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A), and Phase Equilibrium
Published in Kathleen E. Murphy, Thermodynamics Problem Solving in Physical Chemistry, 2020
For pure substances, the molar free energy, G¯i, can be defined as the chemical potential, µ. The chemical potential defines the criteria for equilibrium to exist between two phases or states. A phase is when a substance has a uniform chemical composition and physical structure for a range of P and T values. A phase diagram shows the thermodynamically stable phase at any P and T values and when two phases (such as solid and liquid) are in equilibrium with each other. The phase with the lowest µ under given conditions is the most stable state, based on thermodynamics.The Clapeyron and Clausius–Clapeyron equations are defined for the equilibrium of two phases, as shown on the map.
2 Utilization via Dry Reforming of Methane
Published in Subhas K Sikdar, Frank Princiotta, Advances in Carbon Management Technologies, 2020
Mohamed S Challiwala, Shaik Afzal, Hanif A Choudhury, Debalina Sengupta, Mahmoud M El-Halwagi, Nimir O Elbashir
Reforming reactions generally take place at high temperature and pressure conditions, typically in the range of 900–1100 °C and 15–25 bar, in order to achieve the maximum allowable equilibrium conversion. The equilibrium composition of gas phase reaction is estimated via the Gibbs free energy minimization method. Gibbs free energy (or the chemical potential of the system) is the total free energy available in the system to do useful or external work, and is a function of temperature, pressure and composition of the system.
The Phase Diagram
Published in Alan Cottrell, An Introduction to Metallurgy, 2019
The concept of chemical potential is often used in the discussion of phase equilibria. Suppose that we have a phase at temperature T and pressure P which is composed of nA moles of component A, nB of B, etc. We then write its free energy G in the form G=μAnA+μBnB+⋯
Towards a continuum thermodynamics framework for mechanism-based modelling of oxidative ageing in bitumen
Published in International Journal of Pavement Engineering, 2020
Here, a first attempt is made by proposing a mechanism-based reaction–diffusion framework, suitable for hypothesis testing, in particular hypotheses regarding oxidation mechanisms at molecular scale. This requires to connect molecular level and continuum scale. Continuum thermodynamics of mixtures provides a way of doing this. For instance, diffusion equations derived within the frame of continuum thermodynamics do not rely on the gradient in concentration of the diffusing species but, on the gradient in differences in chemical potentials. The chemical potential of a species in a mixture contains an activity coefficient in order to express the deviation from the chemical potential of the pure substance. Activity models, on the other hand, can be formulated by means of solubilities, molar volumes, etc., of all species in the mixture, which establishes a link between molecular level and continuum scale by means of physically meaningful concepts. This is demonstrated exemplary using the mechanism proposed by Petersen (2009) for the so-called ‘spurt oxidation’.
Calorimetry for studying the adsorption of proteins in hydrophobic interaction chromatography
Published in Preparative Biochemistry and Biotechnology, 2019
Agnes Rodler, Rene Ueberbacher, Beate Beyer, Alois Jungbauer
Norde and Haynes[68,69] described protein adsorption as the accumulation of solute on the liquid–solid phase boundary. Free enthalpy change ΔG is defined as the sum of the component’s chemical potentials μi multiplied by their stoichiometric coefficients νi: where μi is the chemical potential of component i in an ideal mixture and is expressed as sum of the chemical reference potential μi0 and a term which considers the activity a. The superscript “0” denotes thermodynamic quantities at standard conditions: where R is the ideal gas constant and T is the temperature. The chemical potential corresponds to the partial molar free energy of a component or the change of the free energy of a system with the change in the amount of a certain substance ni at constant temperature and pressure:
Generalized entropy production analysis for mechanism reduction
Published in Combustion Theory and Modelling, 2019
Luigi Acampora, Mahdi Kooshkbaghi, Christos E. Frouzakis, Francesco S. Marra
In the simple case of a single-component system, the chemical potential is equal to the specific Gibbs free energy [27] where is the standard state pressure (usually 1 bar) and is the standard state specific Gibbs free energy that is evaluated from standard state enthalpies and entropies: The latter can be computed from thermodynamic data by adopting the NASA polynomials [32].