CHEM 142_Lecture_6

CHEM 142: The Global Impact of Chemistry for Engineering

Instructor: Dr. Levent Inci

Copyright: © 2020 W. W. Norton & Company

Vibrating Molecules

Molecular Dynamics:

In molecular dynamics, atoms within a molecule behave like connected masses, capable of vibrating as if linked by spring-like forces. This vibrational motion is crucial for understanding a wide variety of chemical phenomena, including reaction rates, molecular interactions, and energy transfer processes.

Wavefunction Description

Vibrational Wavefunction (ψvib): The vibrational wavefunction describes the quantum state of an atom in a vibrating molecule, detailing the probability distribution of the atom's position. This wavefunction is governed by the vibrational energy equation given by:

\hbar^2 \frac{d^2 \psi}{dx^2} + V(x) \psi = E \psi

Key constants in this equation consist of the mass of the nuclei and associated energies, reflecting the quantum mechanical nature of molecular vibrations.

Simple Harmonic Oscillator

Potential Energy Function (V(x)):

The potential energy function for a harmonic oscillator is expressed as:

V(x) = \frac{1}{2} kx^2

where 'k' signifies the spring constant, determining the stiffness of the molecular bond. This expression illustrates that molecular vibrations, when treated as harmonic oscillators, will exhibit periodic motion characteristic of vibrating systems.

Absorption of Light and Vibrational Energy

Energy Absorption:

Molecules absorb light energy specifically when the energy corresponds to the differences between quantized vibrational states. The specific absorption is noted in the formula:

E_{vib} = h u

where 'h' is Planck's constant and 'u' represents the frequency of the absorbed light.

Effective Mass Usage:

The effective mass ( μ ) is used to simplify vibrational calculations, particularly in scenarios with diatomic molecules. The formula used for determining vibrational energy levels incorporates effective mass:

E_{vib} = h \sqrt{\frac{k}{\mu}} \quad \text{with} \quad \mu = \frac{m_1 m_2}{m_1 + m_2}

Vibrational Wavefunctions and Infrared Spectroscopy

Measurements:

Infrared (IR) spectroscopy enables the calculation of vibrational frequencies for various molecules, such as hydrogen chloride (HCl). The relation between the spring constant and mass allows for precise determination of molecular vibrational energies and their transitions, crucial for material characterization.

IR Spectroscopy Trends

Absorption Overview:

Vibrational characteristics manifest differently across various compounds, resulting in distinctive IR absorption spectra. For instance, comparisons between HF and HBr reveal the influence of molecular composition and bonding characteristics on absorption capabilities.

The Greenhouse Effect

Understanding Climate Change:

The relationship between greenhouse gases (GHGs) and rising global temperatures is pivotal in understanding climate change. Greenhouse gases trap heat within the Earth’s atmosphere, leading to an increase in average temperatures.

Black-body Radiation:

This principle involves equating solar radiation with the thermal radiation emitted by Earth. The absorption and emission spectra of these two types of radiation differ significantly, influencing the overall energy balance of the planet.

Key Fluids in Atmosphere

Gases and IR Activity:

The atmospheric components, including nitrogen (N2), oxygen (O2), carbon dioxide (CO2), and methane (CH4), play variable roles in IR activity. Important to note is that not all gases actively absorb infrared radiation due to their molecular structure and symmetry which can prevent vibrational transitions from occurring.

IR Windows and Spectroscopy:

The application of spectroscopy is indispensable for quantifying gas concentrations and understanding atmospheric behaviors, significantly aiding in climate modeling and pollution assessment.

Greenhouse Gas Dynamics

Comparative GHG Analysis:

A thorough examination of the infrared absorption characteristics of chief greenhouse gases such as CO2, CH4, and H2O helps understand their impact on global warming. Each gas possesses unique molecular properties influencing its effectiveness as a greenhouse gas.

Residence Times:

The persistence of greenhouse gases, or residence time in the atmosphere, greatly affects their climate impact. Longer-lived gases can lead to more significant long-term warming effects, emphasizing the need for targeted mitigation strategies.

Climate Impact and Mitigation Strategies

Strategies to Address Climate Change:

To combat climate change, strategies include transitioning to renewable energy sources (solar, wind), improving energy efficiency, and implementing sustainable practices across various sectors.

Public Awareness:

Raising awareness about environmental issues is critical in fostering community engagement and driving policy change towards climate-sensitive solutions.

Course Logistics and Assessments

Module Test:

The upcoming module test is scheduled for September 27, encompassing all lectures and specified chapters for comprehensive evaluation.

Summary of Assessments

Weighting Overview:

• Laboratories: 30%

• Assignments: 30%

• Module Test: 40%

Passing Criteria: Students must achieve a total mark greater than 50% and complete all laboratory and examination requirements to pass the course successfully.