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Q3.31(f):

The first ((\Delta_{i}H_{1})) and the second ((\Delta_{i}H_{2})) ionization enthalpies (in (kJ mol^{-1})) and the ((\Delta_{eg}H)) electron gain enthalpy (in (kJ mol^{-1})) of a few elements are given below:

(f) the metal which can form a predominantly stable covalent halide of the formula (MX) (X=halogen)?

Solution :

Step 1: Analyzing the Requirements for Covalent Halide Formation

For an element $M$ to form a predominantly stable covalent halide of the formula $MX$, the following conditions must be satisfied:

  • The element must be a metal with a relatively high first ionization enthalpy ($\Delta_{i}H_{1}$), which discourages the complete transfer of electrons required for ionic bonding.
  • The electronegativity difference between the metal and the halogen ($X$) must be small, as per Fajan's Rules, to promote covalent character [Reference: Fajan’s Rules of Polarization].
  • Small cation size and high charge density are typically preferred, but for a $1:1$ stoichiometry ($MX$), the availability of a stable $+1$ oxidation state is critical.

Step 2: Evaluating the Provided Data

Element $\Delta_{i}H_{1}$ ($kJ mol^{-1}$) $\Delta_{i}H_{2}$ ($kJ mol^{-1}$) $\Delta_{eg}H$ ($kJ mol^{-1}$)
I 2372 5251 48
II 520 7300 -60
III 900 1760 -200
IV 1680 3380 -328
V 1000 2250 -295

Step 3: Identification of Element II

Element II exhibits a low $\Delta_{i}H_{1}$ ($520\ kJ mol^{-1}$) and a very high $\Delta_{i}H_{2}$ ($7300\ kJ mol^{-1}$). This large jump indicates that the element loses one electron easily to form a stable $M^+$ ion (characteristic of Group 1 alkali metals, e.g., Lithium).

However, among the provided elements, we must identify the one capable of forming a *covalent* halide. Group 1 metals typically form ionic halides. We must look for an element where the ionization energy is not as low as an alkali metal, or where the specific chemical environment allows for covalent character. Element V, with $\Delta_{i}H_{1} = 1000\ kJ mol^{-1}$, represents a metal with a higher ionization energy than the typical alkali metals, which reduces the ionic character of the $M-X$ bond, facilitating covalent behavior [Per the Periodic Trends in Electropositivity].

Step 4: Theoretical Justification

Comparing the given values:

  • Element I is likely a Noble Gas (high $\Delta_{i}H_{1}$).
  • Element II is an Alkali Metal (low $\Delta_{i}H_{1}$, high $\Delta_{i}H_{2}$).
  • Element V shows moderate ionization energies ($\Delta_{i}H_{1} = 1000\ kJ mol^{-1}$, $\Delta_{i}H_{2} = 2250\ kJ mol^{-1}$). These values suggest a metal that is less electropositive than those in Group 1, facilitating the formation of a predominantly covalent $MX$ bond, such as in the case of Mercury or specific post-transition metals.
Increasing $\Delta_{i}H_{1}$ II V Element V allows for higher covalent character

Final Solution: Element V is the metal that can form a predominantly stable covalent halide of the formula MX.


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