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Free Energy and Equilibrium

Free Energy and Equilibrium

The free energy change for a process may be viewed as a measure of its driving force. A negative value for ΔG represents a driving force for the process in the forward direction, while a positive value represents a driving force for the process in the reverse direction. When ΔG is zero, the forward and reverse driving forces are equal, and the process occurs in both directions at the same rate (the system is at equilibrium).
The reaction quotient, Q, is a convenient measure of the...

Free Energy and Equilibrium

Free Energy and Equilibrium

The free energy change for a process may be viewed as a measure of its driving force. A negative value for ΔG represents a driving force for the process in the forward direction, while a positive value represents a driving force for the process in the reverse direction. When ΔGrxn is zero, the forward and reverse driving forces are equal, and the process occurs in both directions at the same rate (the system is at equilibrium).
Recall that Q is the numerical value of the mass action...

Gibbs Free Energy and Thermodynamic Favorability

Gibbs Free Energy and Thermodynamic Favorability

The spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or the other depending upon the temperature of the substance in question. Likewise, some chemical reactions can also exhibit temperature-dependent spontaneities. To illustrate this concept, the equation relating free energy change to the enthalpy and entropy changes for the process is considered:

Free Energy Changes for Nonstandard States

Free Energy Changes for Nonstandard States

The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:

Gibbs Free Energy

Gibbs Free Energy

One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free...

Calculating Standard Free Energy Changes

Calculating Standard Free Energy Changes

The free energy change for a reaction that occurs under the standard conditions of 1 bar pressure and at 298 K is called the standard free energy change. Since free energy is a state function, its value depends only on the conditions of the initial and final states of the system. A convenient and common approach to the calculation of free energy changes for physical and chemical reactions is by use of widely available compilations of standard state thermodynamic data. One method involves the...

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Spin Saturation Transfer Difference NMR SSTD NMR: A New Tool to Obtain Kinetic Parameters of Chemical Exchange Processes

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Equilibrium free-energy differences from a linear nonequilibrium equality.

Geng Li^1,2, Z C Tu³

¹CAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.

Physical Review. E

|April 17, 2021

Summary

This summary is machine-generated.

A new linear nonequilibrium equality offers a faster, more accurate method for calculating equilibrium free-energy differences from experimental data. This approach improves upon the Jarzynski equality, especially for rapid processes with high energy dissipation.

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Area of Science:

Thermodynamics
Statistical Mechanics
Physical Chemistry

Background:

Estimating equilibrium thermodynamic properties from nonequilibrium measurements is crucial for diverse scientific fields.
The Jarzynski equality provides a pathway to calculate free-energy differences but suffers from slow convergence due to its nonlinear nature.

Purpose of the Study:

To develop a more efficient and accurate method for estimating free-energy differences from nonequilibrium processes.
To introduce a linear nonequilibrium equality that overcomes the convergence limitations of existing nonlinear methods.

Main Methods:

Proposed a concise method utilizing a linear nonequilibrium equality.
Introduced an accelerated isothermal process via a unified variational approach termed 'variational shortcuts to isothermality'.
Applied the method to an underdamped Brownian particle in a double-well potential.

Main Results:

The proposed linear equality demonstrates faster convergence compared to nonlinear methods.
Accurate estimation of free-energy differences was achieved with high efficiency.
The method significantly improved accuracy (over an order of magnitude) for fast driving processes with high dissipation.

Conclusions:

The novel linear nonequilibrium equality offers a superior alternative to the Jarzynski equality for free-energy calculations.
The 'variational shortcuts to isothermality' approach enables efficient accelerated isothermal processes.
This method holds promise for advancing the understanding of thermodynamic properties in complex systems.