The Gibbs free energy change (ΔG) and how it's related to reaction spontaneity and equilibrium.

Introduction

When you hear the term “free energy,” what do you think of? Well, if you’re goofy like me, maybe a gas station giving away gas. Or, better yet, solar panels being used to power a household for free. There’s even a rock band from Philadelphia called Free Energy (confirming my longtime suspicion that many biology terms would make excellent names for rock bands).
These are not, however, the meanings of “free energy” that we’ll be discussing in this article. Instead, we’re going to look at the type of free energy that is associated with a particular chemical reaction, and which can provide a measure of how much usable energy is released (or consumed) when that reaction takes place.

Free energy

A process will only happen spontaneously, without added energy, if it increases the entropy of the universe as a whole (or, in the limit of a reversible process, leaves it unchanged) – this is the Second Law of Thermodynamics. But to me at least, that's kind of an abstract idea. How can we make this idea more concrete and use it to figure out if a chemical reaction will take place?
Basically, we need some kind of metric that captures the effect of a reaction on the entropy of the universe, including both the reaction system and its surroundings. Conveniently, both of these factors are rolled into one convenient value called the Gibbs free energy.
The Gibbs free energy (G) of a system is a measure of the amount of usable energy (energy that can do work) in that system. The change in Gibbs free energy during a reaction provides useful information about the reaction's energetics and spontaneity (whether it can happen without added energy). We can write out a simple definition of the change in Gibbs free energy as:
In other words, ΔG is the change in free energy of a system as it goes from some initial state, such as all reactants, to some other, final state, such as all products. This value tells us the maximum usable energy released (or absorbed) in going from the initial to the final state. In addition, its sign (positive or negative) tells us whether a reaction will occur spontaneously, that is, without added energy.
When we work with Gibbs free energy, we have to make some assumptions, such as constant temperature and pressure; however, these conditions hold roughly true for cells and other living systems.

Gibbs free energy, enthalpy, and entropy

In a practical and frequently used form of Gibbs free energy change equation, ΔG is calculated from a set values that can be measured by scientists: the enthalpy and entropy changes of a reaction, together with the temperature at which the reaction takes place.
Let’s take a step back and look at each component of this equation.
  • H is the enthalpy change. Enthalpy in biology refers to energy stored in bonds, and the change in enthalpy is the difference in bond energies between the products and the reactants. A negative ∆H means heat is released in going from reactants to products, while a positive ∆H means heat is absorbed. (This interpretation of ∆H assumes constant pressure, which is a reasonable assumption inside a living cell).
  • S is the entropy change of the system during the reaction. If ∆S is positive, the system becomes more disordered during the reaction (for instance, when one large molecule splits into several smaller ones). If ∆S is negative, it means the system becomes more ordered.
  • Temperature (T) determines the relative impacts of the ∆S and ∆H terms on the overall free energy change of the reaction. (The higher the temperature, the greater the impact of the ∆S term relative to the ∆H term.) Note that temperature needs to be in Kelvin (K) here for the equation to work properly.
Reactions with a negative ∆G release energy, which means that they can proceed without an energy input (are spontaneous). In contrast, reactions with a positive ∆G need an input of energy in order to take place (are non-spontaneous). As you can see from the equation above, both the enthalpy change and the entropy change contribute to the overall sign and value of ∆G. When a reaction releases heat (negative ∆H) or increases the entropy of the system, these factors make ∆G more negative. On the other hand, when a reaction absorbs heat or decreases the entropy of the system, these factors make ∆G more positive.
Chart showing how the signs of ∆H and ∆S affect reaction spontaneity. Reactions with a negative ∆H and positive ∆S are spontaneous at all temperatures. Reactions with a positive ∆H and negative ∆S are non-spontaneous at all temperatures. Reactions with a negative ∆H and negative ∆S are spontaneous at low temperatures, while reactions with a positive ∆H and negative ∆S are spontaneous at high temperatures.
By looking at ∆H and ∆S, we can tell whether a reaction will be spontaneous, non-spontaneous, or spontaneous only at certain temperatures. If a reaction both releases heat and increases entropy, it will always be spontaneous (have a negative ∆G), regardless of temperature. Similarly, a reaction that both absorbs heat and decreases entropy will be non-spontaneous (positive ∆G) at all temperatures. Some reactions, however, have a mix of favorable and unfavorable properties (releasing heat but decreasing entropy, or absorbing heat but increasing entropy). The ∆G and spontaneity of these reactions will depend on temperature, as summarized in the table at right.
At this point, you may be wondering why this set of terms (∆H, ∆S, and T) can predict reaction spontaneity. According to the Second Law of Thermodynamics, a reaction will be spontaneous only if it increases the overall entropy of the universe. So, why mess around with ΔH and T?
In the ΔG equation shown above, ΔS (the entropy change of the system) is clearly entropy-related, and an increase in entropy favors spontaneity. However, ΔH and T are also entropy-related, albeit in an indirect way. Released heat can increase (and absorbed heat can decrease) the entropy of the surroundings, and the magnitude of the change depends on temperature. Thus, all three terms of the ΔG equation actually relate to a reaction's effect on the entropy of the universe.
For a more thorough and rigorous explanation of the relationship between ∆G and the entropy of the universe, check out this video on thermodynamics.

Endergonic and exergonic reactions

Reactions that have a negative ∆G release free energy and are called exergonic reactions. (Handy mnemonic: EXergonic means energy is EXiting the system.) A negative ∆G means that the reactants, or initial state, have more free energy than the products, or final state. Exergonic reactions are also called spontaneous reactions, because they can occur without the addition of energy.
Reactions with a positive ∆G (∆G > 0), on the other hand, require an input of energy and are called endergonic reactions. In this case, the products, or final state, have more free energy than the reactants, or initial state. Endergonic reactions are non-spontaneous, meaning that energy must be added before they can proceed. You can think of endergonic reactions as storing some of the added energy in the higher-energy products they formstart superscript, 1, end superscript.
It’s important to realize that the word spontaneous has a very specific meaning here: it means a reaction will take place without added energy, but it doesn't say anything about how quickly the reaction will happenstart superscript, 2, end superscript. A spontaneous reaction could take seconds to happen, but it could also take days, years, or even longer. The rate of a reaction depends on the path it takes between starting and final states (the purple lines on the diagrams below), while spontaneity is only dependent on the starting and final states themselves. We'll explore reaction rates further when we look at activation energy.
Reaction coordinate diagrams for exergonic and endergonic reactions. In the exergonic reaction, the reactants are at a higher free energy level than the products (reaction goes energetically downhill). In the endergonic reaction reaction, the reactants are at a lower free energy level than the products (reaction goes energetically uphill).
Image credit: OpenStax Biology.

Spontaneity of forward and reverse reactions

If a reaction is endergonic in one direction (e.g., converting products to reactants), then it must be exergonic in the other, and vice versa. As an example, let’s consider the synthesis and breakdown of the small molecule adenosine triphosphate (A, T, P), which is the "energy currency" of the cellstart superscript, 3, end superscript.
A, T, P is made from adenosine diphosphate (A, D, P) and phosphate (P, start subscript, i, end subscript) according to the following equation:
A, D, P + P, start subscript, i, end subscript right arrow A, T, P + H, start subscript, 2, end subscript, O
This is an endergonic reaction, with ∆G = plus, 7, point, 3 k, c, a, l, slash, m, o, l under standard conditions (meaning 1 M concentrations of all reactants and products, 1 a, t, m pressure, 25 degrees C, and p, H of 7, point, 0). In the cells of your body, the energy needed to make A, T, P is provided by the breakdown of fuel molecules, such as glucose, or by other reactions that are energy-releasing (exergonic).
The reverse process, the hydrolysis (water-mediated breakdown) of A, T, P, is identical but with the reaction flipped backwards:
A, T, P + H, start subscript, 2, end subscript, O right arrow A, D, P + P, start subscript, i, end subscript
This is an exergonic reaction, and its ∆G is identical in magnitude and opposite in sign to that of the ATP synthesis reaction (∆G = plus, 7, point, 3 k, c, a, l, slash, m, o, l under standard conditions). This relationship of same magnitude and opposite signs will always apply to the forward and backward reactions of a reversible process.

Non-standard conditions and chemical equilibrium

You may have noticed that in the above section, I was careful to mention that the ∆G values were calculated for a particular set of conditions known as standard conditions. The standard free energy change (Gº’) of a chemical reaction is the amount of energy released in the conversion of reactants to products under standard conditions. For biochemical reactions, standard conditions are generally defined as 25 (298 K), 1 M concentrations of all reactants and products, 1 a, t, m pressure, and p, H of 7, point, 0 (the prime mark in ∆Gº’ indicates that p, H is included in the definition).
The conditions inside a cell or organism can be very different from these standard conditions, so ∆G values for biological reactions in vivo may vary widely from their standard free energy change (∆Gº’) values. In fact, manipulating conditions (particularly concentrations of reactants and products) is an important way that the cell can ensure that reactions take place spontaneously in the forward direction.

Chemical equilibrium

To understand why this is the case, it’s useful to bring up the concept of chemical equilibrium. As a refresher on chemical equilibrium, let’s imagine that we start a reversible reaction with pure reactants (no product present at all). At first, the forward reaction will proceed rapidly, as there are lots of reactants that can be converted into products. The reverse reaction, in contrast, will not take place at all, as there are no products to turn back into reactants. As product accumulates, however, the reverse reaction will begin to happen more and more often.
This process will continue until the reaction system reaches a balance point, called chemical equilibrium, at which the forward and reverse reactions take place at the same rate. At this point, both reactions continue to occur, but the overall concentrations of products and reactants no longer change. Each reaction has its own unique, characteristic ratio of products to reactants at equilibrium.
When a reaction system is at equilibrium, it is in its lowest-energy state possible (has the least possible free energy). If a reaction is not at equilibrium, it will move spontaneously towards equilibrium, because this allows it to reach a lower-energy, more stable state. This may mean a net movement in the forward direction, converting reactants to products, or in the reverse direction, turning products back into reactants.
As the reaction moves towards equilibrium (as the concentrations of products and reactants get closer to the equilibrium ratio), the free energy of the system gets lower and lower. A reaction that is at equilibrium can no longer do any work, because the free energy of the system is as low as possiblestart superscript, 4, end superscript. Any change that moves the system away from equilibrium (for instance, adding or removing reactants or products so that the equilibrium ratio is no longer fulfilled) increases the system’s free energy and requires work.

How cells stay out of equilibrium

If a cell were an isolated system, its chemical reactions would reach equilibrium, which would not be a good thing. If a cell's reaction reached equilibrium, the cell would die because there would be no free energy left to perform the work needed to keep it alive.
Cells stay out of equilibrium by manipulating concentrations of reactants and products to keep their metabolic reactions running in the right direction. For instance:
  • They may use energy to import reactant molecules (keeping them at a high concentration).
  • They may use energy to export product molecules (keeping them at a low concentration).
  • They may organize chemical reactions into metabolic pathways, in which one reaction "feeds" the next.
    Example of how a cell can keep reactions out of equilibrium. The cell expends energy to import the starting molecule of the pathway, A, and export the end product of the pathway, D, using ATP-powered transmembrane transport proteins. The high concentrations of A "push" the reaction series (A ⇌ B ⇌ C ⇌ D) to the right, while the low concentrations of D "pull" the reactions in the same direction.
Providing a high concentration of a reactant can "push" a chemical reaction in the direction of products (that is, make it run in the forward direction to reach equilibrium). The same is true of rapidly removing a product, but with the low product concentration "pulling" the reaction forward. In a metabolic pathway, reactions can "push" and "pull" each other because they are linked by shared intermediates: the product of one step is the reactant for the nextstart superscript, 5, comma, 6, end superscript.
Curious how this pushing and pulling actually works? Check out the reaction coupling video to learn more!

Attribution:

This article is a modified derivative of “Potential, kinetic, free, and activation energy,” by OpenStax College, Biology (CC BY 3.0). Download the original article for free at http://cnx.org/contents/185cbf87-c72e-48f5-b51e-f14f21b5eabd@9.85:29/Biology.
The modified article is licensed under a CC BY-NC-SA 4.0 license.

Works cited:

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  2. Reece, J. B., Urry, L. A., Cain, M. L., Wasserman, S. A., Minorsky, P. V., and Jackson, R. B. (2011). The second law of thermodynamics. In Campbell biology (10th ed., p. 144). San Francisco, CA: Pearson.
  3. Meyertholen, E. (n.d.). Gibbs free energy. In Bioenergetics. Retrieved from http://www.austincc.edu/~emeyerth/gibbs.htm.
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  6. Reece, J. B., Urry, L. A., Cain, M. L., Wasserman, S. A., Minorsky, P. V., and Jackson, R. B. (2011). Free energy, stability, and equilibrium. In Campbell biology (10th ed., pp. 145-146). San Francisco, CA: Pearson.

Additional references:

Activation energy. (n.d.). In Bodner research web. Retrieved from. http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch22/activate.php.
Berg, J. M., Tymoczsko, J. L., and Stryer, L. (2002). Entropy and the laws of thermodynamics. In Biochemistry (5th ed, section 1.3.3). New York, NY: W.H. Freeman. Retrieved from http://www.ncbi.nlm.nih.gov/books/NBK22567/#A167.
Berg, J. M., Tymoczsko, J. L., and Stryer, L. (2002). Free energy is a useful thermodynamic function for understanding enzymes. In Biochemistry (5th ed, section 8.2.1). New York, NY: W.H. Freeman. Retrieved from http://www.ncbi.nlm.nih.gov/books/NBK22584/.
Gibbs free energy. (2015, August 11). Retrieved August 25, 2015 from Wikipedia: https://en.wikipedia.org/wiki/Gibbs_free_energy.
Gibbs free energy. (n.d.). In Bodner research web. Retrieved from http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch21/gibbs.
Kotz, J., Treichel, P., Townsend, J., and Treichel, D. (2014). Entropy changes and spontaneity. In Chemistry and chemical reactivity (9E ed., pp. 691-696). Boston, MA: Cengage Learning.
Lambert, Frank L. (2012). Entropy and Gibbs free energy. In Entropy and the second law of thermodynamics! Retrieved from http://2ndlaw.oxy.edu/gibbs.html.
Quílez-Díaz, A. and Quílez-Pardo, J. (2015). Avoiding first-year chemistry textbooks’ misrepresentations in the teaching of spontaneous reactions. Quim. Nova, 38(1), 151-155. http://dx.doi.org/10.5935/0100-4042.20140248.
Reece, J. B., Urry, L. A., Cain, M. L., Wasserman, S. A., Minorsky, P. V., and Jackson, R. B. (2011). An introduction to metabolism. In Campbell biology (10th ed., pp. 141-161). San Francisco, CA: Pearson.
Treptow, Richard S. (1996). Free energy versus extent of reaction. Journal of Chemical Education, 73(1), 51-54.

Acknowledgements:

Thanks to Cuauhtémoc García-García for his editing help on this article.