Question

Which of the following statement is true for \(\Delta \mathrm{G} ?\) (a) it is always proportional to \(\Delta \mathrm{H}\) (b) it may be less than or greater than or equal to \(\Delta \mathrm{H}\) (c) it is always greater than \(\Delta \mathrm{H}\) (d) it is always less than \(\Delta \mathrm{H}\)

Short answer

(b) It may be less than or greater than or equal to 9cH.

Step-by-step solution

Understanding Gibbs Free Energy

Gibbs Free Energy (9cG), also known as Gibbs energy, is a thermodynamic potential that can be used to calculate the maximum reversible work that may be performed by a thermodynamic system at a constant temperature and pressure. It is a thermodynamic property that incorporates both enthalpy (9cH) and entropy (9cS) changes, according to the formula \( \Delta G = \Delta H - T \Delta S \).

Analyzing the Formula

Examine the formula \( \Delta G = \Delta H - T \Delta S \). This formula shows that 9cG depends not only on the enthalpy change 9cH but also on the temperature \( T \) and entropy change 9cS of the system. As a result, 9cG has no fixed relationship with 9cH alone; it can be influenced by the values of \( T \) and \( \Delta S \).

Comparing 9cG with 9cH

From the formula \( \Delta G = \Delta H - T \Delta S \), 9cG could be less than, greater than, or equal to 9cH depending on the term \( -T \Delta S \). If 9cS is positive and \( T \Delta S \) is large, 9cG can be less than 9cH; if 9cS is negative or \( T \Delta S \) has a small value, 9cG may be closer to or greater than 9cH.

Identifying the True Statement

Now evaluate the statements given in the question. (a) suggests proportionality between 9cG and 9cH, which is incorrect as shown by the formula dependency on temperature and entropy. (b) correctly indicates that 9cG can be less, greater, or equal to 9cH depending on temperature and entropy changes. (c) and (d) are incorrect because they imply an absolute relationship which does not align with the formula.

Key concepts

Enthalpy Change

Enthalpy change, denoted as \(\Delta H\), is a measure of the total heat content exchanged in a chemical reaction occurring at constant pressure. It tells us whether a process requires heat (endothermic) or releases heat (exothermic).
In an endothermic reaction, \(\Delta H\) is positive because the system absorbs heat. Conversely, in an exothermic reaction, \(\Delta H\) is negative as the system releases heat to the surroundings.
For example:

• An exothermic reaction like combustion of natural gas releases energy, resulting in a negative \(\Delta H\).
• An endothermic process like melting ice absorbs heat, leading to a positive \(\Delta H\).

Enthalpy change is crucial in understanding the energy requirements or releases in reactions, which in turn helps us comprehend the stability and spontaneity of reactions under given conditions.

Entropy Change

Entropy change, symbolized as \(\Delta S\), signifies the degree of disorder or randomness in a system. In thermodynamics, it is a pivotal concept that tells us how energy is dispersed in a system.
It reflects the number of microstates associated with a macroscopic state, with higher entropy denoting more disorder or spread out energy. During any spontaneous reaction, entropy generally increases.
Here are a few examples of entropy changes:

• When a solid dissolves into a solution, \(\Delta S\) is positive because the solute particles are more randomly distributed.
• For gases, expansion into a larger volume results in increased entropy.

\(\Delta S\) plays a vital role in determining spontaneity of reactions when considered alongside enthalpy changes, as indicated in the Gibbs free energy equation.

Thermodynamics

Thermodynamics is a branch of physics that deals with heat and temperature and their relation to energy and work. Its laws form the foundation for understanding energy transformations in physical and chemical processes.
The three key laws of thermodynamics are:

• The First Law, which embodies the principle of conservation of energy, stating that energy can neither be created nor destroyed, only transformed or transferred.
• The Second Law, which declares that the total entropy of an isolated system can never decrease over time, and is often used to explain why certain processes are irreversible.
• The Third Law, which entails that as temperature approaches absolute zero, the entropy of a perfect crystal approaches a constant minimum.

In the realm of chemical reactions, thermodynamics helps in predicting the direction of reactions, their feasibility, and the balance between energy input/output and disorder, seamlessly connecting concepts like enthalpy and entropy to determine Gibbs free energy.