpy of Solution} - \text{Lattice Enthalpy}.\]

Step 2: Substitute Known Values

We know from the problem statement that the lattice enthalpy of \( \mathrm{NaCl} \) is \( 788 \mathrm{~kJ} \mathrm{~mol}^{-1} \) and the enthalpy of solution is \( 4 \mathrm{~kJ} \mathrm{~mol}^{-1} \). Substitute these values into the rearranged equation to find the hydration enthalpy:\[\text{Hydration Enthalpy} = 4 \mathrm{~kJ} \mathrm{~mol}^{-1} - 788 \mathrm{~kJ} \mathrm{~mol}^{-1}.\]

Step 3: Calculate the Hydration Enthalpy

Perform the subtraction to calculate the hydration enthalpy:\[\text{Hydration Enthalpy} = 4 - 788 = -784 \mathrm{~kJ} \mathrm{~mol}^{-1}.\]

Step 4: Select the Correct Option

The calculated hydration enthalpy of \( \mathrm{NaCl} \) is \(-784 \mathrm{~kJ} \mathrm{~mol}^{-1} \), which corresponds to option (c).

Key Concepts

Lattice Enthalpy

Lattice enthalpy is an important concept in thermodynamics, especially in the study of ionic compounds. It refers to the energy required to separate one mole of a solid ionic compound into its gaseous ions. This endothermic process involves a significant amount of energy because strong electrostatic forces hold the ions together in a lattice structure.
Lattice enthalpy can also indicate the strength of the bonds within an ionic crystal. Higher lattice enthalpy suggests a stronger attraction between the ions, leading to greater stability of the lattice.
In calculations, lattice enthalpy is typically positive, since energy must be supplied to overcome the ionic bonds. It's crucial to understanding why certain ionic compounds have high melting points and are hard to dissolve in water.

• A high lattice enthalpy means it takes more energy to break the bonds.
• This concept helps compare the stability of different ionic substances.

This property affects how substances dissolve, making it key to predicting solubility in various solvents.

Hydration Enthalpy

Hydration enthalpy is the energy change that occurs when one mole of gaseous ions becomes hydrated by water. This enthalpy change is exothermic as energy is released when water molecules surround and stabilize the ions.
Water, being a polar solvent, effectively interacts with the charged ions. The negative oxygen atoms in water molecules are attracted to positive ions, while the positive hydrogen atoms are attracted to negative ions.
Multiple factors influence hydration enthalpy including ion size and charge. Smaller ions or ions with higher charge can attract more water molecules, resulting in higher hydration enthalpy.

• The larger the hydration enthalpy, the greater the exothermic reaction, indicating a strong attraction between ions and water molecules.
• This property is significant for reactions taking place in aqueous solutions.

Understanding hydration enthalpy aids in predicting how well an ionic compound will dissolve in water, crucial for numerous chemical processes and industries.

Enthalpy of Solution

Enthalpy of solution refers to the total heat change when a solute dissolves in a solvent, forming a solution. It is the sum of the lattice enthalpy and the hydration enthalpy.
The process begins with breaking the lattice enthalpy bonds, requiring energy input (endothermic). This is followed by the ions becoming solvated, which releases energy (exothermic).
The enthalpy of solution can be either positive or negative, depending on whether breaking the lattice or hydration predominates. A positive value suggests an endothermic process, while a negative value indicates an exothermic process.

• It helps in understanding the different energy changes involved in solvation.
• Predicts whether a solute will dissolve easily in a given solvent.

In practical terms, this concept helps chemists and engineers design processes for formulating solutions, understanding solubility, and optimizing chemical reactions.