91Ó°ÊÓ

Bertholet's generalization provides a simple rule to predict the spontaneity of chemical reactions. It suggests that reactions are more likely to occur spontaneously if they release energy as heat, known as exothermic reactions. In these cases, the change in enthalpy,

• \( \Delta H \),

is negative. This means that the system loses energy to its surroundings.
On the other hand, if a reaction absorbs heat (endothermic), resulting in a positive \( \Delta H \), it is generally thought to be non-spontaneous.
However, this rule doesn't always hold true. While an exothermic reaction is often spontaneous, not all endothermic reactions are non-spontaneous.
This is because spontaneity is influenced by other factors like entropy and temperature, not just enthalpy alone. Bertholet's generalization is a useful guideline, but it's essential to consider the whole picture.

Entropy, denoted by \( \Delta S \), is a measure of disorder or randomness in a system. In chemical reactions, an increase in entropy typically favors spontaneity.
When a solid turns into a gas, as in the given reaction of

• \( \mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2} \cdot 4 \mathrm{H}_{2} \mathrm{O}(s) \to \mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2}(s)+4 \mathrm{H}_{2} \mathrm{O}(g) \),

entropy increases significantly. This is because gas particles are far more disordered compared to the organized solid state.
In the equation for Gibbs free energy, \( \Delta G = \Delta H - T\Delta S \), entropy plays a key role along with temperature. If \( \Delta S \) is positive and large, it can drive a reaction to be spontaneous, even if it is endothermic.
Therefore, understanding entropy helps in assessing the overall energy changes and predictions about whether a reaction will occur spontaneously.

The spontaneity of a reaction is determined by the change in Gibbs free energy, \( \Delta G \). A reaction is spontaneous if \( \Delta G \) is negative.
The equation \( \Delta G = \Delta H - T\Delta S \) integrates enthalpy and entropy changes to assess the true nature of a reaction's spontaneity.

• If a reaction has positive \( \Delta H \) but also has a strong positive \( \Delta S \) at high temperatures, the term \( -T\Delta S \) becomes significant enough to make \( \Delta G \) negative.

That's why some endothermic reactions can occur spontaneously under the right conditions. Practically, this means that temperature and entropy changes can overpower the enthalpy effect.
In the example given, the large increase in entropy is likely making the reaction spontaneous even though it's absorbing heat. This illustrates the importance of considering both enthalpy and entropy when evaluating reaction spontaneity.