Gibbs Free Energy Change (ΔG)
The Two Forces of Nature: Enthalpy and Entropy
To truly understand Gibbs Free Energy, we must first meet its two components. Imagine you are cleaning your room. You want to finish the job (release energy, like getting tired) and you also end up with a more messy, spread-out feeling afterward (increased disorder). Chemical systems behave similarly.
Example: When you light a campfire, the burning of wood is highly exothermic (ΔH < 0). It releases a lot of heat and light into the surroundings.
Example: A drop of food coloring spreading uniformly in a glass of water is a classic entropy increase. The molecules go from a highly ordered, concentrated droplet to a disordered, mixed state. The process happens on its own.
Sometimes these two forces work together, and sometimes they fight each other. For instance, an ice cube melting is endothermic (it absorbs heat, so ΔH > 0), yet it happens spontaneously at room temperature because the increase in entropy (ΔS > 0) is so strong it wins. Gibbs Free Energy is the brilliant idea that combines these two factors into one decisive number.
The Master Equation: Predicting Spontaneity
Josiah Willard Gibbs[1] gave us the equation that is the heart of this topic. It allows us to calculate the Gibbs Free Energy Change for any process.
$ \Delta G = \Delta H - T \Delta S $
Where:
• ΔG = Gibbs Free Energy change (in joules, J, or kilojoules, kJ)
• ΔH = Enthalpy change (in J or kJ)
• T = Absolute Temperature (in Kelvin, K)[2]
• ΔS = Entropy change (in J/K or kJ/K)
The sign of ΔG is the ultimate predictor:
| Value of ΔG | What It Means | Is the Reaction Spontaneous? |
|---|---|---|
| ΔG < 0 (Negative) | The products have less free energy than the reactants. The reaction can proceed on its own. | YES (in the forward direction) |
| ΔG > 0 (Positive) | The products have more free energy than the reactants. The reaction will not proceed on its own. | NO (Not spontaneous. The reverse reaction is spontaneous.) |
| ΔG = 0 | The system is at equilibrium. No net change occurs. | The reaction is at EQUILIBRIUM |
Think of ΔG as a chemical "downhill" slope. A negative ΔG means the reaction is going downhill—it's easy and happens by itself. A positive ΔG is like going uphill—it won't happen unless you push it (e.g., by adding energy from an electrical source or continuous heat).
How Temperature Plays a Decisive Role
The equation $ \Delta G = \Delta H - T \Delta S $ shows that temperature (T) is a multiplier for entropy. This means a reaction that is not spontaneous at one temperature can become spontaneous at another. We can see this by analyzing the four possible combinations of ΔH and ΔS.
| ΔH | ΔS | Effect of Temperature (T) | Result for ΔG | Example |
|---|---|---|---|---|
| – (Exothermic) | + (Increase disorder) | Spontaneous at all temperatures. | Always ΔG < 0 | Burning of fuel (wood, gasoline). |
| + (Endothermic) | – (Decrease disorder) | Non-spontaneous at all temperatures. | Always ΔG > 0 | $ 3O_2(g) \rightarrow 2O_3(g) $ (making ozone at low energy). |
| – (Exothermic) | – (Decrease disorder) | Spontaneous only at low temperatures. | ΔG < 0 when T is low. | Water freezing. It releases heat (exothermic) and becomes more ordered (negative ΔS). It only happens spontaneously below 0°C. |
| + (Endothermic) | + (Increase disorder) | Spontaneous only at high temperatures. | ΔG < 0 when T is high. | Ice melting. It absorbs heat (endothermic) and becomes more disordered (positive ΔS). It happens spontaneously only above 0°C. |
Applying ΔG: From Car Engines to Your Body
The concept of Gibbs Free Energy isn't just for test tubes in a lab. It explains everyday phenomena and critical technologies.
1. Batteries and Fuel Cells: A battery is a device that harnesses a spontaneous redox reaction (one with a negative ΔG) to produce electrical energy. The ΔG of the reaction inside the battery is directly related to the voltage it can produce. The more negative the ΔG, the greater the potential electrical energy available.
2. Metabolism in Living Things: The food you eat, like glucose ($ C_6H_{12}O_6 $), contains chemical energy. Your cells "burn" this glucose with oxygen in a series of reactions, the overall process being: $ C_6H_{12}O_6(s) + 6O_2(g) \rightarrow 6CO_2(g) + 6H_2O(l) $ This reaction has a large, negative ΔG. Your body doesn't release all this energy as heat at once (like a fire). Instead, it cleverly captures and stores portions of this energy in small molecules like ATP[3], which act as portable energy currency for all cellular activities.
3. Industrial Chemistry - The Haber Process: One of the most important chemical reactions in the world is the synthesis of ammonia ($ NH_3 $) from nitrogen and hydrogen: $ N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) $ This reaction is exothermic (ΔH < 0) but results in a decrease in entropy (ΔS < 0) because four moles of gas become two moles of gas. According to our table, such a reaction is favored at low temperatures. However, at very low temperatures, the reaction is too slow to be practical. Chemical engineers use the principles of ΔG to find an optimal temperature and pressure that gives a reasonably negative ΔG and a fast enough reaction rate to produce fertilizer for global agriculture.
Important Questions
No. Gibbs Free Energy tells us about the feasibility and direction of a reaction, not its speed. A reaction with a very negative ΔG could be extremely slow. For example, the reaction of diamond turning into graphite has a negative ΔG at room temperature, but it is so slow it's practically unnoticeable. Speed is governed by kinetics (activation energy), not thermodynamics (ΔG).
There are two common ways. First, you can use the standard Gibbs Free Energy of formation ($ \Delta G_f^\circ $) values found in chemistry data tables. For a reaction: $ \Delta G^\circ = \sum \Delta G_f^\circ(products) - \sum \Delta G_f^\circ(reactants) $. Second, you can use the master equation if you know ΔH and ΔS: $ \Delta G = \Delta H - T \Delta S $.
Yes, but not on its own. It requires a continuous input of energy from an external source. This is how many non-spontaneous processes are driven. For example, electrolysis of water ($ 2H_2O(l) \rightarrow 2H_2(g) + O_2(g) $) has a positive ΔG. It does not happen by itself. However, by passing an electric current through the water (adding external energy), we can force the reaction to occur.
Footnote
[1] Josiah Willard Gibbs (1839–1903): An American scientist who made major contributions to thermodynamics and statistical mechanics. The Gibbs Free Energy is named in his honor.
[2] Kelvin (K): The base unit of temperature in the International System of Units (SI). It is an absolute scale where 0 K is absolute zero. To convert from Celsius to Kelvin: $ K = °C + 273.15 $.
[3] ATP (Adenosine Triphosphate): A complex organic molecule that functions as the primary energy carrier in all living cells. Energy from spontaneous reactions (negative ΔG) is used to make ATP from ADP. The hydrolysis of ATP back to ADP is also a spontaneous reaction (negative ΔG) that provides energy to drive non-spontaneous cellular processes.
[4] Spontaneity: In thermodynamics, a spontaneous process is one that can occur without needing continuous outside intervention. It does not imply that the process is fast.
[5] Equilibrium: The state of a system where the forward and reverse processes occur at the same rate, resulting in no net change. At equilibrium, ΔG = 0.