Name: predicting spontaneity with gibbs energy
Uploaded: 2020-09-24T15:06:52.000Z
Duration: 2 min 39 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

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Chemistry

CH.7

CH.7.d

Gibbs Free Energy

The second law of thermodynamics states that for all spontaneous processes, the entropy of the universe&#8212;the sum of the entropy of the system and the entropy of the surroundings&#8212;increases.
While the entropy of the system can be calculated from standard molar entropies, the entropy of the surroundings is more difficult to calculate or measure.
Therefore, J. Willard Gibbs defined a new thermodynamic function, which allows spontaneity to be determined solely through the entropy and enthalpy of the system and not the surroundings.
Recall that under constant pressure and temperature conditions, the &#916;S of the surroundings is equal to the negative &#916;H of the system divided by the temperature, T. This term can be substituted into the equation representing the second law.
When both sides are multiplied by negative T, the equation now becomes: &#8722;T&#916;Suniv = &#916;Hsys &#8722; T&#916;Ssys. The thermodynamic functions on the right side of the equation&#8212;enthalpy and entropy&#8212;are both solely dependent on the system.
Because both enthalpy and entropy are state functions, a new state function can be defined as &#8722;T&#916;Suniv. This new term is called Gibbs free energy and is denoted by the letter G.
The equation for &#916;G leads to a new criterion for spontaneous reactions. The difference between the enthalpy change and the temperature or entropy change must be less than zero.
&#916;G is also known as chemical potential because it is similar to the mechanical potential energy of a system.
Just as a ball will always roll downhill to lower its potential energy, a chemical reaction proceeds to lower its chemical potential.
Thus, at constant temperature and pressure, if the free energy of the system decreases (that is, &#916;G &#60; 0), the reaction is spontaneous.
Conversely, if the free energy of the system increases, &#916;G &#62; 0, and the reaction is not spontaneous.
If &#916;G = 0, then the reactants and products are in equilibrium.

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 energy), and it is defined in terms of a system&#8217;s enthalpy and entropy as the following:
<img alt='&#60;p alt="Rydberg formula for hydrogen atom spectral lines, equation representation"&#62;' src="/files/ftp_upload/11427/11427_Equation_1.png" style="text-align: center; height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq1" />
Free energy is a state function, and at constant temperature and pressure, the free energy change (&#916;G) may be expressed as the following:
<img alt="Graph illustrating static equilibrium concept with &#931;Fx=0, &#931;Fy=0 equations, force vector diagram." src="/files/ftp_upload/11427/11427_Equation_2.png" style="text-align: center; height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq2" />
The relationship between this system property and the spontaneity of a process may be understood by recalling the previously derived second law expression:
<img alt="Static equilibrium diagram; &#931;F=0, &#931;M=0 on beam, force analysis, rotational balance study." src="/files/ftp_upload/11427/11427_Equation_3.png" style="text-align: center; height: 90px;" data-altupdatedat="1761830439000" data-alt="Eq3" />
The first law requires that qsurr = &#8722;qsys, and at constant pressure qsys = &#916;H, so this expression may be rewritten as:
<img alt="Static equilibrium; &#931;Fx=0, &#931;Fy=0, and &#931;&#964;=0; forces and torque diagram; physics mechanics principles." src="/files/ftp_upload/11427/11427_Equation_4.png" style="text-align: center; height: 75px;" data-altupdatedat="1761830439000" data-alt="Eq4" />
Multiplying both sides of this equation by &#8722;T and rearranging yields the following:
<img alt="Static equilibrium demonstration, &#931;Fx=0 equation, L-shaped beam diagram, educational physics." src="/files/ftp_upload/11427/11427_Equation_5.png" style="text-align: center; height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq5" />
For simplicity&#8217;s sake, the subscript &#8220;sys&#8221; can be omitted, and the expression becomes
<img alt="DNA transcription process diagram; shows DNA to RNA flow; includes promotor, RNA polymerase." src="/files/ftp_upload/11427/11427_Equation_6.png" style="text-align: center; height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq6" />
Comparing this equation to the previous one for free energy change shows the following relation:
<img alt="Quantum entanglement diagram showing EPR correlations and measurement symbols in physics study." src="/files/ftp_upload/11427/11427_Equation_7.png" style="text-align: center; height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq7" />
The free energy change is, therefore, a reliable indicator of the spontaneity of a process, as it is directly related to the previously identified spontaneity indicator, &#916;Suniv.
If &#916;Suniv &#62; 0, &#916;G &#60; 0 and the reaction is spontaneous.
If &#916;Suniv &#60; 0, &#916;G &#62; 0 and the reaction is nonspontaneous.
If &#916;Suniv = 0, &#916;G = 0 and the reaction is at equilibrium.
This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/16-4-free-energy">Openstax, Chemistry 2e, Chapter 16.4: </a><a href="https://openstax.org/books/chemistry-2e/pages/16-4-free-energy">Free Energy</a>.

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 ...

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predicting spontaneity with gibbs energy

Gibbs free energy helps predict whether a process is spontaneous under constant temperature and pressure. It is a thermodynamic property based on the system’s enthalpy and entropy. Chemists also call it free energy, and it is a state function.

The idea was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. Unlike the second law approach, it uses system properties only. That makes it a useful shortcut when tracking both the system and the surroundings is difficult.

At constant temperature and pressure, the free energy change is written as ΔG. The transcript relates this change to the second law expression for entropy of the universe. Using qsurr = −qsys and qsys = ΔH at constant pressure leads to a form that links ΔG directly to spontaneity.

This link makes free energy a reliable indicator of whether a process will happen on its own. If ΔSuniv is greater than 0, then ΔG is less than 0 and the reaction is spontaneous. If ΔSuniv is less than 0, then ΔG is greater than 0 and the reaction is nonspontaneous. If ΔSuniv equals 0, then ΔG equals 0 and the reaction is at equilibrium.

Predicting Spontaneity with Gibbs Energy

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Gibbs free energy helps predict whether a process is spontaneous under constant temperature and pressure. It is a thermodynamic property based on the system’s enthalpy and entropy. Chemists also call it free energy, and it is a state function. The idea was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. Unlike the second law approach, it uses system properties only. That makes it a useful shortcut when tracking both the system and the surroundings is...

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key terms and concepts

Learn how Gibbs free energy connects enthalpy, entropy, and spontaneity at constant temperature and pressure, and how ΔG predicts whether a process is spontaneous.

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CH.7.g

Predicting Spontaneity with Gibbs Energy

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