A reaction has \(\Delta H=-76 \mathrm{kJ}\) and \(\Delta S=-117 \mathrm{J} / \mathrm{K}\) . Calculate \(\Delta G\) for the reaction at 298.15 \(\mathrm{K}\) . Is the reaction spontaneous?

Enthalpy, represented as \( \Delta H \), is a concept from thermodynamics that measures the total heat content of a system. To understand enthalpy, imagine it as the energy a chemical reaction either absorbs or releases.
When \( \Delta H \) is negative, the reaction releases heat, and we call it exothermic. For instance, in our exercise, \( \Delta H = -76 \mathrm{kJ}\), means the reaction releases 76 kilojoules of energy.
Conversely, a positive value indicates an endothermic reaction, one that absorbs heat from its surroundings. Think of thermal packs you use to keep warm; they release heat in an exothermic reaction, precisely the reverse of keeping heat inside an endothermic reaction.

Entropy, denoted as \( \Delta S \), is a measure of disorder or randomness in a system. Higher entropy means more disorder. To grasp this idea, think of an untidy room versus a clean one - the untidy room has higher entropy.
In the problem given, \( \Delta S \) is \( -117 \mathrm{J} \mathrm{K}^{-1} \), indicating the system becomes less disordered during the reaction. Entropy values are important because they help determine whether a process can occur spontaneously.
Remember, systems naturally progress towards higher entropy. This explains why your room gets messier over time unless you constantly clean it. Similarly, entropy changes affect reaction spontaneity in chemistry.

A spontaneous reaction proceeds on its own without external energy input. Whether a reaction is spontaneous or not is determined by Gibbs Free Energy, \( \Delta G \). The equation we used is: \( \Delta G = \Delta H - T \Delta S \).
We calculated \( \Delta G = -41116.45 \mathrm{J}\), a negative value, indicating a spontaneous reaction. When \( \Delta G \) is negative, reactions can happen without added energy. Positive \( \Delta G \) means the reaction requires energy input.
In practical terms, think of rust forming on iron. It's a spontaneous process because it happens when iron reacts with oxygen in the air, releasing energy in the form of heat.
In summary, by understanding \( \Delta H \) (enthalpy), \( \Delta S \) (entropy), and \( \Delta G \) (Gibbs Free Energy), we can predict and explain whether chemical reactions occur on their own or need external assistance.