Question

According to Born-Haber cycle, the acid strength of Halogen depends upon :
A. Enthalpy of dehydration
B. Enthalpy of dissociation
C. Dipole moment
D. Electron affinity $X^-$
E. Metal ion
Choose the most appropriate answer from the options given below :

• A. A, B, C only
• B. B, C, D only
• C. C, D, E only
• D. A, B, D only

Hint:

For halogen acids, the dominant factor determining their relative acidity order in water (HI > HBr > HCl $\gg$ HF) is the Bond Dissociation Enthalpy, as the H-X bond becomes much weaker down the group, outweighing changes in electron affinity and hydration enthalpy.

Answer 1

The Correct Option is D

Step 1: Concept:
The question asks to identify the thermodynamic factors that govern the acid strength of halogen acids (HX) when applying a Born-Haber cycle (or a similar thermodynamic cycle in aqueous solution).

Step 2: Key Formula or Approach:
The dissociation of a hydrogen halide $HX_{(aq)} \rightarrow H^+_{(aq)} + X^-_{(aq)}$ can be broken down into a theoretical thermodynamic cycle involving several conceptual steps:
1. Dehydration/Desolvation: Removing the aqueous HX species from solution into the gas phase (often ignored or combined, but if considering the full cycle from aqueous, it's a step. More commonly, we look at the hydration of the resulting ions).
2. Bond Dissociation: Breaking the gaseous HX molecule into atoms: $HX_{(g)} \rightarrow H_{(g)} + X_{(g)}$ (Enthalpy of dissociation).
3. Ionization of Hydrogen: $H_{(g)} \rightarrow H^+_{(g)} + e^-$ (Ionization energy).
4. Electron Affinity: The halogen atom gaining an electron: $X_{(g)} + e^- \rightarrow X^-_{(g)}$ (Electron affinity).
5. Hydration: The gaseous ions entering the aqueous phase: $H^+_{(g)} + X^-_{(g)} \rightarrow H^+_{(aq)} + X^-_{(aq)}$ (Enthalpy of hydration, whose reverse process is dehydration).

Step 3: Step-by-step Explanation:

• Based on the cycle above, the overall Gibbs free energy change (which dictates acid strength, $K_a$) is the sum of these energy terms.

• A. Enthalpy of dehydration: In many textbook problems, "enthalpy of hydration" is the term used. Dehydration is simply the energetic opposite. The cycle definitively depends on these solvation energies.

• B. Enthalpy of dissociation: Breaking the H-X bond is a major energy barrier. The weaker the bond, the stronger the acid (e.g., HI > HBr > HCl > HF). This is a critical factor.

• C. Dipole moment: While it influences physical properties, it is not an energetic step defined within a Born-Haber thermodynamic cycle.

• D. Electron affinity: The energy released when the halogen atom accepts an electron to become an anion ($X^-$) strongly drives the thermodynamics of dissociation.

• E. Metal ion: Completely irrelevant to the acid strength of an HX molecule, as no metal ions are involved in the dissociation of HX in water.

• Therefore, the parameters forming the thermodynamic cycle are A, B, and D.

Step 4: Final Answer:
The factors involved in the cycle are A, B, and D, which points to option (D).