Question

(a) For a process that occurs at constant temperature, does the change in Gibbs free energy depend on changes in the enthalpy and entropy of the system? (b) For a certain process that occurs at constant \(T\) and \(P\) , the value of \(\Delta G\) is positive. Is the process spontaneous? (c) If \(\Delta G\) for a process is large, is the rate at which it occurs fast?

Short answer

(a) The change in Gibbs free energy at constant temperature depends on both the enthalpy change (\(\Delta H\)) and entropy change (\(\Delta S\)) of the system, as given by the equation \(\Delta G = \Delta H - T\Delta S\). (b) If \(\Delta G\) is positive for a process occurring at constant \(T\) and \(P\), the process is non-spontaneous. (c) A large value of \(\Delta G\) does not directly imply a fast reaction rate, as the rate depends on activation energy (\(E_a\)) and the Arrhenius equation, not the Gibbs free energy change.

Step-by-step solution

(a) Gibbs free energy dependence on enthalpy and entropy change

Using the definition of Gibbs free energy change (\(\Delta G\)) at constant temperature and pressure, we can write the equation: \[ \Delta G = \Delta H - T\Delta S, \] where \(\Delta H\) is the enthalpy change, \(T\) is the temperature, and \(\Delta S\) is the entropy change. From this equation, we can see that the change in Gibbs free energy at constant temperature depends on the changes in both the enthalpy and entropy of the system.

(b) Spontaneity of the process

For a process to be spontaneous, \(\Delta G\) must be negative. In this case, \(\Delta G\) is given as positive, which implies that the process is non-spontaneous.

(c) Relationship between \(\Delta G\) and reaction rate

The magnitude of \(\Delta G\) is related to the thermodynamic feasibility of a process, so a large value of \(\Delta G\) does not directly imply that the process occurs at a fast rate. It is important to note that the reaction rate is determined by the activation energy (\(E_a\)) and the Arrhenius equation, not the Gibbs free energy change. The large value of \(\Delta G\) could indicate that the process is thermodynamically favorable, but it does not provide information about how fast the process occurs.

Key concepts

Enthalpy Change

The concept of enthalpy change, represented by \( \Delta H \), is essential for understanding how energy is transferred during chemical reactions.

• Enthalpy change is the heat absorbed or released at constant pressure.
• It gives insight into whether a reaction is endothermic (absorbs heat) or exothermic (releases heat).

The formula for Gibbs free energy \( (\Delta G) \) highlights the role of enthalpy:
\[ \Delta G = \Delta H - T\Delta S, \]where \( T \) is the temperature, and \( \Delta S \) is the entropy change.
Understanding \( \Delta H \) helps determine how much heat flows in or out during a reaction, influencing how a system's energy evolves.

Entropy Change

Entropy change, denoted by \( \Delta S \), represents the degree of disorder or randomness in a system.

• Increasing entropy usually means the system becomes more disordered.
• It is a crucial part of predicting reaction spontaneity.

Entropy impacts Gibbs free energy as shown in the equation:
\[ \Delta G = \Delta H - T\Delta S. \]Higher entropy change \( (\Delta S) \) reduces \( \Delta G \), making reactions potentially more spontaneous.
By understanding \( \Delta S \), we gain insight into how a reaction's direction and extent might be influenced by disorder.

Reaction Spontaneity

Understanding whether a reaction occurs spontaneously is pivotal in chemistry.

• A reaction is spontaneous when \( \Delta G \) is negative.
• Spontaneity doesn't imply speed; it means the reaction can occur under specified conditions.

The equation \( \Delta G = \Delta H - T\Delta S \) guides us:
- Negative \( \Delta G \): The process is spontaneous.
- Positive \( \Delta G \): The process is non-spontaneous, requiring external energy.
Evaluating spontaneity helps chemists predict whether a reaction will happen naturally.

Reaction Rate

The reaction rate is different from reaction spontaneity. It's about how fast a reaction proceeds.

• Rate depends on factors like activation energy \( (E_a) \) and temperature.
• Gibbs free energy \( (\Delta G) \) isn't directly linked to speed.

Even if a process is spontaneous \((\Delta G < 0)\), it could still occur slowly.
The Arrhenius equation describes how activation energy affects rate:
\[ k = A e^{-E_a/RT}, \]where \( k \) is the rate constant, \( A \) is the pre-exponential factor, \( R \) is the gas constant, and \( T \) is temperature.
Understanding reaction rate is crucial for controlling processes in industrial and laboratory settings.