Gibbs Energy Change — Revision Notes

⚡ 30-Second Revision

Gibbs Energy Change: — $\Delta G = \Delta H - T\Delta S$
Spontaneity Criteria:

- $\Delta G < 0$: Spontaneous - $\Delta G > 0$: Non-spontaneous - $\Delta G = 0$: Equilibrium

Temperature Dependence:

- $\Delta H < 0, \Delta S > 0$: Always spontaneous - $\Delta H > 0, \Delta S < 0$: Never spontaneous - $\Delta H < 0, \Delta S < 0$: Spontaneous at low $T$ - $\Delta H > 0, \Delta S > 0$: Spontaneous at high $T$

Relation to Equilibrium Constant: — $\Delta G^circ = -RT \ln K$
Non-Standard Conditions: — $\Delta G = \Delta G^circ + RT \ln Q$
Units: — Ensure consistency (e.g., J for $\Delta H$ and $T\Delta S$, $T$ in Kelvin).

2-Minute Revision

Gibbs energy change ($\Delta G$) is the ultimate predictor of spontaneity for processes at constant temperature and pressure. It combines enthalpy change ($\Delta H$, heat factor) and entropy change ($\Delta S$, disorder factor) via the equation $\Delta G = \Delta H - T\Delta S$.

A negative $\Delta G$ means the process is spontaneous, positive means non-spontaneous, and zero means equilibrium. The signs of $\Delta H$ and $\Delta S$ determine how temperature affects spontaneity: if $\Delta H$ is negative and $\Delta S$ is positive, the reaction is always spontaneous.

If both are positive, it's spontaneous only at high temperatures. Crucially, the standard Gibbs energy change ($\Delta G^circ$) is directly related to the equilibrium constant ($K$) by $\Delta G^circ = -RT \ln K$, linking thermodynamics to equilibrium.

For non-standard conditions, the actual $\Delta G$ is calculated using $\Delta G = \Delta G^circ + RT \ln Q$, where $Q$ is the reaction quotient. Always remember to maintain unit consistency (J vs. kJ) and use temperature in Kelvin for calculations.

5-Minute Revision

Gibbs energy change ($\Delta G$) is a critical thermodynamic function that dictates the spontaneity of a process under constant temperature and pressure. It's defined by the Gibbs-Helmholtz equation: $\Delta G = \Delta H - T\Delta S$.

Here, $\Delta H$ is the enthalpy change (heat absorbed/released), $T$ is the absolute temperature in Kelvin, and $\Delta S$ is the entropy change (change in disorder). The criteria for spontaneity are straightforward: $\Delta G < 0$ for a spontaneous process, $\Delta G > 0$ for a non-spontaneous process, and $\Delta G = 0$ for a system at equilibrium.

The interplay of $\Delta H$ and $\Delta S$ determines the temperature dependence of spontaneity:

1
$\Delta H < 0, \Delta S > 0$ — Both factors favor spontaneity. $\Delta G$ is always negative. (e.g., combustion)
2
$\Delta H > 0, \Delta S < 0$ — Both factors disfavor spontaneity. $\Delta G$ is always positive. (e.g., formation of complex ordered structures from simple components)
3
$\Delta H < 0, \Delta S < 0$ — Enthalpy favors, entropy disfavors. Spontaneous at low temperatures where $|\Delta H| > |T\Delta S|$. (e.g., freezing of water below $0^circ\text{C}$)
4
$\Delta H > 0, \Delta S > 0$ — Enthalpy disfavors, entropy favors. Spontaneous at high temperatures where $|T\Delta S| > |\Delta H|$. (e.g., melting of ice above $0^circ\text{C}$)

Key Relationships:

Standard Gibbs Energy Change ($\Delta G^circ$) — This is $\Delta G$ under standard conditions (1 atm, 1 M, 298 K). It's related to the equilibrium constant ($K$) by $\Delta G^circ = -RT \ln K$. A large negative $\Delta G^circ$ means a large $K$ (products favored), while a positive $\Delta G^circ$ means a small $K$ (reactants favored).
Non-Standard Conditions — For reactions not at standard conditions, $\Delta G = \Delta G^circ + RT \ln Q$, where $Q$ is the reaction quotient. This equation shows how actual concentrations/pressures influence spontaneity.

Example: A reaction has $\Delta H = -30 \text{ kJ/mol}$ and $\Delta S = -100 \text{ J/mol.K}$. At what temperature is it at equilibrium? Solution: At equilibrium, $\Delta G = 0$. So, $\Delta H - T\Delta S = 0 \implies T = \frac{\Delta H}{\Delta S}$. Convert $\Delta H$ to J: $-30 \text{ kJ/mol} = -30000 \text{ J/mol}$. $T = \frac{-30000 \text{ J/mol}}{-100 \text{ J/mol.K}} = 300 \text{ K}$. Below $300 \text{ K}$, the reaction is spontaneous; above $300 \text{ K}$, it's non-spontaneous.

Prelims Revision Notes

Gibbs Energy Change ($\Delta G$) - NEET Revision Notes

1. Definition & Formula:

* Gibbs Free Energy ($G$): $G = H - TS$ * Gibbs Energy Change ($\Delta G$): $\Delta G = \Delta H - T\Delta S$ * $H$: Enthalpy, $T$: Absolute Temperature (Kelvin), $S$: Entropy

2. Spontaneity Criteria (at constant T, P):

* $\Delta G < 0$: Spontaneous (reaction proceeds in forward direction) * $\Delta G > 0$: Non-spontaneous (reverse reaction is spontaneous) * $\Delta G = 0$: Equilibrium (no net change)

3. Temperature Dependence of Spontaneity:

* **$\Delta H < 0, \Delta S > 0$**: $\Delta G$ is always negative. Always Spontaneous. * **$\Delta H > 0, \Delta S < 0$**: $\Delta G$ is always positive. Never Spontaneous. * **$\Delta H < 0, \Delta S < 0$**: $\Delta G$ is negative at low $T$.

**Spontaneous at low $T$.** (e.g., freezing) * Equilibrium $T = \Delta H / \Delta S$. Spontaneous if $T < \Delta H / \Delta S$. * **$\Delta H > 0, \Delta S > 0$**: $\Delta G$ is negative at high $T$.

**Spontaneous at high $T$.** (e.g., melting, decomposition) * Equilibrium $T = \Delta H / \Delta S$. Spontaneous if $T > \Delta H / \Delta S$.

4. Standard Gibbs Energy Change ($\Delta G^circ$):

* $\Delta G^circ = \Delta H^circ - T\Delta S^circ$ * Calculated from standard free energies of formation: $\Delta G^circ = \sum n_p \Delta G_f^circ (\text{products}) - \sum n_r \Delta G_f^circ (\text{reactants})$

5. Relation to Equilibrium Constant ($K$):

* $\Delta G^circ = -RT \ln K$ * $R = 8.314 \text{ J/mol.K}$ (gas constant) * If $\Delta G^circ < 0$, $K > 1$ (products favored). * If $\Delta G^circ > 0$, $K < 1$ (reactants favored). * If $\Delta G^circ = 0$, $K = 1$.

6. Non-Standard Conditions:

* $\Delta G = \Delta G^circ + RT \ln Q$ * $Q$: Reaction Quotient. If $Q < K$, $\Delta G < 0$ (spontaneous forward). If $Q > K$, $\Delta G > 0$ (spontaneous reverse).

7. Units & Conversions:

* Always ensure $\Delta H$ (kJ/mol) and $T\Delta S$ (J/mol) are in consistent units (e.g., convert kJ to J by multiplying by 1000). * Temperature $T$ must always be in Kelvin (K). $K = ^\circ C + 273.15$.

8. Common Mistakes to Avoid:

* Forgetting unit conversions (kJ to J). * Sign errors in $\Delta G = \Delta H - T\Delta S$. * Confusing $\Delta G$ with $\Delta G^circ$. * Misinterpreting temperature dependence for $\Delta H, \Delta S$ combinations.

Vyyuha Quick Recall

To remember the spontaneity conditions based on $\Delta H$ and $\Delta S$:

'Happy System, Good Time'

H — ($\Delta H$): Enthalpy
S — ($\Delta S$): Entropy
G — ($\Delta G$): Gibbs Energy
T — (Temperature)

Heavy Snow, Get Thermal ($\Delta H < 0, \Delta S < 0 \implies$ Spontaneous at Low T) Hot Sun, Get Tan ($\Delta H > 0, \Delta S > 0 \implies$ Spontaneous at High T)

Heavenly Smile, Great Triumph ($\Delta H < 0, \Delta S > 0 \implies$ Always Spontaneous) Hellish Scream, Grim Tragedy ($\Delta H > 0, \Delta S < 0 \implies$ Never Spontaneous)