Criteria for Equilibrium — Explained

On this page

1. Conceptual Foundation: What is Equilibrium?
2. Key Principles and Laws Governing Equilibrium:
3. Derivations of Equilibrium Criteria:
4. A. Gibbs Free Energy (G) - For systems at constant Temperature (T) and Pressure (P):
5. B. Helmholtz Free Energy (A) - For systems at constant Temperature (T) and Volume (V):
6. C. Entropy of the Universe ($\Delta S_{universe}$) - For Isolated Systems:
7. Summary of Equilibrium Criteria:
8. Real-World Applications:
9. Common Misconceptions:
10. NEET-Specific Angle:

Detailed Explanation

The concept of equilibrium is central to understanding chemical and physical processes. It represents a state where a system's macroscopic properties remain constant over time, despite ongoing microscopic activity. From a thermodynamic standpoint, equilibrium is not merely a static condition but a dynamic balance governed by fundamental laws of energy and entropy.

Conceptual Foundation: What is Equilibrium?

At its core, equilibrium signifies a state of balance. In chemical reactions, it means the rate of the forward reaction equals the rate of the reverse reaction, leading to no net change in concentrations of reactants and products.

In physical processes, like phase transitions (e.g., melting ice at $0^\circ\text{C}$), it means the rate of melting equals the rate of freezing. This dynamic nature is crucial; equilibrium is not a cessation of activity but a perfect counteraction of opposing processes.

A system at equilibrium is stable; any infinitesimal perturbation will be countered by the system to restore the equilibrium state.

Key Principles and Laws Governing Equilibrium:

1
First Law of Thermodynamics (Conservation of Energy): — This law states that energy cannot be created or destroyed, only transformed. While essential for overall energy accounting, it doesn't predict the direction or spontaneity of a process, nor does it directly define equilibrium criteria.
2
Second Law of Thermodynamics (Entropy and Spontaneity): — This is the cornerstone for understanding spontaneity and equilibrium. It states that for any spontaneous process, the total entropy of the universe ($\Delta S_{universe}$) must increase. For a reversible process (which equilibrium essentially is, when viewed as an infinitesimal change), $\Delta S_{universe} = 0$. The universe consists of the system and its surroundings. Thus, $\Delta S_{universe} = \Delta S_{system} + \Delta S_{surroundings}$.

* For a spontaneous process: $\Delta S_{system} + \Delta S_{surroundings} > 0$ * For a system at equilibrium (reversible process): $\Delta S_{system} + \Delta S_{surroundings} = 0$ * For a non-spontaneous process: $\Delta S_{system} + \Delta S_{surroundings} < 0$ (This implies the reverse process is spontaneous).

The change in entropy of the surroundings is related to the heat exchanged with the surroundings ($q_{surroundings}$) at a given temperature ($T$): $\Delta S_{surroundings} = \frac{q_{surroundings}}{T}$. For a process occurring at constant pressure, $q_{surroundings} = -q_{system} = -\Delta H_{system}$. Therefore, $\Delta S_{surroundings} = -\frac{\Delta H_{system}}{T}$.

Substituting this into the Second Law expression for equilibrium: $\Delta S_{system} - \frac{\Delta H_{system}}{T} = 0$ Multiplying by $T$: $TDelta S_{system} - \Delta H_{system} = 0$ Rearranging: $\Delta H_{system} - TDelta S_{system} = 0$

This expression is precisely the definition of the change in Gibbs free energy ($\Delta G$) for the system. Thus, at equilibrium, $\Delta G_{system} = 0$.

1
Third Law of Thermodynamics: — This law states that the entropy of a perfect crystalline substance at absolute zero (0 K) is zero. While important for calculating absolute entropies, it doesn't directly define equilibrium criteria but provides a reference point for entropy values.

Derivations of Equilibrium Criteria:

A. Gibbs Free Energy (G) - For systems at constant Temperature (T) and Pressure (P):

Most chemical reactions and biological processes occur under conditions of constant temperature and pressure. For such systems, Gibbs free energy is the most convenient thermodynamic potential to predict spontaneity and equilibrium.

We start from the Second Law: $\Delta S_{universe} = \Delta S_{system} + \Delta S_{surroundings}$. For a process at constant T and P, the heat exchanged with the surroundings is $q_{surroundings} = -q_{system} = -\Delta H_{system}$. So, $\Delta S_{surroundings} = -\frac{\Delta H_{system}}{T}$.

Substituting this into the Second Law: $\Delta S_{universe} = \Delta S_{system} - \frac{\Delta H_{system}}{T}$

Multiplying by $-T$ (since $T$ is positive, this reverses the inequality sign): $-TDelta S_{universe} = -TDelta S_{system} + \Delta H_{system}$

We know that for a spontaneous process, $\Delta S_{universe} > 0$, so $-TDelta S_{universe} < 0$. Let's define a new function, Gibbs free energy change, $\Delta G = \Delta H - TDelta S$.

Thus, for a spontaneous process at constant T and P: $\Delta G < 0$ (The system moves towards lower Gibbs free energy)

For a non-spontaneous process: $\Delta G > 0$ (The reverse process is spontaneous)

And most importantly, for a system at equilibrium (where $\Delta S_{universe} = 0$): $\Delta G = 0$

This means that at equilibrium, the Gibbs free energy of the system is at its minimum value for the given temperature and pressure. Any infinitesimal change away from equilibrium would result in an increase in G, making that change non-spontaneous.

B. Helmholtz Free Energy (A) - For systems at constant Temperature (T) and Volume (V):

While less common for typical chemical reactions, some processes (e.g., reactions in a bomb calorimeter) occur at constant temperature and volume. For these conditions, Helmholtz free energy ($A$) is the relevant thermodynamic potential.

Helmholtz free energy is defined as $A = U - TS$, where $U$ is the internal energy. Therefore, $\Delta A = \Delta U - TDelta S$.

Following a similar derivation from the Second Law, but considering constant volume, the heat exchanged with the surroundings is $q_{surroundings} = -q_{system} = -\Delta U_{system}$ (since no P-V work is done). So, $\Delta S_{surroundings} = -\frac{\Delta U_{system}}{T}$.

For a spontaneous process at constant T and V: $\Delta S_{universe} = \Delta S_{system} - \frac{\Delta U_{system}}{T} > 0$ Multiplying by $-T$: $-TDelta S_{universe} = -TDelta S_{system} + \Delta U_{system} < 0$

Thus, for a spontaneous process at constant T and V: $\Delta A < 0$

And for a system at equilibrium at constant T and V: $\Delta A = 0$

This implies that at equilibrium under constant T and V, the Helmholtz free energy of the system is at its minimum.

C. Entropy of the Universe ($\Delta S_{universe}$) - For Isolated Systems:

An isolated system is one that cannot exchange either energy or matter with its surroundings. For such a system, the surroundings are effectively part of the system, or there are no surroundings to consider. Therefore, the criterion for spontaneity and equilibrium directly comes from the Second Law applied to the system itself.

For a spontaneous process in an isolated system: $\Delta S_{system} > 0$

For a system at equilibrium in an isolated system: $\Delta S_{system} = 0$ (at maximum entropy)

Summary of Equilibrium Criteria:

Constant T, P: — $\Delta G = 0$ (Gibbs free energy is at a minimum)
Constant T, V: — $\Delta A = 0$ (Helmholtz free energy is at a minimum)
Isolated System: — $\Delta S_{system} = 0$ (Entropy of the system is at a maximum)

Real-World Applications:

1
Phase Equilibria: — The melting of ice at $0^\circ\text{C}$ and $1\,\text{atm}$ pressure is an example where $\Delta G = 0$. At this specific temperature and pressure, solid ice and liquid water coexist in equilibrium. If the temperature is slightly above $0^\circ\text{C}$, $\Delta G < 0$ for melting, and ice melts. If slightly below, $\Delta G > 0$ for melting (meaning $\Delta G < 0$ for freezing), and water freezes.
2
Chemical Reactions: — The Haber-Bosch process for ammonia synthesis ($N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$) is a classic example. Optimizing conditions (T, P) to shift the equilibrium towards products is crucial for industrial efficiency. At equilibrium, the rate of ammonia formation equals its decomposition rate, and $\Delta G = 0$.
3
Biological Systems: — Many biochemical reactions in living organisms operate near equilibrium, allowing for rapid shifts in response to cellular needs. For instance, the binding of oxygen to hemoglobin is an equilibrium process that is sensitive to oxygen partial pressure.

Common Misconceptions:

1
Equilibrium vs. Static: — Students often confuse equilibrium with a static state where nothing is happening. Emphasize the dynamic nature – forward and reverse rates are equal, not zero.
2
Equilibrium vs. Completion: — A reaction at equilibrium is generally not 'complete' in the sense that all reactants have been converted to products. Significant amounts of both reactants and products can coexist at equilibrium.
3
$\Delta G = 0$ Always: — While $\Delta G = 0$ is the criterion for equilibrium at constant T and P, it's crucial to remember the specific conditions. For an isolated system, it's $\Delta S_{system} = 0$ (at maximum entropy). For constant T, V, it's $\Delta A = 0$.
4
Rate vs. Thermodynamics: — Thermodynamics (like $\Delta G$) tells us if a reaction is possible and to what extent it will proceed to equilibrium, but it says nothing about how fast it will reach equilibrium. A spontaneous reaction ($\Delta G < 0$) can still be very slow.

NEET-Specific Angle:

NEET questions frequently test the understanding of the conditions for spontaneity and equilibrium. Students must be able to:

Identify the correct thermodynamic criterion ($\Delta G$, $\Delta A$, $\Delta S_{universe}$) for different system conditions (constant T, P; constant T, V; isolated).
Relate $\Delta G$ to $\Delta H$ and $\Delta S$ using the equation $\Delta G = \Delta H - TDelta S$. At equilibrium, this becomes $\Delta H = TDelta S$, which can be used to calculate the equilibrium temperature ($T_{eq} = \frac{\Delta H}{\Delta S}$) for phase transitions or reactions where $\Delta G$ changes sign.
Understand how changes in temperature and pressure affect the position of equilibrium (Le Chatelier's Principle, though not directly a 'criterion' for equilibrium, is a consequence of the system shifting to re-establish equilibrium).
Distinguish between spontaneity and equilibrium. A spontaneous process moves towards equilibrium. Equilibrium is the state reached when spontaneity ceases.
Apply these concepts to predict the feasibility of reactions and phase changes.

Often confused with

Side-by-side differences the NEET paper likes to test.

Criteria for Equilibrium vs Spontaneity

Aspect	Criteria for Equilibrium	Spontaneity
Definition	The inherent tendency of a process to occur without continuous external intervention.	A dynamic state where opposing processes occur at equal rates, resulting in no net change in macroscopic properties.
Thermodynamic Criterion (Constant T, P)	$\Delta G < 0$ (Gibbs free energy decreases).	$\Delta G = 0$ (Gibbs free energy is at a minimum).
Thermodynamic Criterion (Isolated System)	$\Delta S_{system} > 0$ (Entropy of the system increases).	$\Delta S_{system} = 0$ (Entropy of the system is at a maximum).
Direction of Change	Indicates the direction in which a process will proceed.	Indicates the state where there is no net direction of change.
Relationship	A spontaneous process drives the system *towards* equilibrium.	Equilibrium is the *final state* achieved by a spontaneous process.

Spontaneity describes the natural tendency of a process to occur, driven by a reduction in Gibbs free energy or an increase in total entropy. It dictates the direction of change. Equilibrium, conversely, is the stable state where no further net change occurs because the forward and reverse rates are balanced.

A spontaneous process will continue until it reaches equilibrium, at which point its spontaneity ceases. Thus, spontaneity is the journey, and equilibrium is the destination, with distinct thermodynamic criteria defining each state.

Why it is tested: For NEET, understanding the distinction between spontaneity and equilibrium is critical. Questions often test whether a student can correctly apply $\Delta G < 0$ for spontaneity versus $\Delta G = 0$ for equilibrium, and how these concepts relate to reaction feasibility and extent. It's a foundational concept for chemical thermodynamics.

Questions students ask

6 answered on this topic.

What is the primary difference between a spontaneous process and a system at equilibrium?

A spontaneous process is one that occurs without external intervention, driven by a decrease in Gibbs free energy ($\Delta G < 0$) at constant temperature and pressure, or an increase in total entropy ($\Delta S_{universe} > 0$).

It represents the system moving towards a more stable state. Equilibrium, on the other hand, is the state where the system has reached its most stable condition under the given constraints, and there is no longer any net driving force for change.

At equilibrium, $\Delta G = 0$ (at constant T, P) or $\Delta S_{universe} = 0$. A spontaneous process ceases to be spontaneous once equilibrium is attained.

Why is Gibbs free energy ($\Delta G$) the preferred criterion for equilibrium in most chemical reactions?

Most chemical reactions and biological processes occur under conditions of constant temperature and pressure, which are typical laboratory and atmospheric conditions. Under these specific conditions, Gibbs free energy provides a direct and convenient measure of spontaneity and equilibrium.

Its change, $\Delta G$, directly indicates whether a process is spontaneous ($\Delta G < 0$), non-spontaneous ($\Delta G > 0$), or at equilibrium ($\Delta G = 0$). Using $\Delta S_{universe}$ would require calculating changes in both the system and surroundings, which is often more complex than directly evaluating $\Delta G$ for the system.

Does $\Delta G = 0$ mean that no reaction is occurring at all?

No, absolutely not. $\Delta G = 0$ signifies a state of dynamic equilibrium. This means that the forward reaction is occurring at the exact same rate as the reverse reaction. Individual molecules are still reacting and transforming, but the net concentrations of reactants and products remain constant over time.

It's a continuous, balanced process, not a static halt. For example, in a saturated salt solution, solid salt is continuously dissolving, and dissolved ions are continuously precipitating, but the overall concentration of dissolved salt remains constant.

How does temperature affect the equilibrium criterion $\Delta G = 0$?

Temperature plays a critical role in the $\Delta G = \Delta H - TDelta S$ equation. At equilibrium, $\Delta G = 0$, which implies $\Delta H = TDelta S$. This means the equilibrium temperature ($T_{eq}$) can be calculated as $T_{eq} = \frac{\Delta H}{\Delta S}$.

For processes like phase transitions, this equation directly gives the transition temperature (e.g., melting point, boiling point). For chemical reactions, changing temperature can shift the equilibrium position by altering the relative contributions of the enthalpy and entropy terms to $\Delta G$, thus changing the point at which $\Delta G$ becomes zero.

What is the criterion for equilibrium in an isolated system?

For an isolated system, which cannot exchange either energy or matter with its surroundings, the criterion for equilibrium is that the entropy of the system ($\Delta S_{system}$) reaches its maximum possible value.

At this maximum entropy, any infinitesimal change within the system would result in $\Delta S_{system} = 0$. This aligns with the Second Law of Thermodynamics, which states that the entropy of an isolated system tends to increase for spontaneous processes until it reaches a maximum at equilibrium.

Can a non-spontaneous reaction ever reach equilibrium?

Yes, but not on its own. A 'non-spontaneous' reaction ($\Delta G > 0$) means that the reverse reaction is spontaneous. For the non-spontaneous forward reaction to proceed and reach equilibrium, external energy input is required.

This is what happens in electrolytic cells or when coupling a non-spontaneous reaction with a highly spontaneous one (e.g., ATP hydrolysis in biological systems). Once the external energy drives the reaction sufficiently, it will eventually reach an equilibrium state where $\Delta G = 0$ under the new conditions, or if the external energy input is removed, it will revert to the original equilibrium state.