Free Energy and Chemical Thermodynamics

2021 ◽  
pp. 149-219
Author(s):  
Daniel V. Schroeder
Keyword(s):  
Free Energy ◽  
Muscle Contraction ◽  
Phase Transformations ◽  
Constant Temperature ◽  
Chemical Equilibrium ◽  
Constant Pressure ◽  
Worked Examples ◽  
Cloud Formation ◽  
Chemical Thermodynamics ◽  
Gas Ionization

When a system is held at constant temperature (and sometimes constant pressure) through interactions with its surroundings, its thermodynamic behavior is governed by a combination of energy and entropy, called free energy. This chapter defines free energy and interprets it in two ways: as available work, and as a force toward equilibrium. Extensive applications follow: electrochemistry, phase transformations, mixtures, and chemical equilibrium. The worked examples and problems explore many specific applications including muscle contraction, cloud formation, geochemistry, metallurgy, and gas ionization.

Thermodynamics of chemical reactions

2005 ◽  
Author(s):  
Boris S. Bokstein ◽  
Mikhail I. Mendelev ◽  
David J. Srolovitz
Keyword(s):  
Free Energy ◽  
Gibbs Free Energy ◽  
Chemical Reactions ◽  
Chemical Reaction ◽  
Chemical Equilibrium ◽  
Chemical Species ◽  
Chemical Thermodynamics ◽  
Chemical Equation ◽  
Definition Of ◽  
The Right

This chapter is devoted to chemical equilibrium. We will use thermodynamics to answer two main questions: (1) ‘‘In which direction will a chemical reaction proceed?’’ and (2) ‘‘What is the composition of the system at equilibrium?’’ These are the oldest and most important questions in all of chemical thermodynamics for obvious reasons. The answers to these questions represent the foundation upon which all modern chemical technologies rest. Consider the following chemical reaction: . . . aA = bB ⇆ cC + dD. (5.1) . . . A, B, C, and D represent the chemical species participating in the reaction and a, b, c, and d are the stoichiometric coefficients of these species. We refer to the species on the left side of this chemical equation as reactants and those on the right as products. The reaction in Eq. (5.1) can either go forward, from left to right (reactants to products), or backward, from right to left (products to reactants). Therefore, we see that the definition of which we call reactants and which products is arbitrary. Assume that Eq. (5.1) occurs at constant temperature and pressure. Under these conditions, the direction of the reaction is determined by the sign of the change of the Gibbs free energy.

Chemical equilibrium and chemical kinetics

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Free Energy ◽  
Equilibrium Constant ◽  
Gibbs Free Energy ◽  
Chemical Kinetics ◽  
Chemical Equilibrium ◽  
First Principles ◽  
Effect Of Temperature ◽  
Total System ◽  
Free Energies

Building on the previous chapter, this chapter examines gas phase chemical equilibrium, and the equilibrium constant. This chapter takes a rigorous, yet very clear, ‘first principles’ approach, expressing the total Gibbs free energy of a reaction mixture at any time as the sum of the instantaneous Gibbs free energies of each component, as expressed in terms of the extent-of-reaction. The equilibrium reaction mixture is then defined as the point at which the total system Gibbs free energy is a minimum, from which concepts such as the equilibrium constant emerge. The chapter also explores the temperature dependence of equilibrium, this being one example of Le Chatelier’s principle. Finally, the chapter links thermodynamics to chemical kinetics by showing how the equilibrium constant is the ratio of the forward and backward rate constants. We also introduce the Arrhenius equation, closing with a discussion of the overall effect of temperature on chemical equilibrium.

Thermodynamics Energy for Both Supervised and Unsupervised Learning Neural Nets at a Constant Temperature

1999 ◽  
Vol 09 (03) ◽  
pp. 175-186 ◽  
Author(s):  
HAROLD SZU
Keyword(s):  
Free Energy ◽  
Constant Temperature ◽  
Helmholtz Free Energy ◽  
Principal Component ◽  
Neural Nets ◽  
Mixing Condition ◽  
Smart Cameras ◽  
Minimization Principle ◽  
Output Entropy ◽  
Artificial Neural Network Ann

Unified Lyaponov function is given for the first time to prove the learning methodologies convergence of artificial neural network (ANN), both supervised and unsupervised, from the viewpoint of the minimization of the Helmholtz free energy at the constant temperature. Early in 1982, Hopfield has proven the supervised learning by the energy minimization principle. Recently in 1996, Bell & Sejnowski has algorithmically demonstrated. Independent Component Analyses (ICA) generalizing the Principal Component Analyses (PCA) that the continuing reduction of early vision redundancy happens towards the "sparse edge maps" by maximization of the ANN output entropy. We explore the combination of both as Lyaponov function of which the proven convergence gives both learning methodologies. The unification is possible because of the thermodynamics Helmholtz free energy at a constant temperature. The blind de-mixing condition for more than two objects using two sensor measurement. We design two smart cameras with short term working memory to do better image de-mixing of more than two objects. We consider channel communication application that we can efficiently mix four images using matrices [AO] and [Al] to send through two channels.

THEORETICALLY MODELING MICROARRAY WITH THE CHEMICAL EQUILIBRIUM AND THERMODYNAMICS

2005 ◽  
Vol 03 (02) ◽  
pp. 477-490
Author(s):  
MEI XU
Keyword(s):  
Data Analysis ◽  
Theoretical Model ◽  
Chemical Equilibrium ◽  
Chemical Thermodynamics ◽  
Microarray Technology ◽  
Microarray Hybridization ◽  
Fundamental Theory ◽  
Array Design ◽  
Cellular Processes ◽  
Hybridization Reaction

To date, the idea that microarray may shed the light on cellular processes by identifying groups of genes that appear to be co-expressed seems to remain a dream. This is partly because that there are some blank (meaning the knowledge is unavailable) or even erroneous areas in the fundamental theory in this field. This paper attempts to present the digest of microarray hybridization system with chemical thermodynamics, theoretically clarifying some misunderstandings and looking for answers to some critical questions around this technology, such as the mechanisms and conditions of quantitative measuring by hybridization reaction, the reasons of inconsistency of the data and the analysis results and the solutions, how to analyze the data, etc. A theoretical model for the next generation of microarray is proposed. We believe that this model is universal, laying the foundation for microarray technology from array design through the data analysis.

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