Name: temperature effects on gibbs free energy
Uploaded: 2023-04-30T18:28:32.000Z
Duration: 2 min 23 s
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Gibbs Free Energy and Thermodynamic Favorability

The change in Gibbs free energy, or delta G, is the energy absorbed or released when energy-storing bonds are formed or broken, respectively.
The sign of delta G depends on the signs and the relative values of enthalpy, entropy, and temperature.
If delta H is negative and delta S is positive, delta G is negative at all temperatures. Thus, exothermic reactions where the entropy of the system increases are always spontaneous.
If both delta H and delta S are negative, delta G depends on the temperature. Reactions with negative enthalpy and entropy changes are spontaneous only at low temperatures.
Delta G is also dependent on temperature if both delta H and delta S are positive. Reactions with positive enthalpy and entropy changes are spontaneous only at higher temperatures.
When delta H is positive and delta S is negative, delta G is always positive, and the reaction is nonspontaneous at all temperatures.
For any reaction mixture composition, the delta G for the reaction is the sum of the standard free energy and RT times the natural log of the reaction quotient.
When the reactants and products are at equilibrium, the free energy change is zero, and the reaction quotient equals the equilibrium constant. So, the standard free energy change equals negative RT ln(K).
If delta G naught is less than zero, ln(K) is positive, meaning K is greater than 1. In this case, product formation is favored at equilibrium. The larger the equilibrium constant, the greater the decrease in Gibbs free energy. 
Reactions with negative delta G values involve the release of free energy to the surroundings and are called &#8216;exergonic&#8217; reactions.
Conversely, if delta G naught is greater than zero, ln(K) is negative, meaning K is less than 1, and the reverse direction of the reaction is favored.
Reactions with a positive delta G absorb free energy from the surroundings and are called &#8216;endergonic&#8217; reactions.

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:
<img alt="Thermodynamic equation, &#916;G=&#916;H&#8722;T&#916;S, diagram; Gibbs free energy change in reactions." src="/files/ftp_upload/11694/11694%20PT%20eq%201.svg" style="text-align: center; height: 15px;" data-altupdatedat="1761830439000" data-alt="Eq1" />
The spontaneity of a process, as reflected in the arithmetic sign of its free energy change, is then determined by the signs of the enthalpy and entropy changes and, in some cases, the absolute temperature. Since T is the absolute (kelvin) temperature, it can only have positive values. Four possibilities therefore exist with regard to the signs of the enthalpy and entropy changes:
<ol>
	<li>Both &#916;H and &#916;S are positive. This condition describes an endothermic process that involves an increase in system entropy. In this case, &#916;G will be negative if the magnitude of the T&#916;S term is greater than &#916;H. If the T&#916;S term is less than &#916;H, the free energy change will be positive. Such a process is spontaneous at high temperatures and nonspontaneous at low temperatures.</li>
	<li>Both &#916;H and &#916;S are negative. This condition describes an exothermic process that involves a decrease in system entropy. In this case, &#916;G will be negative if the magnitude of the T&#916;S term is less than &#916;H. If the T&#916;S term&#8217;s magnitude is greater than &#916;H, the free energy change will be positive. Such a process is spontaneous at low temperatures and nonspontaneous at high temperatures.</li>
	<li>&#916;H is positive and &#916;S is negative. This condition describes an endothermic process that involves a decrease in system entropy. In this case, &#916;G will be positive regardless of the temperature. Such a process is nonspontaneous at all temperatures.</li>
	<li>&#916;H is negative and &#916;S is positive. This condition describes an exothermic process that involves an increase in system entropy. In this case, &#916;G will be negative regardless of the temperature. Such a process is spontaneous at all temperatures.</li>
</ol>
The free energy change for a process may be viewed as a measure of its driving force. A negative value for &#916;G 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 &#916;Grxn 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 expression for the system, and its value may be used to identify the direction in which a reaction will proceed in order to achieve equilibrium. When Q is less than the equilibrium constant, K, the reaction will proceed in the forward direction until equilibrium is reached and Q = K. Conversely, if Q &#62; K, the process will proceed in the reverse direction until equilibrium is achieved.
The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 100 kPa; concentrations other than 1 M) is related to the standard free energy change according to this equation:
<img alt="Thermodynamic equation &#916;G=&#916;G&#176;+RTln(Q), chemical reaction Gibbs free energy formula." src="/files/ftp_upload/11694/11694%20PT%20eq%202.svg" style="text-align: center; height: 18px;" data-altupdatedat="1761830439000" data-alt="Eq2" />
R is the gas constant (8.314 J/K mol), T is the kelvin or absolute temperature, and Q is the reaction quotient. For a system at equilibrium, Q = K and &#916;G = 0, and the previous equation may be written as
<img alt="Equation of Gibbs free energy change at equilibrium; chemical thermodynamics formula." src="/files/ftp_upload/11694/11694%20PT%20eq%203.svg" style="text-align: center; height: 18px;" data-altupdatedat="1761830439000" data-alt="Eq3" />
<img alt="Thermodynamic equation &#916;G&#176;rxn = -RT ln(K), chemical reaction equilibrium analysis." src="/files/ftp_upload/11694/11694%20PT%20eq%204.svg" style="text-align: center; height: 18px;" data-altupdatedat="1761830439000" data-alt="Eq4" />
This form of the equation provides a useful link between these two essential thermodynamic properties, and it can be used to derive equilibrium constants from standard free energy changes and vice versa. The relations between standard free energy changes and equilibrium constants are summarized below.
If K &#62; 1, &#916;G&#176; &#60; 0 and the products are more abundant in the reaction mixture.
If K &#60; 1, &#916;G&#176; &#62; 0 and the reactants are more abundant in the reaction mixture.
If K = 1, &#916;G&#176; = 0 and the reactants and products are comparably abundant in the reaction mixture.
This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/16-4-free-energy">Openstax, Chemistry 2e, Section 16.4: Free Energy.</a>

The spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or ...

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temperature effects on gibbs free energy

Temperature changes can decide whether a process is spontaneous. This idea applies to phase changes and to some chemical reactions. The key link is Gibbs free energy, which connects free energy change with enthalpy and entropy.

The sign of the Gibbs free energy change, or ΔG, depends on the signs of enthalpy change (ΔH) and entropy change (ΔS), and sometimes on the absolute temperature. Because temperature is measured in kelvin, it is always a positive value. That means there are four main sign combinations to consider.

If both ΔH and ΔS are positive, the process is endothermic and the system gains entropy. In this case, ΔG is negative only when the TΔS term is larger than ΔH. So the process is spontaneous at high temperatures and nonspontaneous at low temperatures. If both ΔH and ΔS are negative, the process is exothermic and the system loses entropy. Then ΔG is negative when the TΔS term is smaller than ΔH, which makes the process spontaneous at low temperatures and nonspontaneous at high temperatures.

If ΔH is positive and ΔS is negative, the process is endothermic and the system becomes less disordered. In that case, ΔG stays positive at any temperature, so the process is nonspontaneous at all temperatures. If ΔH is negative and ΔS is positive, the process is exothermic and the system becomes more disordered. Then ΔG stays negative at any temperature, so the process is spontaneous at all temperatures.

Gibbs free energy also shows the driving force of a process. A negative ΔG means the forward direction is favored. A positive ΔG means the reverse direction is favored. When ΔGrxn is zero, the forward and reverse driving forces are equal, and the system is at equilibrium.

The reaction quotient, Q, helps predict which way a reaction will shift to reach equilibrium. When Q is less than the equilibrium constant, K, the reaction moves forward until Q = K. When Q is greater than K, the process moves in reverse until equilibrium is reached. Under nonstandard conditions, the free energy change is related to the standard free energy change by ΔG = ΔG° + RT ln Q, where R is the gas constant and T is the kelvin temperature.

At equilibrium, Q equals K and ΔG is zero, so the equation can be written as a link between ΔG° and K. This relationship lets chemists find equilibrium constants from standard free energy changes, or the reverse. If K is greater than 1, ΔG° is negative and products are more abundant. If K is less than 1, ΔG° is positive and reactants are more abundant. If K equals 1, ΔG° is zero and reactants and products are present in similar amounts.

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Temperature Effects on Gibbs Free Energy

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