Worked example: Interpreting potential energy curves of diatomic molecules | Khan Academy

Summary

In this video, the instructor explains the concept of potential energy for diatomic molecules like H2, N2, and O2 as a function of internuclear distance. Key factors affecting potential energy include atomic size and bond order. Higher bond orders (e.g., triple bonds in N2) result in shorter internuclear distances and higher bond energies. The video provides a practical approach for identifying potential energy graphs for these molecules based on bond order and atomic radius, with N2 having the highest bond energy and shortest internuclear distance, followed by O2 and H2.

Takeaways

• 😀 The script discusses the concept of potential energy as a function of internuclear distance in diatomic molecules.
• 😀 The example of molecular hydrogen (H2) is used to explain how the internuclear distance changes with potential energy.
• 😀 When atoms are brought closer together or pulled apart, energy must be added to the system, increasing the potential energy.
• 😀 The video provides a worked example comparing the potential energy of three diatomic molecules: H2, N2, and O2.
• 😀 The low point in the potential energy graph corresponds to the stable internuclear distance of a diatomic molecule at standard temperature and pressure.
• 😀 Smaller atoms tend to have shorter stable internuclear distances, and higher bond order leads to atoms being closer together.
• 😀 Diatomic hydrogen (H2) has a single covalent bond, nitrogen (N2) has a triple bond, and oxygen (O2) has a double bond.
• 😀 Bond order directly impacts bond energy, with triple bonds having the highest bond energy and single bonds the lowest.
• 😀 Based on bond energy, N2 is identified as having the highest bond energy, followed by O2, and H2 with the lowest.
• 😀 Atomic radius increases as you move down a group and decreases across a period in the periodic table, influencing internuclear distances.
• 😀 Despite similarities in atomic radius between nitrogen and oxygen, the bond order is a more significant factor in determining internuclear distance.

Q & A

What is the concept of potential energy as a function of internuclear distance?

Potential energy as a function of internuclear distance refers to how the energy of a diatomic molecule changes as the distance between its two atoms changes. The lowest potential energy occurs when the atoms are at an optimal distance, while moving them closer or further apart requires additional energy.

How does the internuclear distance relate to the size of the atoms?

Smaller atoms generally have a shorter stable internuclear distance. This is because smaller atomic radii result in the atoms being closer together when they form a bond, optimizing the potential energy.

How does bond order affect the internuclear distance in diatomic molecules?

Higher bond orders, such as in triple bonds, pull the atoms closer together. This results in a shorter internuclear distance and higher bond energy compared to molecules with single or double bonds.

What is the significance of bond energy in determining the internuclear distance?

Bond energy is the amount of energy required to separate two bonded atoms. A higher bond energy indicates a stronger bond and usually corresponds to a shorter internuclear distance, as seen in molecules with higher bond orders.

How does the bond order of H₂, N₂, and O₂ compare?

H₂ has a single covalent bond (bond order of 1), O₂ has a double covalent bond (bond order of 2), and N₂ has a triple covalent bond (bond order of 3). Higher bond orders generally result in shorter internuclear distances and higher bond energies.

How can atomic radius trends help identify the correct potential energy graph for a molecule?

Atomic radius increases as you move down a column in the periodic table and decreases as you move from left to right across a row. By using this trend, you can estimate the relative size of atoms in molecules and predict the internuclear distances, which can then help identify the correct potential energy graph.

Why does nitrogen (N₂) have the shortest internuclear distance among H₂, N₂, and O₂?

Nitrogen (N₂) has the shortest internuclear distance because it has the highest bond order (triple bond), which pulls the atoms closer together, leading to a higher bond energy and a shorter stable distance compared to the other two molecules.

What role do atomic radii play in determining the correct potential energy graph?

Atomic radii affect the internuclear distance at which the lowest potential energy occurs. Smaller atoms, like hydrogen, have shorter stable internuclear distances, while larger atoms like oxygen and nitrogen may have slightly longer distances, though bond order is a more significant factor.

How does the periodic table help explain the differences in bond lengths for these diatomic molecules?

The periodic table shows that hydrogen is the smallest atom, leading to the shortest bond length in H₂. As you move from nitrogen to oxygen, atomic radius slightly decreases, and bond order increases, causing a slight change in bond length between N₂ and O₂.

Why is the potential energy graph for N₂ expected to show the highest bond energy?

The N₂ molecule has a triple bond, which requires the most energy to break compared to a single or double bond. This results in the highest bond energy and the shortest internuclear distance, making the potential energy graph for N₂ show the lowest point at a shorter distance.