Certainly! Let's examine each of the given reactions to determine which one would result in decreased entropy.
Entropy, often denoted by [tex]\( S \)[/tex], is a measure of the disorder or randomness of a system. In general, entropy increases when a system becomes more disordered and decreases when it becomes more ordered. Here is a step-by-step evaluation of each reaction:
Option A:
[tex]\[ CO_2(s) \rightarrow CO_2(g) \][/tex]
- In this reaction, solid carbon dioxide (dry ice) is sublimating into gaseous carbon dioxide.
- Solids have lower entropy compared to gases because particles in a solid are tightly packed and orderly, whereas in a gas, particles are much more dispersed and disordered.
- Therefore, this process results in an increase in entropy.
Option B:
[tex]\[ N_2O_4(g) \rightarrow 2 NO_2(g) \][/tex]
- This reaction involves the dissociation of a single molecule of dinitrogen tetroxide gas into two molecules of nitrogen dioxide gas.
- Both the reactants and products are in the gaseous state, but the number of gas molecules increases, leading to more possible microstates and higher disorder.
- Hence, this also leads to an increase in entropy.
Option C:
[tex]\[ H_2 O(g) \rightarrow H_2 O(l) \][/tex]
- Here, water vapor (gas) is condensing into liquid water.
- Gases have higher entropy than liquids because gas particles are more dispersed and have more freedom of movement compared to liquids where particles are closer together and more restricted in movement.
- Thus, this process results in a decrease in entropy.
Option D:
[tex]\[ 2 O_3(g) \rightarrow 3 O_2(g) \][/tex]
- This reaction involves the decomposition of ozone gas into oxygen gas.
- Even though both reactants and products are gases, breaking down two ozone molecules into three oxygen molecules increases the number of gas particles, thereby increasing disorder.
- Consequently, this leads to an increase in entropy.
After analyzing all the options, we find that the reaction that results in decreased entropy is:
Option C:
[tex]\[ H_2 O(g) \rightarrow H_2 O(l) \][/tex]
So, the reaction involving a decrease in entropy is when water vapor condenses into liquid water.
