Question

Explain in your own words why the energy of two \(\mathrm{H}\) atoms is lower when the atoms are \(74 \mathrm{pm}\) apart than when the atoms are (a) \(25 \mathrm{pm}\) apart; (b) \(100 \mathrm{pm}\) apart.

Short answer

At 74 pm, forces balance, achieving minimum energy. At 25 pm, repulsion increases energy; at 100 pm, weakened attraction raises energy.

Step-by-step solution

Understanding Atomic Interaction

To understand why the energy of two hydrogen atoms varies with distance, we need to consider the forces acting between them. At very close ranges, such as 25 pm, the repulsive forces due to overlapping electron clouds become significant, increasing energy.

Considering Ideal Bond Length

When the atoms are 74 pm apart, they are at an optimal distance known as the bond length for hydrogen—the point at which the attractive forces (e.g., from electron sharing) perfectly balance the repulsive forces, resulting in minimum potential energy.

Evaluating Larger Distances

At larger distances, such as 100 pm, the attractive forces weaken as the atoms move apart, leading to higher potential energy. The atoms are no longer able to adequately share electrons to form a strong bond.

Comparing Energies

Therefore, compared to 25 pm and 100 pm, 74 pm represents a state of lower energy as it is the ideal balance between attractive and repulsive forces, ensuring stability in molecular bonding.

Key concepts

Potential Energy

Potential energy in the context of atomic interactions is the energy stored due to the position of atoms relative to each other. When two atoms approach each other, both attractive and repulsive forces come into play, impacting the potential energy significantly.
- **Attractive Forces**: These are forces that pull the atoms together. They arise due to the sharing of electrons between atoms, predominantly seen in covalent bonds. - **Repulsive Forces**: As atoms get very close, their electron clouds begin to overlap, creating a repulsion due to the like-charges of electrons.
When two hydrogen atoms are at a certain distance, their potential energy is minimized. This happens because the attractive forces are balanced by the repulsive forces. The point of minimum potential energy corresponds to the bond length—the ideal distance where the energy is at its lowest and the atoms are most stable.

Bond Length

The bond length is a crucial concept in understanding molecular stability. It refers to the optimal distance between two bonded atoms where the potential energy reaches its lowest point. In the case of hydrogen atoms, that optimal distance is 74 pm.
- **Stable Equilibrium**: At this bond length, attractive forces such as electron sharing (or bonding interactions) perfectly balance the repulsive interactions from the electron clouds of the hydrogen atoms. - **Molecular Stability**: Achieving this optimal bond length ensures that the molecule remains stable and has minimal potential energy.
Any deviation from this optimal bond length, either getting closer or further apart, results in increased potential energy, making the system less stable.

Electron Cloud Overlap

Electron cloud overlap becomes crucial when explaining why atoms repel each other when too close.
- **Repulsion when too close**: When the distance between two hydrogen atoms shrinks to around 25 pm, their electron clouds overlap significantly. This overlap causes a strong repulsive force due to the electrons in each atom repelling each other. - **Effect on Energy**: This repulsion increases the potential energy of the system, as the atoms are forced apart due to the overlapping electron clouds creating an intense repelling force.
Thus, electron cloud overlap is a key factor in preventing atoms from coming too close, preserving a balance with attraction forces that aim to bond atoms together.

Atomic Interaction

Atomic interaction involves both attraction and repulsion, dictating how atoms behave within molecules. Understanding these interactions helps explain why atoms settle at specific distances.
- **Attraction**: Comes from electron sharing or transfer between atoms, trying to hold them together. - **Repulsion**: Occurs when electron clouds overlap too much, exerting a push back.
These forces are inverse and interactive: as atoms approach, attraction dominates until a point, after which repulsion increases dramatically due to electron cloud overlap.
This delicate balance explains why hydrogen atoms are most stable at 74 pm apart. At this bond length, the forces of atomic interaction are perfectly balanced, creating a stable molecule with minimum potential energy.