The potential energy as a function of internuclear distance for three diatomic molecules, X2, Y2, an — Bonding Chemistry Question

STEPS:

1. Understand how to read a potential energy curve for a covalent bond:
* X-axis position of the minimum (well): Represents the equilibrium bond length (the internuclear distance at which the molecule is most stable). A minimum located further to the left indicates a shorter bond length.
* Y-axis depth of the minimum (well): Represents the bond dissociation energy (the energy required to break the bond). A deeper well (more negative potential energy) indicates a stronger bond with higher bond energy.
2. Analyze the physical properties of the three molecules ($\text{H}_2$, $\text{N}_2$, $\text{O}_2$):
* Atomic Radii and Sizes: Hydrogen ($\text{H}$) is a Period 1 element with only a $1s$ electron shell, making it exceptionally small. Nitrogen ($\text{N}$) and Oxygen ($\text{O}$) are Period 2 elements with $n=2$ valence shells. Because hydrogen atoms are so small, the $\text{H}-\text{H}$ bond length is significantly shorter than both the $\text{N}-\text{N}$ and $\text{O}-\text{O}$ bond lengths.
* Bond Order and Bond Strength:
* $\text{H}_2$ contains a single covalent bond (bond order = 1), which is the weakest of the three.
* $\text{O}_2$ contains a double covalent bond (bond order = 2), which has intermediate strength and length.
* $\text{N}_2$ contains a triple covalent bond (bond order = 3), which is exceptionally strong and short.
3. Analyze the minimum positions (bond lengths) on the x-axis:
* Looking at the graph, the curve for $X_2$ has its minimum point located furthest to the left (shortest internuclear distance). Since hydrogen has the smallest atomic size by far, $X_2$ must be $\text{H}_2$.
* The curve for $Y_2$ has its minimum in the middle.
* The curve for $Z_2$ has its minimum located furthest to the right (longest internuclear distance).
* Comparing $\text{N}_2$ and $\text{O}_2$, because nitrogen's triple bond pulls the atoms closer together than oxygen's double bond, $\text{N}_2$ has a shorter bond length than $\text{O}_2$. Therefore, the intermediate distance $Y_2$ corresponds to $\text{N}_2$ and the longest distance $Z_2$ corresponds to $\text{O}_2$.
4. Correlate with the well depths (bond energy) on the y-axis to verify:
* $Y_2$ has the deepest potential energy well (around $-950\text{ kJ/mol}$). This matches the extremely high bond energy of $\text{N}_2$'s triple bond.
* $Z_2$ has an intermediate well depth (around $-500\text{ kJ/mol}$). This matches the moderate bond energy of $\text{O}_2$'s double bond.
* $X_2$ has the shallowest well depth (around $-436\text{ kJ/mol}$). This matches the lower bond energy of $\text{H}_2$'s single bond.
5. Select the correct match: Combining these observations: $X_2 = \text{H}_2$, $Y_2 = \text{N}_2$, and $Z_2 = \text{O}_2$, which corresponds to Option A.

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WHY_OTHERS_WRONG:

• B is incorrect: This option swaps the identities of $Y_2$ and $Z_2$, labeling $Y_2$ as $\text{O}_2$ and $Z_2$ as $\text{N}_2$. However, $\text{N}_2$ has a triple bond, which is much stronger (deeper well) and shorter (further left) than the double bond in $\text{O}_2$. The graph shows that $Y_2$ has a much deeper well and a shorter internuclear distance than $Z_2$, meaning $Y_2$ must be $\text{N}_2$ and $Z_2$ must be $\text{O}_2$.
• C is incorrect: This option identifies $X_2$ as $\text{N}_2$ and $Z_2$ as $\text{H}_2$. This is incorrect because $\text{H}_2$ is composed of tiny hydrogen atoms and has a much shorter bond length than $\text{N}_2$, meaning the curve for $\text{H}_2$ must have its minimum further to the left (which is $X_2$, not $Z_2$).
• D is incorrect: This option identifies $X_2$ as $\text{O}_2$ and $Y_2$ as $\text{H}_2$. This contradicts both bond length and bond strength trends. $\text{H}_2$ has a much shorter bond length than $\text{O}_2$ and should have its minimum further to the left (at $X_2$ rather than $Y_2$). Furthermore, $\text{H}_2$'s single bond is much weaker than $\text{N}_2$'s triple bond, yet this option assigns the deepest well ($Y_2$) to $\text{H}_2$.