Is Delta G 0 At Equilibrium

Is ΔG° 0 at Equilibrium? Understanding Gibbs Free Energy and Equilibrium

The question of whether the standard Gibbs Free Energy change (ΔG°) is zero at equilibrium is a common point of confusion in thermodynamics. The short answer is: no, ΔG° is not zero at equilibrium. However, the actual Gibbs Free Energy change (ΔG) is zero at equilibrium. Understanding the subtle but crucial difference between ΔG° and ΔG is key to grasping this concept. This article will delve into the intricacies of Gibbs Free Energy, equilibrium, and the conditions under which ΔG equals zero.

Understanding Gibbs Free Energy (G)

Gibbs Free Energy (G) is a thermodynamic potential that measures the maximum reversible work that may be performed by a thermodynamic system at a constant temperature and pressure. It's a crucial concept for predicting the spontaneity of a reaction. The change in Gibbs Free Energy (ΔG) is given by:

ΔG = ΔH - TΔS

Where:

• ΔG is the change in Gibbs Free Energy
• ΔH is the change in enthalpy (heat content)
• T is the absolute temperature (in Kelvin)
• ΔS is the change in entropy (disorder)

A negative ΔG indicates a spontaneous process (occurs without external intervention), a positive ΔG indicates a non-spontaneous process (requires energy input), and a ΔG of zero indicates a system at equilibrium.

Standard Gibbs Free Energy Change (ΔG°)

The standard Gibbs Free Energy change (ΔG°) refers to the change in Gibbs Free Energy under standard conditions: typically 298 K (25°C) and 1 atm pressure, with all reactants and products present at a concentration of 1 M (for solutions) or a partial pressure of 1 atm (for gases). It's a crucial value because it provides a reference point for comparing the spontaneity of different reactions. However, it doesn't tell us about the spontaneity under non-standard conditions.

The Relationship Between ΔG and ΔG°

The relationship between ΔG and ΔG° is described by the following equation:

ΔG = ΔG° + RTlnQ

Where:

• R is the ideal gas constant (8.314 J/mol·K)
• T is the absolute temperature (in Kelvin)
• Q is the reaction quotient

The reaction quotient (Q) is a measure of the relative amounts of products and reactants present at any given time during a reaction. It has the same form as the equilibrium constant (K), but it's calculated using the current concentrations or partial pressures, not the equilibrium concentrations.

This equation highlights the importance of both ΔG° and the reaction conditions (reflected in Q) in determining the spontaneity of a reaction. ΔG° tells us about the inherent tendency of a reaction to proceed under standard conditions, while Q accounts for deviations from standard conditions.

Understanding the Equilibrium Constant (K)

At equilibrium, the forward and reverse reaction rates are equal, and there is no net change in the concentrations of reactants or products. At equilibrium, Q becomes equal to the equilibrium constant (K). Therefore, the equation becomes:

ΔG = ΔG° + RTlnK

This equation directly links the standard Gibbs Free Energy change (ΔG°) to the equilibrium constant (K). A large value of K indicates a reaction that strongly favors products at equilibrium, while a small value of K indicates a reaction that strongly favors reactants at equilibrium.

ΔG at Equilibrium

As previously stated, at equilibrium, the change in Gibbs Free Energy (ΔG) is always zero. This is because there is no further net change in the system. The forward and reverse reactions are occurring at the same rate, and the system is in a state of dynamic balance. Setting ΔG to zero in the equation above:

0 = ΔG° + RTlnK

We can rearrange this to solve for ΔG°:

ΔG° = -RTlnK

This equation is extremely important because it directly relates the standard Gibbs Free Energy change to the equilibrium constant. It allows us to calculate ΔG° from K (or vice-versa) and provides a powerful tool for predicting the position of equilibrium. This equation clearly shows that ΔG° is not zero at equilibrium; it is related to the equilibrium constant K.

Interpreting ΔG° and K

• Large K (K >> 1): This indicates that the equilibrium lies far to the right, meaning that the products are strongly favored at equilibrium. This corresponds to a large negative value of ΔG°, indicating a highly spontaneous reaction under standard conditions.

• K = 1: This means that the equilibrium concentrations of reactants and products are equal. The reaction is neither strongly favored in the forward nor reverse direction under standard conditions. In this case, ΔG° = 0.

• Small K (K << 1): This signifies that the equilibrium lies far to the left, with reactants being strongly favored at equilibrium. This corresponds to a large positive value of ΔG°, indicating a non-spontaneous reaction under standard conditions.

Non-Standard Conditions and the Importance of Q

It's crucial to remember that ΔG° only applies to standard conditions. In real-world scenarios, reactions rarely occur under standard conditions. The reaction quotient (Q) accounts for the deviation from standard conditions and is vital for calculating ΔG under non-standard conditions.

If Q < K, the reaction will proceed spontaneously in the forward direction to reach equilibrium. If Q > K, the reaction will proceed spontaneously in the reverse direction to reach equilibrium. Only when Q = K is the system at equilibrium, and ΔG = 0.

Examples Illustrating the Concepts

Let's consider two hypothetical reactions:

Reaction 1: A + B ⇌ C (ΔG° = -10 kJ/mol)

This reaction has a large negative ΔG°, indicating a high tendency to favor product formation under standard conditions. The equilibrium constant K will be significantly greater than 1.

Reaction 2: D + E ⇌ F (ΔG° = +20 kJ/mol)

This reaction has a large positive ΔG°, indicating that product formation is not favored under standard conditions. The equilibrium constant K will be significantly less than 1.

Even though Reaction 1 is spontaneous under standard conditions, if we were to start with a very high concentration of product C (making Q very large), the reaction would proceed spontaneously in the reverse direction to reach equilibrium (ΔG would be negative for the reverse reaction).

Conversely, if we started Reaction 2 with very low concentrations of D and E (making Q very small), the reaction might proceed in the forward direction even though ΔG° is positive (ΔG could be negative for the forward reaction under these specific conditions).

Conclusion

In summary, ΔG° is not zero at equilibrium. ΔG° represents the standard free energy change under specific conditions and is related to the equilibrium constant K via the equation ΔG° = -RTlnK. It provides information about the inherent tendency of a reaction to proceed under standard conditions. However, the actual Gibbs Free Energy change (ΔG) is zero at equilibrium, reflecting the dynamic balance between forward and reverse reactions. The reaction quotient (Q) is essential for determining the spontaneity of a reaction under non-standard conditions using the equation ΔG = ΔG° + RTlnQ. Understanding these distinctions is paramount for accurately interpreting and predicting the behavior of chemical reactions.