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The technique is closely related to using gas adsorption to measure pore sizes, but uses the Gibbs–Thomson equation rather than the Kelvin equation.They are both particular cases of the Gibbs Equations of Josiah Willard Gibbs: the Kelvin equation is the constant temperature case, and the Gibbs–Thomson equation is the constant pressure case. [1]
The Gibbs adsorption isotherm for multicomponent systems is an equation used to relate the changes in concentration of a component in contact with a surface with changes in the surface tension, which results in a corresponding change in surface energy. For a binary system, the Gibbs adsorption equation in terms of surface excess is
If the composition, i.e. the amounts of the chemical components, in a system of uniform temperature and pressure can also change, e.g. due to a chemical reaction, the fundamental thermodynamic relation generalizes to:
When a system transforms reversibly from an initial state to a final state under these conditions, the decrease in Gibbs free energy equals the work done by the system to its surroundings, minus the work of the pressure forces. [1] The Gibbs energy is the thermodynamic potential that is minimized when a system reaches chemical equilibrium at ...
If multiple phases of matter are present, the chemical potentials across a phase boundary are equal. [6] Combining expressions for the Gibbs–Duhem equation in each phase and assuming systematic equilibrium (i.e. that the temperature and pressure is constant throughout the system), we recover the Gibbs' phase rule.
Two methods to extract the Gibbs free energy based on the value of CMC and exist; Phillips method [3] based on the law of mass action and the pseudo-phase separation model. The law of mass action postulates that the micelle formation can be modeled as a chemical equilibrium process between the micelles M n {\displaystyle M_{n}} and its ...
where T = temperature, S = entropy, p = pressure, V = volume. N i is the number of particles of type i in the system and μ i is the chemical potential for an i-type particle.The set of all N i are also included as natural variables but may be ignored when no chemical reactions are occurring which cause them to change.
which relates the Gibbs energy to a chemical equilibrium constant, the van 't Hoff equation can be derived. [ 9 ] Since the change in a system's Gibbs energy is equal to the maximum amount of non-expansion work that the system can do in a process, the Gibbs-Helmholtz equation may be used to estimate how much non-expansion work can be done by a ...