Physical Chemistry

The enthalpy of formation of a metal halide is mainly related to its lattice energy, which is the energy released when the ions form the solid lattice.
• Fluoride (F-): Fluoride ions are the smallest halide ions, which results in a high lattice energy and therefore, most negative enthalpy of formation when they combine with metals.
• Chloride (Cl-): Chloride ions are larger than fluoride, which leads to a smaller lattice energy than fluorides but still greater than the other halides, with correspondingly less negative enthalpy of formation.
• Bromide (Br-): Bromide ions are larger than chloride ions, resulting in even smaller lattice energy and correspondingly lower negative enthalpy of formation.
• Iodide (I-): Iodide ions are the largest among halides, leading to the smallest lattice energy and thus the least negative enthalpy of formation.
Thus, the order of enthalpy of formation from most negative to least negative is Fluoride > Chloride > Bromide > Iodide.

The strength of an acid is inversely related to the strength of its conjugate base.
• Strong acids dissociate completely, producing stable conjugate bases with little tendency to accept a proton. Therefore statement (A) is correct, that is, the stronger the acid, the weaker is the conjugate base.
• pKa value: is the indicator of acid strength; the larger the pKa value, the weaker the acid.
Therefore a higher pKa indicates a weaker acid, which leads to a stronger conjugate base and statement (D) is correct, that is, the larger the pKa value of the conjugate acid, the stronger its base. Statements B and C are incorrect.

The ion exhibits a linear geometry due to its electronic arrangement. According to the Valence Shell Electron Pair Repulsion (VSEPR) theory:
The central iodine atom in has three lone pairs of electrons and forms bonds with two outer iodine atoms.
The lone pairs arrange symmetrically to minimize electron repulsion, resulting in a bond angle of .
This linear geometry is a characteristic of triatomic species with symmetric electron distribution.

An isobaric process occurs when the pressure of a system remains constant, even as volume and temperature change. Examples include:
• Heating or cooling of a gas in a piston-cylinder setup.
• Phase changes at constant atmospheric pressure.
Other processes:
• Isothermal: Constant temperature.
• Adiabatic: No heat exchange.
• Isochoric: Constant volume.

Electronegativity is the measure of an atom’s ability to attract shared electrons in a chemical bond. Factors influencing electronegativity include:
• Atomic size: Smaller atoms have higher electronegativity as the nucleus is closer to the bonding electrons.
• Nuclear charge: Higher positive charge in the nucleus increases the attraction for bonding electrons.
For example, fluorine is the most electronegative element due to its small size and high nuclear charge.

The Carnot engine is a theoretical thermodynamic cycle that is reversible and operates with the maximum possible efficiency. The proof that the Carnot engine is reversible is deeply rooted in the Second Law of Thermodynamics, particularly its implications for entropy changes and the direction of thermodynamic processes. The Second Law states that in a reversible process, the total entropy of an isolated system remains constant (∆S = 0), while irreversible processes lead to an increase in entropy (∆S > 0).
The Carnot cycle is a series of reversible steps. Because each step is reversible, the process can run in reverse and the total change in entropy for the entire cycle is zero. The proof involves showing that no other engine operating between the same two temperatures could be more efficient than the Carnot engine without violating the Second Law. This analysis uses the fact that reversible processes can be reversed without leaving a trace and that if another engine was more efficient the process would violate the Second Law.

Molar concentration, also known as molarity, is defined as the number of moles of a solute present in 1 liter of solution. It is expressed as:

This concept is critical in stoichiometric calculations and solution preparation. Other related terms include:
Activity: Effective concentration of a species in a solution.
Normal solution: Concentration expressed in equivalents per liter.
Active mass: An older term used in reaction rate expressions.

Ionization energy, the energy required to remove an electron from a gaseous atom,
depends on the following factors:
• Atomic Size: Smaller atoms have higher ionization energy due to stronger nuclear attraction.
• Nuclear Charge: Higher nuclear charge increases the attraction between the nucleus and electrons, raising ionization energy.
• Type of Electron: Electrons in the s-orbital experience less shielding than those in p, d, or f orbitals, making them harder to remove.
For example, elements in the same period show increasing ionization energy as nuclear charge increases.

The acidic strength of oxoacids increases with the number of oxygen atoms attached to the central atom. This is because more oxygen atoms stabilize the conjugate base through resonance.
• HOCl has one oxygen atom
• HOClO has two oxygen atoms
• HOClO2 has three oxygen atoms
• HOClO3 has four oxygen atoms.
The order of increasing acid strength is HOCl

Crystal systems are classified based on their axial lengths and angles:
• Cubic: All sides are equal, and all angles are 90°
• Tetragonal: Two sides are equal, one different, all angles 90°
• Orthorhombic: All sides unequal, all angles 90°
• Hexagonal: Two sides equal, one different, two angles 90° and one 120°
Therefore, the correct matching is: (A) - (I), (B) - (III), (C) - (II), (D) - (IV).

The Hume-Rothery rules describe the necessary conditions for forming a substitutional solid solution.
• Atomic size: The two metals should have similar atomic sizes, with metallic radii differing by not more than 15%.
• Crystal structure: They should have the same crystal structure for atoms to replace each other in the lattice.
• Electronegativity: The chemical properties should be similar, particularly their electronegativity, so that they bond with similar strengths to their neighbors in the crystal lattice.
• Electrical conductivity: Electrical conductivity is not a requirement for forming solid solution.
Therefore, B and C are correct conditions.

A reversible isothermal process is a thermodynamic process where the temperature remains constant throughout and the process is carried out infinitely slowly.
• Isothermal: means that the temperature remains constant.
• Reversible: It occurs when the system is in equilibrium at all times, requiring an infinitesimally slow change and therefore infinitesimally slow process.
Pressure may change during an isothermal reversible process. Therefore, correct conditions are Infinitesimally slow process and constant temperature.