Question

For which of the following processes, $\Delta S$ is negative ?

• A. $H _{2}( g ) \rightarrow 2 H ( g )$
• B. $N _{2}( g , 1 atm ) \rightarrow N _{2}( g , 5 atm )$
• C. $C ($ diamond $) \rightarrow C ($ graphite $)$
• D. $N _{2}( g , 273 K ) \rightarrow N _{2}( g , 300 K )$

Answer 1

The Correct Option is B

The question asks us to identify the process for which the change in entropy, $\Delta S$, is negative. Entropy, a measure of disorder or randomness in a system, typically increases when a system becomes more disordered and decreases when it becomes more ordered. A negative value of $\Delta S$ indicates a decrease in entropy, which occurs when the system moves to a more ordered state.

Let's analyze each option:

1. $H_{2}(g) \rightarrow 2H(g)$: This process involves the dissociation of a diatomic hydrogen molecule into individual hydrogen atoms. Breaking a bond increases disorder since the single atoms are more randomly distributed compared to the ordered diatomic molecule. Therefore, $\Delta S$ is positive.
2. $N_{2}(g, 1 atm) \rightarrow N_{2}(g, 5 atm)$: In this process, nitrogen gas is compressed from 1 atm to 5 atm. Compressing a gas decreases its volume and increases its order because the molecules are closer together and have less freedom of movement. Thus, the entropy decreases, making $\Delta S$ negative.
3. $C ($ diamond $) \rightarrow C ($ graphite $)$: This involves the transformation of diamond to graphite. Graphite has more disorder due to its layered structure compared to the tightly packed diamond structure. Therefore, $\Delta S$ is positive.
4. $N_{2}(g, 273 K) \rightarrow N_{2}(g, 300 K)$: Heating a gas raises its temperature, increasing the kinetic energy of the gas molecules, and thus its entropy. Consequently, $\Delta S$ is positive.

From the analysis, the only process with a negative $\Delta S$ is the compression of nitrogen gas from 1 atm to 5 atm. Therefore, the correct answer is $N_{2}(g, 1 atm) \rightarrow N_{2}(g, 5 atm)$.