In which of the following entropy decreases?

Question

Accepted Answer

Entropy is a measure of the disorder or randomness in a system. When entropy decreases, it indicates a transition to a more ordered state. Let's analyze each option to understand why Option 3 is the correct answer.

1. **$H_{2}(g)\rightarrow2H(g)$**: In this reaction, a diatomic hydrogen molecule ($H_{2}$) dissociates into two individual hydrogen atoms ($H$). This process increases the number of particles and the disorder in the system, leading to an increase in entropy, not a decrease.

2. **$2NaHCO_{3}(s)\rightarrow Na_{2}CO_{3}(s)+ CO_{2}(g)+H_{2}O(g)$**: This reaction involves the decomposition of solid sodium bicarbonate into solid sodium carbonate, carbon dioxide gas, and water vapor. The production of gaseous products from a solid increases the disorder and randomness, thus increasing the entropy of the system.

3. **A liquid crystallizes into a solid**: When a liquid crystallizes, it transitions from a less ordered liquid state to a more ordered solid state. This process involves the arrangement of molecules into a structured lattice, which decreases the randomness and disorder in the system. Therefore, the entropy decreases during crystallization, making this option correct.

4. **Temperature of a crystalline solid is raised from 0 K to 115 K**: Raising the temperature of a crystalline solid increases the kinetic energy of its particles, leading to greater vibrational motion and disorder. As a result, the entropy of the system increases with temperature, not decreases.

In conclusion, Option 3 is the correct answer because the process of crystallization involves a transition to a more ordered state, resulting in a decrease in entropy. The other options involve processes that increase disorder and thus increase entropy.