4.5.2. Influence of Temperature on Spontaneity

The relationship ΔG = ΔH - TΔS shows how temperature (T) influences spontaneity by affecting the TΔS term.

Gibbs free energy (ΔG) determines whether a reaction will happen spontaneously. The equation ΔG = ΔH - TΔS combines the concepts of enthalpy (ΔH) and entropy (ΔS) while accounting for the temperature (T). As temperature changes, the term TΔS changes, which can affect the sign of ΔG. If ΔG is negative, the reaction is spontaneous; if it's positive, the reaction will not proceed without added energy.

Think about how the ice melts on a warm day. The sun (heat) provides energy, which increases the disorder or entropy of the ice crystals, allowing them to transition to water. This aligns with the Gibbs equation, where higher temperatures help make ΔG negative, allowing the melting to be spontaneous.

It summarizes different cases of spontaneity based on the signs of ΔH and ΔS:

• ΔH negative, ΔS negative → ΔG negative: Always spontaneous at all temperatures (e.g., combustion).
• ΔH positive, ΔS negative → ΔG positive: Never spontaneous at any temperature (e.g., separating mixed gases).
• ΔH negative, ΔS positive → ΔG negative at low T; spontaneous at low temperatures, non-spontaneous at high temperatures (e.g., freezing water).
• ΔH positive, ΔS positive → ΔG negative at high T; spontaneous at high temperatures, non-spontaneous at low temperatures (e.g., melting ice).

The spontaneity of chemical reactions is influenced by the signs of ΔH (enthalpy change) and ΔS (entropy change). Each combination provides insight into whether a reaction will happen naturally:

1. Negative ΔH and negative ΔS: The reaction is always spontaneous since it releases heat and decreases disorder at all temperatures.
2. Positive ΔH and negative ΔS: The reaction is never spontaneous since it requires energy input and does not favor disorder.
3. Negative ΔH and positive ΔS: At lower temperatures, the reaction can happen spontaneously, but at higher temperatures, it turns non-spontaneous as entropy does not compensate for the enthalpy required for spontaneity.
4. Positive ΔH and positive ΔS: The reaction will be spontaneous at high temperatures where the increase in disorder outweighs the heat absorbed.

Consider the freezing and melting of water as an analogy. Below 0 °C (273 K), water freezes, and this process is non-spontaneous without energy input (ΔG > 0). However, above 0 °C, water melts spontaneously, turning from solid ice into liquid water (ΔG < 0). This reflects how temperature changes influence the spontaneity of reactions, determined through Gibbs free energy considerations.

When ΔG = 0, the reaction is at equilibrium. At this point, ΔH = TΔS. Therefore, the temperature at which a reaction shifts from being spontaneous to non-spontaneous (or vice-versa) can be calculated: T_eq = ΔH / ΔS

The equilibrium temperature (T_eq) is the critical point where the Gibbs free energy change (ΔG) equals zero. This implies that the enthalpy and entropy driving forces are balanced, making the reaction neither favor product nor reactant formation. T_eq can be computed using the equation T_eq = ΔH / ΔS. This temperature indicates where a reaction's behavior changes concerning spontaneity based on thermodynamic conditions.

Think of T_eq as the moment when a seesaw is perfectly balanced. When one side goes up, the other goes down; similarly, in thermodynamics, at T_eq, the 'forces' of enthalpy and entropy are perfectly aligned, determining whether a reaction can proceed in either direction. For example, melting ice at exactly 0 °C is analogous to being balanced—the temperature where ice remains stable, neither fully melting nor freezing.

For the melting of ice: H₂O(s) → H₂O(l)

• ΔH > 0 (endothermic; needs heat to melt)
• ΔS > 0 (liquid is more disordered than solid) At temperatures below 0 °C (273 K), ΔG > 0, and melting is non-spontaneous (water freezes). At temperatures above 0 °C (273 K), ΔG < 0, and melting is spontaneous. At 0 °C (273 K), ΔG = 0, and ice and liquid water are in equilibrium.

The transition from solid ice to liquid water serves as a classic example to illustrate spontaneity influenced by temperature. The melting of ice takes in heat (ΔH > 0), making it an endothermic process. This phase change increases disorder (ΔS > 0) since liquids are less ordered than solids. At temperatures below the freezing point (0 °C), the Gibbs free energy is positive, indicating that ice is stable. Conversely, above 0 °C, the value of ΔG becomes negative, leading to spontaneous melting. At 0 °C, the system is at equilibrium where ΔG equals zero, signifying that both liquid water and ice co-exist stably.

You can visualize this by considering a frosty winter day. When the temperature rises above 0 °C, the ice you see on the ground starts turning into water. Below that freezing point, the water has no enthusiasm to change its state until heat from the sun softens it—this is a case of spontaneity being temperature-dependent, highlighting the real-life implications of Gibbs free energy.

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