Concept: Standard state ionization and electron-gain enthalpies reveal an element's tendency to lose or gain electrons, directly indicating metallic/non-metallic character and reactivity.

Analysis:

Metals have low $\Delta_i H_1$ (easy electron loss); non-metals have large negative $\Delta_{eg}H$ (strong electron gain). Reactivity correlates with ease of these processes.

• (a) Least reactive element: V has very high $\Delta_i H_1 = 2372$ (won't lose electrons) and positive $\Delta_{eg}H = +48$ (won't gain electrons) — a noble gas.

• (b) Most reactive metal: II has the lowest $\Delta_i H_1 = 419$ (easiest to lose one electron) and a huge jump to $\Delta_i H_2 = 3051$ (stable $M^+$ ion) — an alkali metal.

• (c) Most reactive non-metal: III has the most negative $\Delta_{eg}H = -328$ (strongest electron affinity) — a halogen.

• (d) Least reactive non-metal: IV has moderately negative $\Delta_{eg}H = -295$ but high $\Delta_i H_1 = 1008$; less eager than III — likely oxygen (Group 16). …

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

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.

(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. …