Question

Explain briefly why (a) the change in entropy in a system is not always a suitable criterion for spontaneous change; (b) \(\Delta G^{\circ}\) is so important in dealing with the question of spontaneous change, even though the conditions employed in a reaction are very often nonstandard.

Short answer

Entropy alone is not a sufficient criterion for deciding spontaneity since it does not account for energy changes within a system, which are also imperative for a process to be spontaneous. \(\Delta G^{\circ}\), on the other hand, is important even under nonstandard conditions because it indicates the general trend of spontaneity and, moreover, serves as a reference point to calculate the actual Gibbs Free Energy under the given conditions.

Step-by-step solution

Understanding the concept

For a process to be spontaneous, it should reduce the system's overall energy while increasing its disorder or randomness. However, while entropy can account for disorder, it does not effectively measure energy changes in the system.

Explanation for part (a)

Entropy (\(\Delta S\)) provides a measure of the disorder in a system. In an isolated system, according to the second law of thermodynamics, entropy always increases. However, in a real-world non-isolated system, even if entropy increases, a process might not be spontaneous if it results in a net increase in the system's energy. This is because for a process to be spontaneous, the system's overall energy should decrease or remain unchanged.

Understanding Gibbs Free Energy

Gibbs Free Energy (\(\Delta G\)) is a thermodynamic potential that measures the maximum reversible work that a system can perform at constant temperature and pressure. It accounts for both the system's disorder (entropy) and energy (enthalpy).

Explanation for part (b)

Even if the reaction conditions are non-standard, \(\Delta G^{\circ}\) is still important because it gives a initial 'general' idea of whether a process will be spontaneous. Though \(\Delta G\) is affected by changes in concentration, temperature, and pressure, one can still use \(\Delta G^{\circ}\) (under standard conditions) as a reference point and then adjust it to calculate the actual Gibbs Free Energy for the non-standard conditions, using the equation \(\Delta G = \Delta G^{\circ} + RT \ln Q\). Thus, evaluating \(\Delta G^{\circ}\) is still crucial even under nonstandard conditions since it serves as the reference for any thermodynamical calculations.

Key concepts

Spontaneity of Chemical Processes

Understanding spontaneous chemical processes is fundamental in chemistry, particularly in predicting whether a reaction will occur without external influence. A spontaneous process is one that can proceed on its own, once initiated, without any continuous external intervention. However, it's a common misconception that spontaneous means 'instantaneous'; some spontaneous processes can take millennia to complete!

For a spontaneous process to occur, typically two factors are taken into account:

• The system’s overall energy should decrease, or at least remain unchanged.
• The system’s disorder, known as entropy, should increase.

Now, spontaneous change might not always align with the entropy increase because the energy factor could counteract it. An endothermic reaction where heat is absorbed can still be spontaneous if the disorder of the system increases enough to offset the energy input, reflecting the nuanced interplay between energy and entropy in chemical processes.

Entropy in Thermodynamics

In the world of thermodynamics, entropy is essentially a measurement of randomness or disorder within a system. The second law of thermodynamics famously states that in an isolated system (one that does not exchange heat or matter with its surroundings), the total entropy can never decrease over time. It's like saying that a room, if left unattended, tends to get messier over time – the natural tendency is towards disorder, not order.

The concept of entropy is central to understanding why some processes occur spontaneously. For instance, when ice melts into water at room temperature, entropy increases because the water molecules move more freely than ice molecules. The significance of entropy is that it provides insight into the ‘direction’ a process will naturally take. Although it's a key factor, it's not the only one; hence, there are scenarios where a process can result in an entropy decrease but still be spontaneous because other driving forces, such as enthalpy changes, play a role.

Standard vs Nonstandard Reaction Conditions

So, we know that the Gibbs Free Energy (\(\Delta G\)) is vital for determining spontaneity, but what about when conditions deviate from the ideal or ‘standard’? The 'standard' conditions refer to a specific set of pre-defined conditions: a temperature of 298K, 1 atm pressure, and all solutes at 1 M concentration. Under these conditions, the value of Gibbs Free Energy change (\(\Delta G^\circ\)) gives a baseline from which we can predict the behavior of substances. But reactions often occur under nonstandard reaction conditions, so we need to adjust our approach.

When conditions are nonstandard, concentrations, pressures, or temperatures will differ from the 'ideal' ones. Consequently, the actual Gibbs Free Energy (\(\Delta G\)) can still be determined by calculating deviations from standard state properties. This adjusted value tells us how far a system is from equilibrium under the given nonstandard conditions, informing us whether and in which direction a reaction will spontaneously proceed. Thus, assessing the reaction under both standard and nonstandard conditions paints a more accurate picture of the chemical process.