NationMaster - Encyclopedia: Gibbs energy

In thermodynamics, the Gibbs energy or Gibbs energy function is the energy portion of a thermodynamic system available to do work. (Note: many sources still use the superceded nomenclature 'Gibbs free energy', or just 'free energy', or even 'free enthalpy'.) The Gibbs energy is a thermodynamic potential and is therefore a state function of a thermodynamic system. It is defined as: This article needs to be cleaned up to conform to a higher standard of quality. ... The internal energy of a system (abbreviated E or U) is the total kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the total potential energy associated with the vibrational and electric energy of atoms within molecules or crystals. ... Enthalpy (symbolized H, also called heat content) is the sum of the internal energy of matter and the product of its volume multiplied by the pressure. ... In thermodynamics, the Gibbs energy or Gibbs energy function is the energy portion of a thermodynamic system available to do work. ... Thermodynamics (from the Greek thermos meaning heat and dynamis meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Thermodynamics (Greek: thermos = heat and dynamic = change) is the physics of energy, heat, work, entropy and the spontaneity of processes. ... In thermodynamics, four quantities, measured in units of energy, are called thermodynamic potentials: where T = temperature, S = entropy, p = pressure, V = volume Differential definitions The following differential relations hold for the four potentials: If we write the above four equations generally as Then it is seen that yielding expressions for... In thermodynamics, a state function (or state quantity) is a property of a system that depends only on the current state of the system, not on the way in which the system got to that state. ...

$G equiv H-TS ,$

where (in SI units) Cover of brochure The International System of Units. ...

G is the Gibbs energy, (Joule)
H is the enthalpy (Joule)
T is the temperature (Kelvin)
S is the entropy (Joules per Kelvin)

Each quantity in the equation above can be divided by the amount of substance, measured in moles, to form molar Gibbs energy. The Gibbs energy is one of the most important thermodynamic functions for the characterization of a system. It is a factor in determining outcomes such as the voltage of an electrochemical cell, and the equilibrium constant for a reversible reaction. It is named after American physicist Josiah Willard Gibbs. The joule (symbol: J) is the SI unit of energy, or work with base units of kgÂ·mÂ²/sÂ² (NÂ·m). ... Enthalpy (symbolized H, also called heat content) is the sum of the internal energy of matter and the product of its volume multiplied by the pressure. ... The joule (symbol: J) is the SI unit of energy, or work with base units of kgÂ·mÂ²/sÂ² (NÂ·m). ... Temperature is also the name of a song by Sean Paul. ... The kelvin (symbol: K) is the SI unit of temperature, and is one of the seven SI base units. ... For other uses of the term entropy, see Entropy (disambiguation) The thermodynamic entropy S, often simply called the entropy in the context of thermodynamics, is a measure of the amount of energy in a physical system that cannot be used to do work. ... The mole and its simple conversions into different units of measurements. ... International danger high voltage symbol. ... An electrochemical cell is a setup used for creating an electromotive force(voltage) in a conductor separating two reactions. ... In chemistry, the equilibrium constant is a quantity characterizing a chemical equilibrium in a chemical reaction which is a useful tool to determine the concentration of various reactants or products in a system where chemical equilibrium occurs. ... A reversible reaction is a chemical reaction that may proceed in both the forward and reverse directions. ... Josiah Willard Gibbs (February 11, 1839 â€“ April 28, 1903) was an American mathematical physicist who contributed much of the theoretical foundation for chemical thermodynamics. ...

1 Overview
2 Useful identities
3 Derivation of Gibbs Energy
- 3.1 Back to Entropy
4 References
5 See also

Overview

In a simple manner, with respect to STP reacting systems, a general rule of thumb is: Temperature and air pressure can vary from one place to another on the Earth, and can also vary in the same place with time. ... A rule of thumb is an easily learned and easily applied procedure for approximately calculating or recalling some value, or for making some determination. ...

Every system seeks to achieve a minimum of Gibbs energy.

Hence, out of this general natural tendency, a quantitative measure as to how near or far a potential reaction is from this minimum is when the calculated energetics of the process indicate that the change in Gibbs energy ΔG is negative. Essentially, this means that such a reaction will be favored and release energy in the form of work. Conversely, if conditions indicated a positive ΔG then energy, in the form of work, would have to be added to the reacting system to make the reaction go. Image File history File links Cquote1. ... Image File history File links Cquote2. ...

Useful identities

$Delta G = Delta H - T Delta S ,$ for constant temperature

$Delta G^circ = -R T ln K ,$

$Delta G = Delta G^circ + R T ln Q ,$

$Delta G = -nF Delta E ,$

and rearranging gives

which relates the electrical potential of a reaction to the equilibrium coefficient for that reaction.

where

ΔG = change in Gibbs energy

ΔH = change in enthalpy

T = temperature

ΔS = change in entropy

R = gas constant

ln = natural logarithm

K = equilibrium constant

Q = reaction quotient

n = number of electrons/mole product

F = Faraday constant (coulombs/mole)

ΔE = electrical potential of the reaction

We also have: Enthalpy (symbolized H, also called heat content) is the sum of the internal energy of matter and the product of its volume multiplied by the pressure. ... Temperature is also the name of a song by Sean Paul. ... Ice melting - a classic example of entropy increasing Entropy is a concept in thermodynamics, statistical mechanics and information theory. ... The gas constant (also known as the universal or ideal gas constant, usually denoted by symbol R) is a physical constant used in equations of state to relate various groups of state functions to one another. ... The natural logarithm is the logarithm to the base e, where e is equal to 2. ... In chemistry, the equilibrium constant is a quantity characterizing a chemical equilibrium in a chemical reaction which is a useful tool to determine the concentration of various reactants or products in a system where chemical equilibrium occurs. ... In a chemical reaction with certain initial concentrations of reactants and products, it is useful to know if the reaction will shift to the right (increasing the concentrations of the products) or if it will shift to the left (increasing the concentrations of the reactants). ... Properties The electron (also called negatron, commonly represented as e−) is a subatomic particle. ... The mole and its simple conversions into different units of measurements. ... In physics and chemistry, the Faraday constant is the amount of electric charge of one mole of electrons. ... The coulomb (symbol: C) is the SI unit of electric charge. ... The mole and its simple conversions into different units of measurements. ... This article is being considered for deletion in accordance with Wikipedias deletion policy. ...

$K_{eq}=e^{- frac{Delta G^circ}{RT}}$

$Delta G^circ = -RT(ln K_{eq}) = -2.303RT(log K_{eq})$

which relates the equilibrium constant with Gibbs energy.

Derivation of Gibbs Energy

Let S_tot be the total entropy of a thermally closed system. An isolated system cannot exchange heat with its surroundings. Total entropy is only defined for an isolated system, an open system has internal entropy instead. A physical system is said to be isolated if it does not interact with anything. ...

The second law of thermodynamics states that if a process is possible, then The second law of thermodynamics states that the entropy of an isolated system not at equilibrium will tend to increase over time, approaching a maximum value. ...

$Delta S_{tot} ge 0 ,$

and if $Delta S_{tot} = 0 ,$ then the process is reversible.

Since the heat transfer Δq vanishes for a closed system, then any reversible process will be adiabatic, and an adiabatic process is also isentropic $left( {Delta qover T} = Delta S = 0 right) ,$ . This article covers adiabatic processes in thermodynamics. ... An isentropic process (a combination of the Greek word iso -same- and entropy) is one during which the entropy of working fluid remains constant. ...

Now consider an open system. It has internal entropy S_int, and the system is thermally connected to its surroundings, which have entropy S_ext.

The entropy form of the second law does not apply directly to the open system, it only applies to the closed system formed by both the system and its surroundings. Therefore a process is possible if

$Delta S_{int} + Delta S_{ext} ge 0 ,$ .

We will try to express the left side of this equation entirely in terms of internal state functions. ΔS_ext is defined as:

$Delta S_{ext} = - {Delta qover T} ,$

Temperature T is the same both internally and externally, since the system is thermally connected to its surroundings. Also, Δq_rev is heat transferred to the system, so -Δq_rev is heat transferred to the surroundings, and −ΔQ/T is entropy gained by the surroundings. We now have:

$Delta S_{int} - {Delta qover T} ge 0 ,$

Multiply both sides by T:

$T Delta S_{int} - Delta qge 0 ,$

ΔQ is heat transferred to the system; if the process is now assumed to be isobaric, then Δq_p = ΔH: An isobaric process is a thermodynamic process in which the pressure stays constant; . The heat transferred to the system does work but also changes the internal energy of the system: according to the first law of thermodynamics, where W is work done by the system, E is internal energy, and...

$T Delta S_{int} - Delta H ge 0,$

ΔH is the enthalpy change of reaction (for a chemical reaction at constant pressure and temperature). Then

$Delta H - T Delta S_{int} le 0 ,$

for a possible process. Let the change ΔG in Gibbs energy be defined as

$Delta G = Delta H - T Delta S_{int} ,$ (1)

Notice that it is not defined in terms of any external state functions, such as ΔS_ext or ΔS_tot. Then the second law becomes:

$Delta G < 0 ,$ favored reaction

$Delta G = 0 ,$ reversible reaction

$Delta G > 0 ,$ disfavored reaction

Also, the sign of Delta G tells us about the spontaneity of the reaction.

$Delta G < 0 ,$ Spontaneous

$Delta G = 0 ,$ Equilibrium

$Delta G > 0 ,$ Nonspontaneous

Gibbs energy G itself is defined as

$G = H - T S_{int} ,$ (2)

but notice that to obtain equation (2) from equation (1) we must assume that T is constant.

Thus, Gibbs energy is most useful for thermochemical processes at constant temperature and pressure: both isothermal and isobaric. Such processes don't move on a P-V diagram; and therefore appear to be thermodynamically static. However, chemical reactions do undergo changes in chemical potential, which is a state function. Thus, thermodynamic processes are not confined to the two dimensional P-V diagram. There is a third dimension for n, the quantity of gas. Naturally for the study of explosive chemicals, the processes are not necessarily isothermal and isobaric. For these studies, Helmholtz energy is used. The precise meaning of the term chemical potential depends on the context in which it is used. ...