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Sep 28, 2023 · The free energy change is therefore a reliable indicator of the spontaneity of a process, being directly related to the previously identified spontaneity indicator, ΔSuniv. Table 16.4.1 summarizes the relation between the spontaneity of a process and the arithmetic signs of these indicators.
It is expressed in two forms: the Helmholtz free energy F, sometimes called the work function, and the Gibbs free energy G. If U is the internal energy of a system, PV the pressure-volume product, and TS the temperature- entropy product ( T being the temperature above absolute zero ), then F = U − TS and G = U + PV − TS.
- The Editors of Encyclopaedia Britannica
- Overview
- Introduction
- Free energy
- Gibbs free energy, enthalpy, and entropy
- Endergonic and exergonic reactions
- Spontaneity of forward and reverse reactions
- Non-standard conditions and chemical equilibrium
- Chemical equilibrium
- How cells stay out of equilibrium
The Gibbs free energy change (ΔG) and how it's related to reaction spontaneity and equilibrium.
•∆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.
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.
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.
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:
ΔG=Gfinal–Ginitial
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.
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.
ΔG=ΔH−TΔS
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 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 form1 .
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 (ATP ), which is the "energy currency" of the cell3 .
ATP is made from adenosine diphosphate (ADP ) and phosphate (Pi ) according to the following equation:
ADP + Pi → ATP + H2O
This is an endergonic reaction, with ∆G = +7.3 kcal/mol under standard conditions (meaning 1 M concentrations of all reactants and products, 1 atm pressure, 25 degrees C , and pH of 7.0 ). In the cells of your body, the energy needed to make ATP 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 ATP , is identical but with the reaction flipped backwards:
ATP + H2O → ADP + Pi
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 °C (298 K ), 1 M concentrations of all reactants and products, 1 atm pressure, and pH of 7.0 (the prime mark in ∆Gº’ indicates that pH 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.
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 possible4 . 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.
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.
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 next5,6 .
This new property is called the Gibbs free energy (G) (or simply the free energy ), and it is defined in terms of a system’s enthalpy and entropy as the following: G = H − TS (9.3.1) (9.3.1) G = H − T S. Free energy is a state function, and at constant temperature and pressure, the free energy change (ΔG) may be expressed as the following:
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Figure 16.14 These plots show the free energy versus reaction progress for systems whose standard free energy changes are (a) negative, (b) positive, and (c) zero. Nonequilibrium systems will proceed spontaneously in whatever direction is necessary to minimize free energy and establish equilibrium. Previous Next.
Gibbs free energy and spontaneity. When a process occurs at constant temperature T and pressure P , we can rearrange the second law of thermodynamics and define a new quantity known as Gibbs free energy: Gibbs free energy = G = H − TS. where H is enthalpy, T is temperature (in kelvin, K ), and S is the entropy.
Jan 30, 2023 · The Helmholtz free energy becomes a measure of the sum of energy you have to put in to generate a system once the spontaneous energy transfer of the system from the environment is taken into account. Helmholtz Free Energy is generally used in Physics, denoted with the leter F, while Chemistry uses, G, Gibbs' Free Energy.
