Spontaneity — Revision Notes

⚡ 30-Second Revision

Spontaneity: — Process occurs without continuous external input.
Gibbs Free Energy: — $\Delta G = \Delta H - T\Delta S$
Conditions for Spontaneity:

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

Second Law: — $\Delta S_{universe} = \Delta S_{system} + \Delta S_{surroundings} > 0$ for spontaneous process.
Temperature Effects:

- $\Delta H < 0, \Delta S > 0 \Rightarrow$ Always spontaneous - $\Delta H > 0, \Delta S < 0 \Rightarrow$ Never spontaneous - $\Delta H < 0, \Delta S < 0 \Rightarrow$ Spontaneous at low $T$ ($T < \Delta H/\Delta S$) - $\Delta H > 0, \Delta S > 0 \Rightarrow$ Spontaneous at high $T$ ($T > \Delta H/\Delta S$)

Equilibrium Constant: — $\Delta G^circ = -RT \ln K$

2-Minute Revision

Spontaneity determines if a process will occur naturally. It's distinct from reaction speed. The key to understanding spontaneity is Gibbs Free Energy ($Delta G$), which combines enthalpy ($Delta H$, energy change) and entropy ($Delta S$, disorder change) at a given absolute temperature ($T$) via the equation $Delta G = Delta H - TDelta S$. A process is spontaneous if $Delta G < 0$, non-spontaneous if $Delta G > 0$, and at equilibrium if $Delta G = 0$.

When $Delta H$ is negative (exothermic) and $Delta S$ is positive (increased disorder), the reaction is always spontaneous. If $Delta H$ is positive (endothermic) and $Delta S$ is negative (decreased disorder), it's never spontaneous.

For cases where $Delta H$ and $Delta S$ have the same sign, temperature becomes crucial. For instance, if both are negative, spontaneity occurs at low temperatures; if both are positive, it occurs at high temperatures.

Remember to always use consistent units (e.g., Joules for all energy terms) and Kelvin for temperature. The standard Gibbs free energy change ($Delta G^circ$) is related to the equilibrium constant ($K$) by $Delta G^circ = -RT ln K$, which helps predict the extent of a reaction at equilibrium.

5-Minute Revision

Spontaneity is a thermodynamic concept indicating the natural tendency of a process to occur without continuous external energy input. It does not imply speed. The driving force for spontaneity is the increase in the total entropy of the universe ($Delta S_{universe} > 0$), as stated by the Second Law of Thermodynamics. For processes at constant temperature and pressure, this is conveniently expressed using Gibbs Free Energy ($Delta G$).

Key Equation: $\Delta G = \Delta H - T\Delta S$

Here, $\Delta H$ is the enthalpy change (heat absorbed/released), $\Delta S$ is the entropy change (change in disorder), and $T$ is the absolute temperature in Kelvin.

Conditions for Spontaneity:

$\Delta G < 0$ — Spontaneous process.
$\Delta G > 0$ — Non-spontaneous process (the reverse is spontaneous).
$\Delta G = 0$ — System is at equilibrium.

Interplay of $\Delta H$, $\Delta S$, and $T$:

1
Exothermic ($\Delta H < 0$) and Entropy-Increasing ($\Delta S > 0$): — $\Delta G$ is always negative. Reaction is always spontaneous. (e.g., combustion)
2
Endothermic ($\Delta H > 0$) and Entropy-Decreasing ($\Delta S < 0$): — $\Delta G$ is always positive. Reaction is never spontaneous. (e.g., formation of ozone from oxygen)
3
Exothermic ($\Delta H < 0$) and Entropy-Decreasing ($\Delta S < 0$): — $\Delta G = (\text{negative}) - T(\text{negative}) = (\text{negative}) + (\text{positive})$. Spontaneous only at low temperatures where $|\Delta H| > |T\Delta S|$. (e.g., freezing of water below $0^circ C$)
4
Endothermic ($\Delta H > 0$) and Entropy-Increasing ($\Delta S > 0$): — $\Delta G = (\text{positive}) - T(\text{positive})$. Spontaneous only at high temperatures where $|T\Delta S| > |\Delta H|$. (e.g., melting of ice above $0^circ C$)

Relationship with Equilibrium Constant ($K$):

$\Delta G^circ = -RT \ln K$

If $\Delta G^circ < 0$, then $K > 1$ (products favored).
If $\Delta G^circ > 0$, then $K < 1$ (reactants favored).
If $\Delta G^circ = 0$, then $K = 1$.

Example: For a reaction with $\Delta H = -40,\text{kJ/mol}$ and $\Delta S = -100,\text{J/mol·K}$. To find the temperature for spontaneity: Set $\Delta G < 0 \Rightarrow \Delta H - T\Delta S < 0$ $-40000,\text{J/mol} - T(-100,\text{J/mol·K}) < 0$ $-40000 + 100T < 0 \Rightarrow 100T < 40000 \Rightarrow T < 400,\text{K}$. So, the reaction is spontaneous below $400,\text{K}$.

Always pay attention to units (J vs. kJ) and the sign conventions. This topic is frequently tested in NEET, often involving calculations and conceptual understanding of the interplay of thermodynamic factors.

Prelims Revision Notes

Spontaneity refers to the inherent tendency of a process to occur without continuous external energy input. It is a thermodynamic concept, distinct from reaction rate. A spontaneous reaction can be very slow (e.g., rusting). The ultimate criterion for spontaneity at constant temperature and pressure is the change in Gibbs free energy ($Delta G$).

Key Formula: $\Delta G = \Delta H - T\Delta S$

$\Delta G$ — Gibbs free energy change (in J/mol or kJ/mol).
$\Delta H$ — Enthalpy change (in J/mol or kJ/mol). Negative for exothermic, positive for endothermic.
$T$ — Absolute temperature (in Kelvin).
$\Delta S$ — Entropy change (in J/mol·K or kJ/mol·K). Positive for increased disorder, negative for decreased disorder.

Conditions for Spontaneity:

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

Temperature Dependence:

1
$\Delta H < 0, \Delta S > 0$ — Always spontaneous ($\Delta G$ always negative).
2
$\Delta H > 0, \Delta S < 0$ — Never spontaneous ($\Delta G$ always positive).
3
$\Delta H < 0, \Delta S < 0$ — Spontaneous at low temperatures (when $|\Delta H| > |T\Delta S|$).
4
$\Delta H > 0, \Delta S > 0$ — Spontaneous at high temperatures (when $|T\Delta S| > |\Delta H|$).

Threshold Temperature: For cases 3 and 4, the crossover temperature where $\Delta G = 0$ is $T = \frac{\Delta H}{\Delta S}$.

Second Law of Thermodynamics: For any spontaneous process, $\Delta S_{universe} = \Delta S_{system} + \Delta S_{surroundings} > 0$. Note that $\Delta S_{surroundings} = -\frac{\Delta H_{system}}{T}$.

Relationship with Equilibrium Constant ($K$):

$\Delta G^circ = -RT \ln K$

$R = 8.314,\text{J/mol·K}$ (use J for $\Delta G^circ$ here).
If $\Delta G^circ$ is negative, $K > 1$ (products favored).
If $\Delta G^circ$ is positive, $K < 1$ (reactants favored).

Important Points for NEET:

Always ensure consistent units (J vs. kJ) in calculations.
Temperature must be in Kelvin.
Do not confuse spontaneity with reaction rate. They are independent concepts.
Be able to predict the signs of $\Delta H$ and $\Delta S$ for common processes (e.g., phase changes, dissolution, gas expansion).

Vyyuha Quick Recall

Great Hydrogen Thinks Spontaneously! ($\Delta G = \Delta H - T\Delta S$)

For conditions: Exothermic Increased Disorder = Always Spontaneous ($\Delta H < 0, \Delta S > 0$) Endothermic Decreased Disorder = Never Spontaneous ($\Delta H > 0, \Delta S < 0$) Exothermic Decreased Disorder = Low Temp Spontaneous ($\Delta H < 0, \Delta S < 0$) Endothermic Increased Disorder = High Temp Spontaneous ($\Delta H > 0, \Delta S > 0$)

(EID = Exothermic Increased Disorder, EDD = Endothermic Decreased Disorder, etc.)