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5.7: Gibbs (Free) Energy to the Rescue

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    52345
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    We must consider changes in entropy for both the system and its surroundings when we predict which way a change will occur, or in which direction a process is thermodynamically favorable. Because it is almost always easier to look at the system than it is to look at the surroundings (after all, we define the system as that part of the universe we are studying), it would be much more convenient to use criteria for change that refer only to the system. Fortunately, there is a reasonably simple way to do this. Let us return to water freezing again and measure the enthalpy change for this process. The thermal energy change for the system, ΔHfreezing, is about – 6 kJ/mol. That is, 6 kJ of thermal energy are released into the surroundings for every mole of water that freezes. We can relate this thermal energy release to the entropy change of the surroundings. Entropy is measured in units of J/K (energy/temperature). Because we know how much energy is added to the surroundings, we can calculate the entropy change that this released (enthalpic) energy produces.

    Mathematically we can express this as ΔSsurroundings = –ΔHsurroundings/T. And because we know that ΔHsystem = –ΔHsurroundings, or that the energy lost by the system equals minus (–) the energy gained by the surroundings, we can express the entropy change of the surroundings in terms of measurable variables for the system. That is,

    ΔSsurroundings = –ΔHsystem / T.

    If you recall, we can express the total entropy change (the one relevant for the second law) as ΔStotal = ΔSsystem + ΔSsurroundings. Substituting for the ΔSsurroundings term, we get ΔStotal = ΔSsystem –ΔHsystem/T. Now we have an equation that involves only variables that relate to the system, which are much easier to measure and calculate. We can rearrange the equation by multiplying throughout by -T, which gives us:

    –TΔStotal = ΔHsystem – TΔSsystem

    The quantity –TΔStotal has units of energy, and is commonly known as the Gibbs energy change, ΔG (or sometimes as the free energy). The equation is normally written as:

    ΔG = ΔH – TΔS.

    The Gibbs energy change of a reaction is probably the most important thermodynamic term that you will need to learn about. In most biological and biochemical systems, it is ΔG that is commonly used to determine whether reactions are thermodynamically favorable. It is important to remember that ΔG is a proxy for the entropy change of the universe: if it is negative, universal entropy is increasing (and the reaction occurs); if it is positive, universal entropy would decrease if the reaction occurred (and so it does not). It is possible, however, for reactions with a positive ΔG to occur, but only if they are coupled with a reaction with an even greater negative ΔG (see Chapters 8 and 9).

    There are numerous tables of thermodynamic data in most texts and on many websites. Because we often want to use thermodynamic data such as ΔH, ΔS, and ΔG, it is useful to have some reference state. This is known as the standard state and is defined as 298 K temperature, 1 atmosphere pressure, 1M concentrations. When thermodynamic data refer to the standard state they are given the superscript o (nought), so ΔHo, ΔSo, and ΔGo all refer to the standard state. However, we often apply these data at temperatures other than 298 K and although small errors might creep in, the results are usually accurate enough.


    5.7: Gibbs (Free) Energy to the Rescue is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.

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