Consider the \(\mathrm{H}_{2}^{+}\) ion. (a) Sketch the molecular orbitals of the ion and draw its energy-level diagram. (b) How many electrons are there in the \(\mathrm{H}_{2}^{+}\) ion? (c) Write the electron configuration of the ion in terms of its MOs. (d) What is the bond order in \(\mathrm{H}_{2}^{+}\) ? (e) Suppose that the ion is excited by light so that an electron moves from a lower-energy to a higher- energy MO. Would you expect the excited-state \(\mathrm{H}_{2}^{+}\) ion to be stable or to fall apart? (f) Which of the following statements about part (e) is correct: (i) The light excites an electron from a bonding orbital to an antibonding orbital, (ii) The light excites an electron from an antibonding orbital to a bonding orbital, or (iii) In the excited state there are more bonding electrons than antibonding electrons?

Step by step solution

01

(a) Sketch the molecular orbitals of the H₂⁺ ion and its energy-level diagram.

To sketch the molecular orbitals of the H₂⁺ ion (a hydrogen molecule with one positive charge), we need to understand that the H₂⁺ ion has two atomic orbitals from the two hydrogen atoms. When they combine, they form two molecular orbitals: one bonding and one antibonding. The bonding molecular orbital is lower in energy (more stable), while the antibonding molecular orbital is higher in energy. The energy level diagram shows these MOs with their respective energy levels.

02

(b) Number of electrons in H₂⁺ ion

In a neutral hydrogen molecule, there are two electrons, one from each hydrogen atom. However, in a H₂⁺ ion, one electron has been removed, leaving only one electron.

03

(c) Electron configuration of the ion in terms of MOs

Since there is only one electron, it will occupy the lowest energy molecular orbital, which is the bonding orbital (denoted as σ). Thus, the electron configuration is \(\mathrm{1\sigma^1}\).

04

(d) Bond order of H₂⁺ ion

The bond order is given by the formula: \(Bond\,order = \frac{1}{2} (number\, of\, electrons\,in\,bonding\,MOs - number\,of\,electrons\,in\,antibonding\,MOs)\) In the case of H₂⁺, there is only one electron in the bonding MO with none in the antibonding MO. So, the bond order is: \( \frac{1}{2} (1-0) = \frac{1}{2}\).

05

(e) Stability of excited-state H₂⁺ ion

Suppose an electron moves from a lower-energy MO to a higher-energy MO when the ion is excited by light. In this case, the electron would move from the bonding orbital to the antibonding orbital. This would result in a weaker bond or no bond at all between the hydrogen atoms. Therefore, the excited-state H₂⁺ ion would be unstable and likely to fall apart.

06

(f) Choose the correct statement about part (e)

Out of the given options, (i) The light excites an electron from a bonding orbital to an antibonding orbital, (ii) The light excites an electron from an antibonding orbital to a bonding orbital, (iii) In the excited state, there are more bonding electrons than antibonding electrons, The correct statement is (i) The light excites an electron from a bonding orbital to an antibonding orbital, because when an electron in the H₂⁺ ion becomes excited, it moves from the lower-energy (bonding) orbital to the higher-energy (antibonding) orbital, weakening or breaking the bond between 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!