NH3(g) + HCl(s) → NH 4Cl (s) The entropy change in the system above is

Analysis of the Question

The question asks for the sign of the entropy change ($\Delta S$) for the reaction:

(Note: While the question lists HCl as a solid, the reaction between ammonia and hydrogen chloride gas is a classic example of a gas-phase reaction forming a solid.)

Concept Explanation

Entropy ($S$) is a measure of the degree of disorder or randomness in a system.

• Gases have the highest entropy because their particles move randomly and occupy a large volume.
• Liquids have intermediate entropy.
• Solids have the lowest entropy because their particles are fixed in a rigid, ordered lattice structure.

The entropy change ($\Delta S$) is calculated as:

If the system moves from a state of high disorder (gases) to a state of high order (solid), the entropy decreases, meaning $\Delta S$ is negative.

Step-by-Step Solution

1. Examine the reactants: We have two moles of gaseous substances ($\text{NH}_3$ and $\text{HCl}$). Gases have high entropy.
2. Examine the product: We have one mole of a solid substance ($\text{NH}_4\text{Cl}$). Solids have very low entropy.
3. Compare: The reaction involves the conversion of highly disordered gaseous molecules into a highly ordered solid crystal lattice.
4. Conclusion: Since the system is becoming more ordered (moving from gas to solid), the final entropy is lower than the initial entropy. Therefore, $\Delta S$ must be negative.

Identification of the Answer

The correct option is C.

Exam Tip

Whenever you see a reaction where the number of moles of gas decreases (or gas is converted to solid/liquid), the entropy change is almost always negative. Conversely, if a solid decomposes into gases, the entropy change is positive.