Question

The formation of \(\mathrm{H}_{2}\) from two \(\mathrm{H}\) atoms is an energetically favorable process. Yet statistically there is less than a 100 percent chance that any two \(\mathrm{H}\) atoms will undergo the reaction. Apart from energy considerations, how would you account for this observation based on the electron spins in the two \(\mathrm{H}\) atoms?

Short answer

Electron spins must be opposite to bond, resulting in a 50% chance.

Step-by-step solution

Understanding Electron Spin

Each hydrogen (H) atom has one electron. These electrons have a property called spin, which can be either 'up' (+1/2) or 'down' (-1/2). When two hydrogen atoms come together to form molecular hydrogen (H₂), the electrons must pair up with opposite spins to satisfy the Pauli Exclusion Principle.

Spin Pairing Requirement

For the two hydrogen atoms to successfully bond and form H₂, their electrons must have opposite spins. This spin pairing lowers the energy of the system, making the formation of a chemical bond possible.

Statistical Probability of Spin Configuration

Statistically, for any two random hydrogen atoms, there is only a 50% chance that their spins will be opposite. This is because there are two potential spin alignments for any pair of electrons: both spins aligned (either both up or both down) or spins opposite (one up, one down). Only the opposite spin alignment leads to bond formation.

Conclusion

Because of the statistical nature of electron spin alignment, not every pair of hydrogen atoms can form a bond, even though it is energetically favorable. This is why there is less than a 100% chance of the reaction occurring.

Key concepts

Hydrogen Atom Bonding

When two hydrogen atoms come together to form a hydrogen molecule ( H_2 ), they engage in a bonding process driven by the need to achieve a stable electronic configuration. Each hydrogen atom contains a single electron, and upon forming H_2 , these electrons pair up. This pairing enhances stability for both atoms. Unlike lone hydrogen atoms that have a single electron each, bonded hydrogen atoms share their electrons in such a way that they can collectively achieve a more stable electronic arrangement.
The hydrogen molecule forms because the two electrons occupy a lower energy state when paired. This energy reduction makes the bond formation energetically favorable. Though this process seems straightforward, it's inherently influenced by the characteristics of these electrons and their spins. The way electrons spin plays a pivotal role in determining whether these atoms successfully bond.

Pauli Exclusion Principle

The Pauli Exclusion Principle is an essential concept in quantum mechanics that governs how electrons are arranged within atoms and molecules. It states that no two electrons in an atom can have identical sets of quantum numbers. This means each electron must have a unique identity, manifested through properties like spin.
Spin is a fundamental property of electrons, much like charge and mass. It can have one of two orientations: 'up' (+1/2) or 'down' (-1/2). This principle is critical to the bonding process of hydrogen atoms because it necessitates that electrons in a shared orbital must have opposite spins. Thus, during bonding, one hydrogen atom's electron must be 'spin up', while the other atom's electron must be 'spin down'.

• Ensures that each electron in an orbital has a unique spin configuration.
• Drives the spin pairing that enables efficient bonding.

By enforcing this spin distinctness, the Pauli Exclusion Principle prevents electrons from occupying the same quantum state, thereby affecting how atoms can form bonds.

Spin Pairing in Chemistry

Spin pairing is a crucial mechanism in chemistry that underpins the formation of stable molecules. In the context of hydrogen atoms forming H_2 , spin pairing occurs when the electrons from each hydrogen atom adopt opposite spins, allowing them to share space in a bonding orbital. This configuration minimizes the total energy of the system, stabilizing the resultant hydrogen molecule.
In essence, spin pairing reduces repulsion between electrons by ensuring they don't adopt the same spin state when sharing an orbital. The statistical nature of electron spin implies that there's a 50% chance of achieving the correct spin alignment for bonding.

• Facilitates energy-efficient electron sharing.
• Leads to the formation of stable chemical bonds.
• Depends on random distribution of electron spins.

Spin pairing thus explains why not every encounter between hydrogen atoms results in bond formation, as atoms must meet the specific condition of opposite spins, which isn't guaranteed in every interaction.