91Ó°ÊÓ

Entropy change (\( \Delta S \)) is a measure of how the disorder or randomness of a system changes during a reaction. Generally, reactions where gases form from solids or liquids lead to an increase in entropy because gases have more ways to arrange themselves.
In the given reaction, 2 magnesium atoms (\( \text{Mg} \)) and oxygen gas (\( \text{O}_2 \)) react to form magnesium oxide (\( \text{MgO} \)) which is solid. Here, a gaseous molecule (\( \text{O}_2 \)) changes to a solid (\( \text{MgO} \)). This transformation decreases the system's entropy.
- **Gases have higher entropy** because gas particles move more freely.- When a gas reacts to form a solid, \( \Delta S \) is negative.
In this reaction, the negative entropy change is expected because we're going from a state with more disorder (containing a gas) to one with less disorder (only solids). Therefore, your classmate's negative value for \( \Delta S \) is indeed correct.

Enthalpy change (\( \Delta H \)) reflects the heat absorbed or released by a system at constant pressure. It's often used to determine whether a reaction is exothermic (releases heat, \( \Delta H < 0 \)) or endothermic (absorbs heat, \( \Delta H > 0 \)).
In the context of the given reaction, it is important to note that forming magnesium oxide from magnesium and oxygen is highly exothermic. It means that a considerable amount of energy is released to the surroundings, which is why the reaction still proceeds spontaneously even when the entropy change is negative.
- **Exothermic reactions** release energy, causing \( \Delta H \) to be negative.- The large negative \( \Delta H \) can compensate for a less favorable \( \Delta S \) in the overall spontaneity of the reaction.
Thus, the large negative enthalpy change ensures that the Gibbs free energy (\( \Delta G \)) of the system is negative, confirming the reaction's spontaneity under standard conditions.

The spontaneity of a reaction is determined by the Gibbs free energy change (\( \Delta G \)), defined by the equation:
\[\Delta G = \Delta H - T\Delta S \]
A reaction is spontaneous if \( \Delta G \) is negative. Both enthalpy and entropy changes influence this. - If \( \Delta H \) is negative and \( \Delta S \) is positive, the reaction is spontaneous.- If both \( \Delta H \) and \( \Delta S \) are negative, the reaction might still be spontaneous if the enthalpy change outweighs the entropy change.
In our case, although \( \Delta S \) for the reaction of magnesium with oxygen is negative, \( \Delta H \) is sufficiently large and negative. This results in a negative \( \Delta G \), implying the process is spontaneous at common temperatures.
Therefore, the key to understanding spontaneity lies in managing the balance between \( \Delta H \) and \( \Delta S \) and knowing that sometimes, a negative entropy change doesn’t prevent a reaction from being spontaneous as long as the enthalpy change can drive the system forward.