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Q. The first $\left(\right.\left(\Delta \right)_{i}H_{1}\left.\right)$ and second $\left(\right.\left(\Delta \right)_{i}H_{2}\left.\right)$ ionization enthalpies (in kJ $mol^{- 1}$ ) and the electron gain enthalpy $\left(\right.\left(\Delta \right)_{e g}H\left.\right)$ (in kJ $mol^{- 1}$ ) of the elements I, II, III, IV and V are given below:
Element $\Delta _{i}H_{1}$ $\Delta _{i}H_{2}$ $\Delta _{e g}H$
I $520$ $7300$ $-60$
II $419$ $3051$ $-48$
III $1681$ $3374$ $-328$
IV $1008$ $1846$ $-295$
V $2372$ $5251$ $+48$

The most reactive metal and the least reactive non-metal of these are respectively

NTA AbhyasNTA Abhyas 2022

Solution:

$\Delta H_{1}=520$
$\Delta H_{2}=7300$
$\Delta H_{2}$ is $10$ times greater than $\Delta H_{1}$ mean first $e^{-}$ remove from inner shell {Ionisation energy decreases the number of shells increases because $Z_{e f f}$ decreases hence, removal of electron is easy so, $I.E.\downarrow$
III $\Delta _{i}H_{1} < \Delta _{i}H_{2}$
IV $\Delta _{i}H_{1} < \Delta _{i}H_{2}$
V $\Delta _{i}H_{1} < \Delta _{i}H_{2}$
$\Delta H_{e f f}H=+ve$
$\Delta H_{e f f}H=+ve$ Means it belongs to inert gas & these are belongs to non-metal and very less reactive
So, II most reactive metal.
V is least reactive non-metal.