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: | Elements | $\Delta_i H_1$ | $\Delta_i H_2$ | $\Delta_{eg}H$ | | --- | --- | --- | --- | | I | 520 | 7300 | -60 | | II | 419 | 3051 | -48 | | III | 1681 | 3374 | -328 | | IV | 1008 | 1846 | -295 | | V | 2372 | 5251 | +48 | | VI | 738 | 1451 | -40 | Which of the above elements is likely to be: (a) the least reactive element. (b) the most reactive metal. (c) the most reactive non-metal. (d) the least reactive non-metal. (e) the metal which can form a stable binary halide of the formula $MX_2$ (X = halogen). (f) the metal which can form a predominantly stable covalent halide of the formula MX (X = halogen)?

> [!TLDR] > Ionization and electron-gain enthalpies reveal an element's reactivity and bonding character. Element **V** is the least reactive (noble gas), **II** the most reactive metal (alkali), **III** the most reactive non-metal (halogen), **IV** the least reactive non-metal (group 17, lower period), **VI** forms stable $MX_2$ (alkaline earth), and **I** forms covalent $MX$ (group 11 metal). --- ## Understanding Standard State Conditions and Periodic Trends Ionization enthalpy measures how easily an atom loses electrons (lower = more metallic), while electron-gain enthalpy measures how readily it accepts electrons (more negative = more non-metallic). The pattern of these values across the periodic table is diagnostic: - **Metals** have low $\Delta_i H_1$ and small or positive $\Delta_{eg}H$ (they don't want electrons). - **Non-metals** have high $\Delta_i H_1$ and large negative $\Delta_{eg}H$ (they crave electrons). - **Noble gases** have very high $\Delta_i H_1$ and positive $\Delta_{eg}H$ (stable, inert). - The jump from $\Delta_i H_1$ to $\Delta_i H_2$ tells us about electronic configuration: a huge jump means removing an electron from a much more stable inner shell. Let's decode each element by examining these signatures. --- ## Step-by-Step Analysis **1. Classify each element by its ionization pattern** | Element | $\Delta_i H_1$ | $\Delta_i H_2$ | Ratio $\frac{\Delta_i H_2}{\Delta_i H_1}$ | $\Delta_{eg}H$ | Likely Identity | |---------|---------------|---------------|------------------------------------------|---------------|-----------------| | I | 520 | 7300 | 14.0 | −60 | Group 11 metal (Cu, Ag) — huge jump after 1e⁻ loss | | II | 419 | 3051 | 7.3 | −48 | Alkali metal (Na, K) — very low $\Delta_i H_1$, large jump | | III | 1681 | 3374 | 2.0 | −328 | Halogen (Cl, Br) — high $\Delta_i H_1$, very negative $\Delta_{eg}H$ | | IV | 1008 | 1846 | 1.8 | −295 | Group 16/17 non-metal (O, S, or lower halogen) | | V | 2372 | 5251 | 2.2 | +48 | Noble gas (N

The first (Δᵢ H₁) and the second (Δᵢ H₂) ionization enthalpies (in kJ mol⁻¹) and the (ΔegH) electron gain enth

Exercises · 3.31

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:

Elements	$\Delta_i H_1$	$\Delta_i H_2$	$\Delta_{eg}H$
I	520	7300	-60
II	419	3051	-48
III	1681	3374	-328
IV	1008	1846	-295
V	2372	5251	+48
VI	738	1451	-40

Which of the above elements is likely to be: (a) the least reactive element. (b) the most reactive metal. (c) the most reactive non-metal. (d) the least reactive non-metal. (e) the metal which can form a stable binary halide of the formula $MX_2$ (X = halogen). (f) the metal which can form a predominantly stable covalent halide of the formula MX (X = halogen)?

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Ionization and electron-gain enthalpies reveal an element's reactivity and bonding character. Element V is the least reactive (noble gas), II the most reactive metal (alkali), III the most reactive non-metal (halogen), IV the least reactive non-metal (group 17, lower period), VI forms stable $MX_2$ (alkaline earth), and I forms covalent $MX$ (group 11 metal).

Understanding Standard State Conditions and Periodic Trends

Ionization enthalpy measures how easily an atom loses electrons (lower = more metallic), while electron-gain enthalpy measures how readily it accepts electrons (more negative = more non-metallic). The pattern of these values across the periodic table is diagnostic:

Metals have low $\Delta_i H_1$ and small or positive $\Delta_{eg}H$ (they don't want electrons).
Non-metals have high $\Delta_i H_1$ and large negative $\Delta_{eg}H$ (they crave electrons).
Noble gases have very high $\Delta_i H_1$ and positive $\Delta_{eg}H$ (stable, inert).
The jump from $\Delta_i H_1$ to $\Delta_i H_2$ tells us about electronic configuration: a huge jump means removing an electron from a much more stable inner shell.

Let's decode each element by examining these signatures.

Step-by-Step Analysis

1. Classify each element by its ionization pattern

Element	$\Delta_i H_1$	$\Delta_i H_2$	Ratio $\frac{\Delta_i H_2}{\Delta_i H_1}$	$\Delta_{eg}H$	Likely Identity
I	520	7300	14.0	−60	Group 11 metal (Cu, Ag) — huge jump after 1e⁻ loss
II	419	3051	7.3	−48	Alkali metal (Na, K) — very low $\Delta_i H_1$ , large jump
III	1681	3374	2.0	−328	Halogen (Cl, Br) — high $\Delta_i H_1$ , very negative $\Delta_{eg}H$
IV	1008	1846	1.8	−295	Group 16/17 non-metal (O, S, or lower halogen)
V	2372	5251	2.2	+48	Noble gas (Ne, Ar) — very high $\Delta_i H_1$ , positive $\Delta_{eg}H$
VI	738	1451	2.0	−40	Alkaline earth metal (Mg, Ca) — moderate $\Delta_i H_1$ , small jump to $\Delta_i H_2$

The ratio $\frac{\Delta_i H_2}{\Delta_i H_1}$ is crucial: a ratio above ~7 signals that the second electron comes from a closed shell (group 1 or 11), while a ratio near 2 suggests both electrons are valence electrons (group 2, or successive ionizations in non-metals).

2. Answer each part using periodic reasoning

(a) The least reactive element

Reactivity requires either losing or gaining electrons easily. Element V has the highest $\Delta_i H_1 = 2372$ kJ/mol and a positive $\Delta_{eg}H = +48$ kJ/mol, meaning it resists both oxidation and reduction. This is the hallmark of a noble gas.

Tip

A positive electron-gain enthalpy is the smoking gun for a noble gas — adding an electron is endothermic because the stable octet is disrupted.

(b) The most reactive metal

Metals react by losing electrons. Element II has the lowest $\Delta_i H_1 = 419$ kJ/mol and a huge jump to $\Delta_i H_2 = 3051$ kJ/mol (ratio 7.3), indicating it readily loses one electron to form $M^+$ but strongly resists losing a second. This is an alkali metal (group 1), the most reactive metal family.

(c) The most reactive non-metal

Non-metals react by gaining electrons. Element III has $\Delta_{eg}H = -328$ kJ/mol, the most negative value in the table, meaning it releases the most energy when gaining an electron. Combined with high $\Delta_i H_1 = 1681$ kJ/mol (it won't lose electrons), this is a halogen (group 17), specifically one from the upper periods (Cl or Br). Halogens are the most reactive non-metals.

(d) The least reactive non-metal

Among non-metals, reactivity decreases down a group. Element IV has $\Delta_{eg}H = -295$ kJ/mol (less negative than III) and $\Delta_i H_1 = 1008$ kJ/mol (lower than III), suggesting a non-metal lower in the periodic table or from group 16. It's less eager to gain electrons than element III, making it the least reactive non-metal in this set. …

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Understanding Standard State Conditions and Periodic Trends

Step-by-Step Analysis

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