91Ó°ÊÓ

Gibbs free energy is a fundamental concept in thermodynamics. It helps us determine if a chemical reaction can occur spontaneously. The symbol used to represent Gibbs free energy is \( \Delta G \). In simple terms, think of it as a kind of energy that can predict the direction a reaction will tend to go.
At a constant temperature and pressure, if \( \Delta G \) is negative, the reaction is spontaneous. That means it can proceed without any external help.
If \( \Delta G \) is zero, like in the example problem, the reaction is barely spontaneous. This means the two states of the reaction are in equilibrium.

• The main equation used is: \[ \Delta G = \Delta H - T \Delta S \]
• Where \( \Delta H \) is enthalpy change, \( T \) is the temperature in Kelvin, and \( \Delta S \) is entropy change.

When a reaction is barely spontaneous, the balance between enthalpy change and entropy change makes \( \Delta G \) equal to zero.

The enthalpy change, represented as \( \Delta H \), is a crucial aspect of understanding how energy is transferred during a chemical reaction. Enthalpy itself refers to the total heat content of a system.
When we talk about \( \Delta H \), we are looking at how much energy is absorbed or released when a reaction happens.

• If \( \Delta H \) is positive, like in the problem we are considering, the reaction absorbs energy. It is endothermic.
• Conversely, a negative \( \Delta H \) indicates an exothermic reaction, where energy is released.

In the example given, \( \Delta H = +15.2 \) kJ indicates that the reaction requires heat to proceed.

Entropy is a concept that describes disorder or randomness in a system. When we talk about entropy change, noted as \( \Delta S \), we're interested in how this disorder changes as the reaction takes place.
A positive \( \Delta S \) means the system becomes more disordered, while a negative \( \Delta S \) indicates an increase in order.
In our problem, we use the relationship \[ \Delta S = \frac{\Delta H}{T} \]to calculate the entropy change at the given temperature.

• An increased entropy (\( \Delta S > 0 \)) often helps a reaction be spontaneous, especially at higher temperatures, as it contributes to making \( \Delta G \) more negative.
• In our scenario, the calculated \( \Delta S \) of 47.5 J/K suggests an increase in disorder, aligning with the nearly spontaneous nature of the reaction.

The spontaneity of a reaction is crucial to understanding whether it will occur without outside influence. Generally, a reaction is spontaneous if \( \Delta G \) is negative.
However, if \( \Delta G \) is zero, the reaction is at the brink of spontaneity, which means it can go forward or backward equally.

• For spontaneity, both entropy and enthalpy changes may play a role.
  A favorable entropy change can help overcome a less favorable enthalpy change to make \( \Delta G \) zero or negative.
• The temperature is also key, as seen in the equation \( \Delta G = \Delta H - T \Delta S \).For instance, an endothermic reaction (\( \Delta H > 0 \)) can be made spontaneous at high temperatures if the entropy increases significantly.

In essence, spontaneity depends on the delicate balance between energy input/output and the increase in entropy.