Q.a. Using Born-Haber cycle, calculate the lattice enthalpy of magnesium fluoride ($MgF_2$). Given: Sublimation enthalpy of Mg=146.4 KJmol$^{-1}$; Dissociation enthalpy of Fluorine=158.8 KJmol$^{-1}$; Ionisation enthalpy of Mg($IE_2$)=2186 KJmol$^{-1}$; Electron gain enthalpy of fluorine = -332.6 KJmol$^{-1}$; Enthalpy of formation of $MgF_2$ = -1096.5 KJmol$^{-1}$. OR b. i) Derive the relation $C_p-C_v=R$. ii) What is the $C_p/C_v$ ratio for monoatomic gases? iii) An ideal gas is allowed to expand against a constant pressure of 2 bar from 10L to 50L in one step. Calculate the amount of work done by the gas. [1L bar=100J]

Why do atoms form ionic bonds? The intuition first

Imagine two people standing on opposite sides of a room. One has a bag of marbles (electrons) and is desperate to get rid of them — they're heavy, annoying, and the person feels unstable carrying them. The other person is missing a few marbles and feels incomplete without them. If the first person throws their extra marbles to the second, both feel stable and satisfied. That's the core idea behind ionic bonding: one atom gives away electrons, another atom takes them, and the resulting opposite charges stick together.

But why does one atom want to give and the other want to take? It all comes down to stability. Atoms want to achieve a stable electronic configuration — usually a full outermost shell (octet, or duplet for hydrogen and helium). The path to that stability determines whether an atom will lose, gain, or share electrons.

The precise statement

Ionic bonding is the electrostatic force of attraction between oppositely charged ions (cations and anions) formed by the complete transfer of one or more electrons from a metal atom to a non-metal atom.

The key phrase: complete transfer of electrons. Unlike covalent bonding where electrons are shared, here one atom loses electrons and another gains them.

The three factors that decide if ionic bonding happens

Not every metal-nonmetal pair forms an ionic bond. Three factors determine whether the transfer will actually occur and how strong the resulting bond will be.

1. Low ionization enthalpy of the metal (the giver)

Ionization enthalpy (or ionization energy) is the energy required to remove an electron from an isolated gaseous atom. If a metal has a low ionization enthalpy, it can easily lose electrons to form a positive ion (cation).

• Example: Sodium ($\text{Na}$) has a low first ionization enthalpy ($496\ \text{kJ/mol}$). It readily loses its one valence electron to become $\text{Na}^+$.
• Counterexample: Magnesium ($\text{Mg}$) has a higher first ionization enthalpy ($738\ \text{kJ/mol}$) and an even higher second one ($1451\ \text{kJ/mol}$). It can still form $\text{Mg}^{2+}$, but it requires more energy — so the bonding partner must compensate with a strong attraction.

2. High electron gain enthalpy of the non-metal (the taker)

Electron gain enthalpy (or electron affinity) is the energy change when an electron is added to a neutral gaseous atom. If a non-metal has a high negative electron gain enthalpy, it strongly attracts an extra electron and releases a lot of energy when it gains one.

• Example: Chlorine ($\text{Cl}$) has a highly negative electron gain enthalpy ($-349\ \text{kJ/mol}$). It eagerly accepts an electron to become $\text{Cl}^-$.
• Counterexample: Noble gases have positive electron gain enthalpies — they resist gaining electrons, so they never form ionic bonds.

3. Lattice energy — the glue that holds it together

Even if a metal can lose electrons and a non-metal can gain them, the process still costs energy overall (ionization is endothermic). What makes the reaction spontaneous is the lattice energy — the energy released when gaseous ions come together to form a solid crystal lattice.

Lattice energy depends on two things:

• Charge on the ions: Higher charge means stronger attraction. $\text{MgO}$ (with $\text{Mg}^{2+}$ and $\text{O}^{2-}$) has a much higher lattice energy than $\text{NaCl}$ (with $\text{Na}^+$ and $\text{Cl}^-$).
• Size of the ions: Smaller ions can get closer together, increasing the electrostatic attraction. $\text{LiF}$ has higher lattice energy than $\text{CsI}$.

The total energy change for ionic bond formation is:

For the bond to form, $\Delta H$ must be negative (exothermic overall). The lattice energy is always negative and large enough to compensate for the positive ionization enthalpy.

Putting it all together: a real example

Take sodium chloride ($\text{NaCl}$):

1. Sodium (Group 1) has low ionization enthalpy — it easily loses its one valence electron.
2. Chlorine (Group 17) has high negative electron gain enthalpy — it eagerly accepts that electron. …