Q.Match the correct ionisation enthalpies and electron gain enthalpies of the following elements.
Elements:

The key idea is to understand the periodic trends of ionization enthalpy and electron gain enthalpy.

1. Most reactive metal (e.g., alkali metals) has very low first ionization enthalpy ($\Delta H_1$) and a very high second ionization enthalpy ($\Delta H_2$) due to stable noble gas configuration after losing one electron. Its electron gain enthalpy ($\Delta_{eg}H$) is slightly negative. This matches A (419, 3051, – 48).
2. Most reactive non-metal (e.g., halogens) has high ionization enthalpies and a highly negative electron gain enthalpy, indicating a strong tendency to gain electrons. This matches B (1681, 3374, – 328).
3. Least reactive element (e.g., noble gases) has very high ionization enthalpies and a positive electron gain enthalpy, reflecting its stable electron configuration. This matches D (2372, 5251, + 48). …

To correctly match the elements with their respective enthalpy values, we first need to understand what ionization enthalpy and electron gain enthalpy represent and how they relate to an element's chemical reactivity.

Ionization Enthalpy ($\Delta_i H$)

Ionization enthalpy is the energy required to remove an electron from an isolated gaseous atom in its ground state.

• The first ionization enthalpy ($\Delta_i H_1$) is for removing the first electron: $X(g) \rightarrow X^+(g) + e^-$.
• The second ionization enthalpy ($\Delta_i H_2$) is for removing the second electron from the unipositive ion: $X^+(g) \rightarrow X^{2+}(g) + e^-$.
• Ionization enthalpies are always positive (endothermic), meaning energy must be supplied to remove an electron.
• Trends: Generally, ionization enthalpy increases across a period (due to increasing nuclear charge and decreasing atomic size) and decreases down a group (due to increasing atomic size and shielding effect).
• Reactivity: Elements with low ionization enthalpies (metals) tend to lose electrons easily and are chemically reactive. Elements with very high ionization enthalpies (noble gases) are unreactive because they resist losing electrons.

Electron Gain Enthalpy ($\Delta_{eg}H$)

Electron gain enthalpy is the energy change when an electron is added to an isolated gaseous atom in its ground state.

• $X(g) + e^- \rightarrow X^-(g)$.
• It can be positive (energy absorbed, endothermic) or negative (energy released, exothermic).
• Trends: Generally, electron gain enthalpy becomes more negative across a period (due to increasing nuclear charge and smaller size, making it easier to attract an electron) and less negative down a group. Halogens have the most negative electron gain enthalpies. Noble gases have positive electron gain enthalpies because adding an electron would disrupt their stable electron configuration.
• Reactivity: Elements with highly negative electron gain enthalpies (non-metals, especially halogens) tend to gain electrons easily and are chemically reactive. Elements with positive electron gain enthalpies (noble gases, alkaline earth metals) are unreactive or resist gaining electrons.

Now, let's analyze the given elements and values based on these concepts:

Elements:

1. Most reactive non-metal: This element will have a strong tendency to gain electrons, meaning a very negative electron gain enthalpy, and a high ionization enthalpy (it doesn't want to lose electrons). This describes halogens.
2. Most reactive metal: This element will have a strong tendency to lose electrons, meaning a very low first ionization enthalpy. This describes alkali metals.
3. Least reactive element: This element will neither easily lose nor gain electrons. It will have very high ionization enthalpies and a positive (or least negative) electron gain enthalpy. This describes noble gases.
4. Metal forming binary halide: This is a typical metal, likely from Group 2 (alkaline earth metals) or Group 13. It will have relatively low ionization enthalpies (to form a cation) and a slightly negative or positive electron gain enthalpy. Values (all in kJ/mol): A. $\Delta H_1 = 419$, $\Delta H_2 = 3051$, $\Delta_{eg}H = -48$ B. $\Delta H_1 = 1681$, $\Delta H_2 = 3374$, $\Delta_{eg}H = -328$ C. $\Delta H_1 = 738$, $\Delta H_2 = 1451$, $\Delta_{eg}H = -40$ D. $\Delta H_1 = 2372$, $\Delta H_2 = 5251$, $\Delta_{eg}H = +48$ Let's match them step-by-step:

1. Identify the least reactive element (iii).

   The least reactive element (a noble gas) will have exceptionally high ionization enthalpies and a positive electron gain enthalpy.

   • Value set D has $\Delta H_1 = 2372$ and $\Delta H_2 = 5251$ (the highest among all given $\Delta H$ values), and $\Delta_{eg}H = +48$ (the only positive value). This perfectly matches the characteristics of a noble gas.
   • Therefore, (iii) Least reactive element $\rightarrow$ D.

2. Identify the most reactive metal (ii). …