Concept:

The electronic configuration [Kr] 5s² 4d¹⁰ 5p⁵ belongs to one of the groups in the periodic table.

General electronic configuration of mentioned groups:

• Group 14: ns² np²
• Group 15: ns² np³
• Group 16: ns² np⁴
• Group 17: ns² np⁵

Explanation:

The given configuration can be broken down as follows:

• [Kr]: represents the core electrons equivalent to krypton (atomic number 36).

• 5s²: 2 electrons in the 5s orbital.

• 4d¹⁰: 10 electrons in the 4d orbital.

• 5p⁵: 5 electrons in the 5p orbital.

Elements in Group 17 of the periodic table are known as halogens. They have seven electrons in their outermost shell (ns² np⁵) where n is the principal quantum number. In this case, n = 5 which matches the outermost electron configuration of 5s² 5p⁵.

Conclusion:

Therefore, the electronic configuration [Kr] 5s² 4d¹⁰ 5p⁵ belongs to: Group 17

CONCEPT:

Rate of Reaction

• The rate of a reaction is defined as the change in concentration of a reactant or product per unit time.
• For a reaction involving gases, the rate can be measured in terms of change in pressure.
• The rate of disappearance of a reactant is the negative of the rate of change of its concentration (or pressure) over time.

CONCEPT:

Bond Angle and Factors Affecting It

• The bond angle in a molecule is influenced by factors such as the number of lone pairs on the central atom, the electronegativity of surrounding atoms, and the repulsion between electron pairs.
• Lone pairs on the central atom exert more repulsive force than bonding pairs. As the number of lone pairs increases, the bond angle decreases due to the increased lone pair-bond pair repulsion.
• Electronegativity also plays a role. Highly electronegative atoms pull bonding pairs closer to themselves, affecting the bond angles.

CONCEPT:

Equilibrium Constant (Kp) for Gaseous Decomposition

• The decomposition of a solid into gases establishes an equilibrium where Kp (equilibrium constant in terms of partial pressures) can be calculated based on the partial pressures of the gaseous products.
• When a solid decomposes into two gases in a 1:1 molar ratio, each gas will have an equal partial pressure at equilibrium.
• In this case, Kp can be expressed as the square of the partial pressure of one gas (since both partial pressures are equal).

CONCEPT:

Bond Dissociation Energy and Bond Types

• The bond dissociation energy refers to the amount of energy required to break a bond in a molecule.
• Sigma ((σ ) bonds are formed by the head-on overlap of atomic orbitals, resulting in greater orbital overlap.
• Pi (π ) bonds are formed by the side-to-side overlap of atomic orbitals, resulting in less orbital overlap compared to sigma bonds.
• Greater orbital overlap in sigma bonds makes them generally stronger and thus, they have higher bond dissociation energies compared to pi bonds.

• Statement I: The bond dissociation energy of a molecule is higher for a sigma bond than for a pi bond.
• Reason: Sigma bonds are stronger due to greater orbital overlap.
• Statement II: Sigma bonds have greater orbital overlap compared to pi bonds, making them stronger.

The correct answer is: Both Statement I and Statement II are true.

CONCEPT:

Understanding Common Ion Effect on Solubility

• The common ion effect states that the solubility of a sparingly soluble salt (like AgCl) decreases when a solution already contains one of its ions (either Ag⁺ or Cl^-).
• According to Le Chatelier's principle, adding a common ion shifts the dissolution equilibrium of the salt back towards the undissolved solid, lowering its solubility.
• The solubility of AgCl is most reduced in a solution with a high concentration of either Ag⁺ or Cl^- ions, depending on which ion is present in excess.

CALCULATION:

• For each option, let’s examine the concentration of ions provided:
  •  AgNO₃ (0.1 M):
    • AgNO₃ dissociates in water to provide Ag⁺ and NO₃^- ions.
    • Since it has a concentration of 0.1 M, it provides 0.1 M of Ag⁺ ions in the solution.
    • This addition of Ag⁺ ions directly impacts the solubility of AgCl due to the common ion effect, as Ag⁺ is a product of the AgCl dissolution reaction.
  •  H₂O (ℓ):
    • Pure water contains no additional ions (neither Ag⁺ nor Cl^-), so AgCl will dissolve with its inherent solubility, unaffected by any common ions.
  •  NaCl (0.4 M):
    • NaCl dissociates to provide Na⁺ and Cl^- ions.
    • With a concentration of 0.4 M, NaCl adds 0.4 M of Cl^- ions to the solution, reducing AgCl solubility by the common ion effect with Cl^-.
  •  BaCl₂ (0.3 M):
    • BaCl₂ dissociates into Ba²⁺ and two Cl^- ions.
    • This means a 0.3 M solution of BaCl₂ provides 0.6 M of Cl^- ions, which significantly decreases AgCl’s solubility due to the high Cl^- concentration.
• Comparing Effects:
  • The addition of Ag⁺ ions (Option 1) will have the most substantial effect on reducing AgCl’s solubility because Ag⁺ is the direct product of the dissolution of AgCl, shifting equilibrium towards the solid form of AgCl more efficiently.
  • Although Options 3 and 4 also decrease solubility by adding Cl^-, the impact is slightly less than the direct addition of Ag⁺ from AgNO₃.

CONCLUSION:

• The correct option is: Option 1 (AgNO₃ (0.1 M))

Concept:

When two solutions are isotonic, they have the same osmotic pressure. The osmotic pressure depends on the concentration of solute particles in the solution, which is influenced by dissociation for electrolytes. The van 't Hoff factor (i) represents the number of particles formed in solution per formula unit of solute.

Explanation:

• Given:

  • 0.004 M-Na₂SO₄

  • 0.01 M-Glucose

• For isotonic solutions:
  • π(Na₂SO₄) = π(Glucose)
• Osmotic pressure (π): π = i × C × R × T
• For glucose (a non-electrolyte), i = 1
• For Na₂SO₄, which dissociates into 2 Na⁺ and 1 SO₄^2-:
• Let the degree of dissociation be α.
  • i(Na₂SO₄) = 1 + (2 + 1 - 1)α = 1 + 2α
• Equating osmotic pressures:
  • (1 + 2α) × 0.004 = 1 × 0.01
  • 0.004 + 0.008α = 0.01
  • 0.008α = 0.006
  • α = 0.75
• The percentage dissociation α% is:
  • α% = 0.75 × 100% = 75%

Conclusion:

The percentage dissociation of Na₂SO₄ is 75%.

CONCEPT:

Osmosis, Entropy, and Free Energy

• Osmosis: Osmosis is the movement of solvent molecules through a semipermeable membrane from a region of lower solute concentration (higher solvent concentration) to a region of higher solute concentration (lower solvent concentration). This process occurs naturally and aims to equalize the concentration on both sides of the membrane.
• Entropy Change: Entropy is a measure of randomness or disorder in a system. During osmosis, solvent molecules move towards the side with a higher solute concentration, resulting in a more mixed, disordered solution. This increase in disorder leads to an increase in entropy.
• Free Energy Change: Free energy (Gibbs free energy,  ΔG ) determines the spontaneity of a process. A decrease in free energy indicates a spontaneous process. In osmosis, as the system moves toward equilibrium, the free energy of the system decreases, reflecting the spontaneous nature of the process.

EXPLANATION:

• Statement I: Osmosis takes place with an increase of entropy
  • Explanation: Since osmosis leads to a more mixed solution with solvent molecules dispersing into a region of higher solute concentration, the system’s disorder (entropy) increases.
  • Conclusion: This statement is correct.
• Statement II: Osmosis is a non-spontaneous process
  • Explanation: Osmosis occurs spontaneously without external energy, as it moves towards an equilibrium state.
  • Conclusion: This statement is incorrect.
• Statement III: Free energy decreases during osmosis
  • Explanation: As osmosis progresses towards equilibrium, the system’s free energy decreases, which is characteristic of spontaneous processes.
  • Conclusion: This statement is correct.

CONCLUSION:

The correct option is: Option 4) I and III

CONCEPT:

pH Change During Neutralization of a Weak Acid by a Strong Base

Conclusion:

The 25% completion time calculation shows it is approximately 28.8 sec, not 34.7 sec, making option 3 false. Thus, the correct answer is option 3.