Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Problem 169

Show the molecular orbital structure of \(\mathrm{H}_{2}\). Explain the molecular orbital structure both in terms of electron configuration and LCAO. Show the bonding orbital and antibonding orbital, and calculate the bond order.

Short Answer

Expert verified
The molecular orbital structure of H₂ consists of one bonding orbital (ψ_bond) formed by the constructive addition of the 1s orbitals from both hydrogen atoms and one antibonding orbital (ψ_antibond) formed by the destructive interference of these orbitals. The electron configuration of H₂ is (ψ_bond)². The calculated bond order of H₂ is 1, indicating that it has a single bond between the two hydrogen atoms.

Step by step solution

01

Identify atomic orbitals involved

Hydrogen atoms have only one electron in their 1s orbital. Since we need to explain the molecular orbital structure of H₂ molecule, we must consider two 1s atomic orbitals (orbitals from both the hydrogen atoms).
02

Combine atomic orbitals using LCAO

To form molecular orbitals, we will use Linear Combination of Atomic Orbitals (LCAO) to combine 1s orbitals of both hydrogen atoms. LCAO involves adding or subtracting the wave functions of the original atomic orbitals. When we add the wave functions, we get a bonding molecular orbital (ψ_bond). When we subtract the wave functions, we get an antibonding molecular orbital (ψ_antibond). ψ_bond = ψ(1s)_A + ψ(1s)_B ψ_antibond = ψ(1s)_A - ψ(1s)_B
03

Electron Configuration

As each hydrogen atom has only one electron, the H₂ molecule will have a total of two electrons. These electrons will occupy the lowest energy molecular orbitals (Aufbau principle). In the case of H₂, the bonding molecular orbital (ψ_bond) will have lower energy than the antibonding molecular orbital (ψ_antibond). Thus, both electrons will occupy the bonding orbital, or the molecular orbital formed from the constructive addition of both atomic orbitals. Electron configuration: (ψ_bond)²
04

Bonding and Antibonding Orbitals

The bonding molecular orbital (ψ_bond) is the result of the constructive interference (addition) of the 1s orbitals from both hydrogen atoms, and this leads to increased electron density between the two nuclei, stabilizing the molecule. The antibonding molecular orbital (ψ_antibond) is the result of the destructive interference (subtraction) of the 1s orbitals, leading to decreased electron density between the two nuclei and an unstable region due to the presence of a nodal plane.
05

Calculate Bond Order

Bond order is a measure of the bond strength and stability of a molecule. It can be determined using the following formula: Bond Order = (Number of electrons in bonding orbitals - Number of electrons in antibonding orbitals) / 2 For H₂: Bond Order = (2 - 0) / 2 = 1 In conclusion, the molecular orbital structure of H₂ consists of one bonding orbital (ψ_bond) formed by the constructive addition of the 1s orbitals and one antibonding orbital (ψ_antibond) formed by the destructive interference of these orbitals. The electron configuration of H₂ is (ψ_bond)². The calculated bond order of H₂ is 1, indicating that it has a single bond between the two hydrogen atoms.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Discuss the direct, concerted addition of \(\mathrm{H}_{2}\) to an alkene from the standpoint of orbital symmetry. (a) In the absence of catalyst, and (b) in the presence of photochemical stimulation.

Draw the LCAO model of ethylene in the bonding and antibonding orbital. Distinguish the ground state of ethylene from its excited state. Distinguish \(\pi^{2}\) from \(\pi^{*} \pi\).

(a) Define the following terms, and draw a diagram showing their relationship to each other. Amplitude Nodes Nodal plane Phase "Out of phase" Wave equation (b) How do they pertain to molecular orbitals?

Explain the molecular orbital structure of \(\mathrm{O}_{2}\). Calculate the bond order.

Discuss the various bonding and antibonding orbital of butadiene. Place them in order of increasing energy. What is the electronic configuration of butadiene in both the ground and the excited state.
See all solutions

Recommended explanations on Chemistry Textbooks

The Earths Atmosphere

Read Explanation

Chemical Reactions

Read Explanation

Inorganic Chemistry

Read Explanation

Chemistry Branches

Read Explanation

Chemical Analysis

Read Explanation

Kinetics

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.

Sign-up for free