/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 1 Why does an electron shared by t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 1

Why does an electron shared by two nuclei have a lower potential energy than an electron on a single atom? Why does an electron shared by two nuclei have a lower kinetic energy than an electron on a single atom? How does this sharing result in a stable molecule? How can this affect be measured experimentally?

Short Answer

Expert verified
Shared electrons lower potential and kinetic energy, stabilizing molecules, measurable via spectroscopy or X-ray diffraction.

Step by step solution

01

Understanding Potential Energy with Shared Electrons

Potential energy is linked to the position of an electron in a field of forces. When an electron is shared by two nuclei, it is being pulled by both, which spreads its position across a greater volume; this distribution decreases its potential energy. This is due to the increased probability of finding the electron between the nuclei, lowering the energy associated with its position in the potential well of the dual-nuclei system.
02

Linking Kinetic Energy and Quantum States

Kinetic energy of an electron is related to its spatial confinement: more confinement results in higher kinetic energy as per the uncertainty principle. An electron shared by two nuclei is less confined compared to being around a single atom, because its wave function extends over a larger area. This extension lowers the average momentum and thus the kinetic energy.
03

Formation of a Stable Molecule

Lower potential and kinetic energy contribute to system stability. A molecule forms when these energy reductions during electron sharing create a more energetically favorable (lower energy) state than if the atoms were apart. This means the energy required to break the bond is greater, making the molecule stable.
04

Experimental Measurement Methods

Experimental measurement can be approached using techniques such as spectroscopy, which examines energy levels, or using calorimetry to measure energy changes during bond formation. Additionally, X-ray diffraction can provide insight into electron density distribution, indirectly revealing changes in energy states.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

potential energy in molecules
Potential energy in molecules is crucial for understanding why electron sharing leads to stability. When an electron is part of a molecule, the potential energy depends on how it is positioned relative to the surrounding atoms or nuclei.
  • With shared electrons, the potential energy decreases because the electron is attracted by multiple nuclei.
  • This dispersal of attraction across several nuclei reduces the electron's potential energy.
When an electron is solely under the influence of a single atom, it experiences higher potential energy, as it's more localized and less influenced by surrounding atoms. In a molecule, the electron's position is less certain, enhancing the chance it's located between nuclei, thus lowering potential energy overall.
kinetic energy in electrons
Kinetic energy in electrons is an important factor driving molecular stability. In quantum mechanics, an electron's kinetic energy is related to its confinement by the Heisenberg Uncertainty Principle.
  • An electron confined to a small space has higher kinetic energy due to limited movement freedom.
  • When electrons are shared, as in a molecule, they gain more freedom to move over a bigger volume.
This increased space for movement means the electron's wave function spreads out, leading to a decrease in kinetic energy. Lower kinetic energy contributes to the stability of the molecule by making it more energetically favorable for atoms to stay bonded.
electron sharing
Electron sharing is a fundamental concept in chemistry that enhances molecular stability. When two atoms come together to form a bond, they often share electrons to fill their outer energy levels and achieve stability.
  • Shared electrons create a chance for electrons to balance the attractive forces from multiple nuclei.
  • This sharing leads to a lower combined energy state than would be possible for individual, separated atoms.
Through sharing, atoms effectively "merge" their electron clouds, allowing an electron to exist in a larger space. It becomes energetically favorable for them to stay in a stable, bonded configuration due to decreased energy in shared electrons.
bond formation
Bond formation is the process where atoms link up to form molecules, significantly influenced by shared electrons. Energetically, bond formation can be viewed as a shift toward a state where shared electrons stabilize interactions between atoms.
  • Lowered potential and kinetic energy result in stronger bonds.
  • The energy of the entire molecular system is reduced, requiring energy input to break these bonds later.
Solid bonds between atoms contribute to molecular properties, like rigidity and thermal stability, as breaking them demands significant energy comparable to the energy released during their formation.
experimental chemistry techniques
Experimental chemistry techniques are used to measure and observe the effects of electron sharing and bond formation in molecules. Techniques like spectroscopy, calorimetry, and X-ray diffraction help in elucidating molecular structures and energies.
  • Spectroscopy: Used to inspect energy levels and transitions by studying how matter interacts with electromagnetic radiation.
  • Calorimetry: Measures the heat involved in chemical reactions or physical changes, especially to study energy changes during bond formation.
  • X-ray diffraction: Offers insights into the electron density and arrangement of atoms, revealing how electron sharing affects molecular structure.
These techniques provide crucial data that allow chemists to understand the stability and characteristics of molecules formed through electron sharing and bonding.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Less energy is required to remove an electron from an \(F_{2}\) molecule than to remove an electron from an \(\mathrm{F}\) atom. Therefore, the energy of that electron is higher in the molecule than in the atom. Explain why, nevertheless, \(F_{2}\) is a stable molecule, i.e., the energy of an \(F_{2}\) molecule is less than the energy of two F atoms.

Calculate the bond orders of the following molecules and predict which molecule in each pair has the stronger bond: a. \(C_{2}\) or \(C_{2}^{+}\) b. \(B_{2}\) or \(B_{2}^{+}\) c. \(F_{2}\) or \(F_{2}^{-}\) d. \(O_{2}\) or \(O_{2}^{+}\)

Explain why the bond in an \(H_{2}\) molecule is almost twice as strong as the bond in the \(H_{2}^{+}\) ion. Explain why the \(H_{2}\) bond is less than twice as strong as the \(H_{2}^{+}\) bond.

\(B_{2}\) is observed to be paramagnetic. Using this information, draw an appropriate molecular orbital energy level diagram for \(B_{2}\).

Which of the following diatomic molecules are paramagnetic: \(\mathrm{CO}, \mathrm{Cl}_{2}, \mathrm{NO}, \mathrm{N}_{2} ?\)
See all solutions

Recommended explanations on Chemistry Textbooks

Physical Chemistry

Read Explanation

Chemical Reactions

Read Explanation

Kinetics

Read Explanation

Inorganic Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Nuclear Chemistry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.