5.6. Thermodynamic Feasibility

ΔG = ΔH – TΔS. A reaction is spontaneous (thermodynamically favorable) if ΔG < 0 under given conditions.

Gibbs Free Energy (3Delta G) is a crucial concept in thermodynamics that helps us determine whether a reaction can occur spontaneously. The equation states that the change in Gibbs Free Energy (3Delta G) equals the change in enthalpy (3Delta H) minus the product of temperature (T) and the change in entropy (3Delta S). If 3Delta G is less than zero, the reaction is favorable and can proceed on its own without external energy. This means that the reaction will likely occur under the specified conditions.

Think of a hiker standing at the top of a hill (representing a high energy state). If they want to walk down to the valley (a lower energy state), they will naturally do so because gravity will help them. Here, moving down relates to having a negative Gibbs Free Energy (3Delta G < 0) which indicates a spontaneous process. Conversely, if the hiker tried to walk uphill, they would need to input energy (like throwing a ball uphill), much like a positive 3Delta G scenario where the reaction is non-spontaneous.

Exothermic + Positive Entropy Change: Always spontaneous (ΔH negative, ΔS positive → ΔG always negative).

When a reaction is exothermic, it releases heat to the surroundings, leading to a negative change in enthalpy (3Delta H < 0). If the reaction also has a positive change in entropy (3Delta S > 0), meaning the disorder of the system increases, the combination assures that the Gibbs Free Energy (3Delta G) will be negative. Thus, this type of reaction is always spontaneous, indicating that it will proceed without any additional energy input.

Imagine lighting a fire in a fireplace. The fire releases warmth to the room (exothermic reaction) while the smoke and ashes spread out, creating more disorder (positive entropy change). This process happens without needing further energy input, making it akin to a spontaneous reaction.

Endothermic + Positive Entropy Change: May be spontaneous if TΔS > ΔH.

In some cases, a reaction that absorbs heat (endothermic, 3Delta H > 0) can still be spontaneous if the increase in entropy (3Delta S) multiplied by the temperature (T) exceeds the enthalpy change (3Delta H). This means that even if the reaction requires energy to proceed, the increase in disorder at operating temperatures can drive the reaction to occur spontaneously.

Consider the melting of ice into water on a warm day. The process absorbs heat from the surroundings (endothermic) but results in increased molecular disorder as the solid ice transitions to liquid water. If the temperature is high enough, the heat absorbed is compensated by the greater disorder introduced, leading to a spontaneous melting event.

Exothermic + Negative Entropy Change: Spontaneous at lower temperatures (|ΔH| > T|ΔS|), may become nonspontaneous at high T.

This case features a reaction that releases heat (exothermic, 3Delta H < 0) but also results in a decrease in entropy (3Delta S < 0). At lower temperatures, the negative enthalpy can dominate, allowing the Gibbs Free Energy to remain negative, thus allowing the reaction to proceed spontaneously. However, as temperature increases, the term T3Delta S becomes larger, potentially leading to a situation where the overall 3Delta G becomes positive, making the reaction nonspontaneous.

An analogy could be a volcano erupting. The eruption releases heat and can create order by forming solid lava rock (negative entropy). At cooler temperatures, the eruption can happen readily, but as the environment heats up over time (like during a hot summer day), the likelihood of a new eruption might decrease, reflecting on how temperature changes impact spontaneity.

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