Animated Solution for Chemistry - Chemical Bonding and Molecular Structure: The intermolecular potential energy for the molecules A, B, C and D given below suggests that:

Finding the Stiffest Bond

Imagine two atoms floating in space, slowly approaching each other. As they get closer, their electron clouds begin to interact, and a delicate dance of attractive and repulsive forces begins. This entire cosmic ballet can be beautifully summarized in a single graph: the Potential Energy Curve.

In this problem, we are presented with a graph showing the potential energy ($E_p$) versus the interatomic distance ($r$) for four different diatomic molecules: A-A, A-B, A-C, and A-D. Our mission is to extract the physical properties of these bonds just by looking at the shapes of these curves.

To master this graph, you must understand what the axes represent. The horizontal x-axis represents the distance between the nuclei of the two atoms. The vertical y-axis represents the potential energy of the system.

When atoms are far apart, their potential energy is essentially zero. As they draw closer, attractive forces dominate, and the system releases energy, causing the potential energy to drop into negative territory.

Eventually, the curve hits a rock-bottom point—the minimum. This is the sweet spot! At this exact point, the attractive and repulsive forces are perfectly balanced. The molecule is in its most stable, equilibrium state.

The minimum point of the curve is a goldmine of information. It gives us two critical pieces of data:

1. Bond Length: The x-coordinate of the minimum point tells us the equilibrium distance between the atoms. A smaller x-value means a shorter bond. 2. Bond Enthalpy (Strength/Stiffness): The y-coordinate (the depth of the well) tells us how much energy was released when the bond formed. A more negative value means a deeper well, which translates to a stronger, more stable, and stiffer bond.

Let's put our knowledge to the test and evaluate the given options by analyzing the curves:

Analyzing A-B: Look at the red curve for A-B. It plunges the deepest, reaching a minimum potential energy between $-500$ and $-600{\text{ kJ mol}}^{-1}$. Because it has the most negative potential energy, it released the maximum amount of energy upon formation. This massive energy release makes it the most stable and, consequently, the stiffest bond*. This makes option (a) correct.

Analyzing A-A: Look at the blue curve for A-A. Its minimum point is the furthest to the left on the x-axis (around $75\text{ pm}$). This indicates that A-A actually has the shortest bond length*, not A-D. Furthermore, its energy well is not as deep as A-B's, so it does not have the largest bond enthalpy. This invalidates option (c).

Analyzing A-D: Look at the orange curve for A-D. Its minimum point is the furthest to the right, exactly at $150\text{ pm}$. This means A-D has the longest bond length* among the four, completely contradicting option (d).

What about Electronegativity?* Option (b) claims atom D is the most electronegative. However, a potential energy curve only provides data on bond length and bond energy. It does not give us direct information about the individual electronegativities of the atoms involved.

By carefully reading the coordinates of the minimum points, we can confidently conclude that the depth of the potential energy well directly correlates with bond stiffness. Since A-B has the deepest well, it undeniably possesses the stiffest bond.