Gibb’s Free Energy & Temperature
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Core Concept
Gibbs Free Energy ($\Delta G$) is the maximum energy available in a system to do useful work. It's the ultimate predictor of reaction spontaneity. The core relationship is defined by the Gibbs equation:
$$\Delta G = \Delta H - T\Delta S$$
where:
$\Delta H$ (Enthalpy): The change in heat of the reaction.
$T$ (Temperature): The absolute temperature in Kelvin.
$\Delta S$ (Entropy): The change in the system's disorder.
Practice Tips
The spontaneity of a reaction depends on the relationship between ΔH, T, and ΔS.
Temperature plays a critical role in determining ΔG, especially when ΔH and ΔS have the same sign.
Understanding $T_{\text{crit}}$ helps predict when a reaction becomes spontaneous or non-spontaneous.
Temperature Dependence of ΔG
The spontaneity of a reaction, represented by the Gibbs Free Energy ($\Delta G$), depends on the interplay between Enthalpy ($\Delta H$), Entropy ($\Delta S$), and Absolute Temperature ($T$).
Enthalpy ($\Delta H$)
This term represents the heat absorbed or released during the reaction.
$\Delta H < 0$: Exothermic reactions (release heat) are generally favored for spontaneity.
$\Delta H > 0$: Endothermic reactions (absorb heat) are generally unfavored.
Entropy ($\Delta S$)
This term represents the disorder or energy dispersal of the system.
$\Delta S > 0$: Increased disorder (more ways to distribute energy) favors spontaneity.
$\Delta S < 0$: Decreased disorder is generally unfavored.
Temperature Term ($T\Delta S$)
The Absolute Temperature ($T$) term determines whether the entropy or enthalpy factor will dominate the overall spontaneity of the reaction. The temperature is always measured in Kelvin (K).
Key Scenarios
| ΔH | ΔS | -TΔS | ΔG | Spontaneity |
|---|---|---|---|---|
| + | - | + | + | Nonspontaneous |
| - | + | - | - | Spontaneous |
| - | - | + | + or - |
Low Temp: Spontaneous High Temp: Nonspontaneous |
| + | + | - | + or - |
Low Temp: Nonspontaneous High Temp: Spontaneous |
Critical Temperature (TcritT_{\text{crit}}Tcrit)
Definition
The Critical Temperature ($T_{\text{crit}}$) is the specific temperature at which the Gibbs Free Energy is zero ($\Delta G = 0$), meaning the reaction is precisely at equilibrium.
Calculation
Since $\Delta G = \Delta H - T\Delta S$ and $\Delta G=0$ at $T_{\text{crit}}$, we can calculate it as:
$$T_{\text{crit}} = \frac{\Delta H}{\Delta S}$$
Temperature Dependence of Spontaneity
The critical temperature acts as a boundary to determine which thermodynamic factor ($\Delta H$ or $\Delta S$) dominates the spontaneity of the reaction:
If $T > T_{\text{crit}}$: The spontaneity of the reaction is primarily determined by the entropy term ($\Delta S$).
If $T < T_{\text{crit}}$: The spontaneity of the reaction is primarily determined by the enthalpy term ($\Delta H$).