Q.Assertion (A): Among the two O–H bonds in H2O molecule, the energy required to break the first O–H bond and the other O–H bond is the same.
Reason (R): This is because the electronic environment around oxygen is the same even after breakage of one O–H bond.

The key idea here is sequential bond dissociation enthalpy.

When a polyatomic molecule like H₂O undergoes bond breaking, the energy required to break successive identical bonds is generally not the same.

1. Breaking the first O–H bond in H₂O forms an H atom and an •OH radical ($H_2O(g) \rightarrow H(g) + OH(g)$).
2. Breaking the second O–H bond in the •OH radical forms an H atom and an O atom ($OH(g) \rightarrow H(g) + O(g)$). …

When we talk about breaking bonds in a polyatomic molecule like water ($H_2O$), it's important to distinguish between sequential bond dissociation energies and average bond energy. The energy required to break a specific bond in a molecule depends on the molecule's overall structure and the electronic environment surrounding that bond.

Concept and Intuition

1. Bond Dissociation Energy: This is the energy required to break a specific bond in a gaseous molecule, forming two radicals. For a molecule with multiple identical bonds (like the two O-H bonds in water), the energy required to break the first bond is generally different from the energy required to break the second, third, and so on. This is because once the first bond breaks, the remaining fragment is a new chemical species with a different electronic structure and stability.

2. Electronic Environment: The electronic environment around an atom refers to the arrangement of its valence electrons, including bonding pairs and lone pairs. This environment dictates the atom's hybridization, bond angles, and overall electron density distribution, which in turn affects the strength and reactivity of the bonds it forms.

Let's evaluate the Assertion and Reason based on these concepts.

Step-by-step Evaluation

1. Evaluate Assertion (A): "Among the two O–H bonds in H2O molecule, the energy required to break the first O–H bond and the other O–H bond is the same."
   • Consider the sequential breaking of O-H bonds in a water molecule:
     • First bond breakage: $H_2O(g) \rightarrow \cdot OH(g) + \cdot H(g)$ The energy required for this step is the first O-H bond dissociation enthalpy, $D_1(O-H)$.
     • Second bond breakage: $\cdot OH(g) \rightarrow \cdot O(g) + \cdot H(g)$ The energy required for this step is the second O-H bond dissociation enthalpy, $D_2(O-H)$.
   • After the first O-H bond breaks, the remaining species is a hydroxyl radical ($\cdot OH$), which is chemically distinct from the original water molecule ($H_2O$). The electronic structure, bond lengths, and overall stability of $\cdot OH$ are different from $H_2O$.
   • Consequently, the energy required to break the remaining O-H bond in the $\cdot OH$ radical ($D_2(O-H)$) will be different from the energy required to break the first O-H bond in $H_2O$ ($D_1(O-H)$). For water, $D_1(O-H)$ is approximately $502 \text{ kJ/mol}$, while $D_2(O-H)$ is approximately $427 \text{ kJ/mol}$. They are clearly not the same.
   • Therefore, Assertion (A) is false. …