Problem 23 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following has \(\Delta \mathrm{S}^{\circ}\) greater than zero? (a) \(\mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CaCO}_{3}(\mathrm{~g})\) (b) \(\mathrm{NaCl}(\mathrm{aq}) \rightleftharpoons \mathrm{NaCl}(\mathrm{s})\) (c) \(\mathrm{NaNO}_{3}(\mathrm{~s}) \rightleftharpoons \mathrm{Na}^{+}(\mathrm{aq})+\mathrm{NO}_{3}^{-}(\mathrm{aq})\) (d) \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons-2 \mathrm{NH}_{3}(\mathrm{~g})\)

Step-by-Step Solution

Answer

Reaction (c) has \( \Delta \mathrm{S}^{\circ} \) greater than zero.

Step 1: Review the Concept of Entropy

To solve this problem, we need to recall the concept of entropy, denoted as \( \Delta \mathrm{S} \). Entropy is a measure of the randomness or disorder of a system. When \( \Delta \mathrm{S}^{\circ} \) is greater than zero, the disorder of the system increases after the reaction.

Step 2: Analyze Reaction (a)

For reaction (a), \( \mathrm{CaO} (\mathrm{s}) + \mathrm{CO}_{2} (\mathrm{~g}) \rightarrow \mathrm{CaCO}_{3} (\mathrm{~g}) \), we are starting with one solid and one gas, and forming a gaseous compound. Since gases generally have higher entropy than solids, if the reaction goes from a solid plus a gas to forming more orderly complex molecules, \( \Delta \mathrm{S}^{\circ} \) might be negative.

Step 3: Analyze Reaction (b)

In reaction (b), \( \mathrm{NaCl} (\mathrm{aq}) \rightarrow \mathrm{NaCl} (\mathrm{s}) \), a soluble ionic compound in solution is forming a solid. Typically, this decreases the disorder since ions in solution are more disordered than in a lattice structure. Thus, \( \Delta \mathrm{S}^{\circ} \) is likely negative here.

Step 4: Analyze Reaction (c)

Reaction (c), \( \mathrm{NaNO}_{3} (\mathrm{~s}) \rightarrow \mathrm{Na}^{+} (\mathrm{aq}) + \mathrm{NO}_{3}^{-} (\mathrm{aq}) \), involves a solid dissociating into ions in solution. This increases the randomness as the structured solid lattice dissolves into freely moving ions, suggesting \( \Delta \mathrm{S}^{\circ} \) is positive.

Step 5: Analyze Reaction (d)

In reaction (d), \( \mathrm{N}_{2} (\mathrm{~g}) + 3 \mathrm{H}_{2} (\mathrm{~g}) \rightarrow 2 \mathrm{NH}_{3} (\mathrm{~g}) \), three molecules of gas react to form two molecules of gas. Since the number of gas molecules decreases, disorder often decreases, suggesting \( \Delta \mathrm{S}^{\circ} \) is negative.

Step 6: Conclusion: Identify the Reaction with Positive Entropy Change

Based on the analyses, reaction (c) \( \mathrm{NaNO}_{3} (\mathrm{~s}) \rightleftharpoons \mathrm{Na}^{+} (\mathrm{aq}) + \mathrm{NO}_{3}^{-} (\mathrm{aq}) \) has \( \Delta \mathrm{S}^{\circ} \) greater than zero, as the solid crystal dissolves into more disordered ions in solution.

Key Concepts

Entropy change

Entropy is a fundamental concept in thermodynamics, representing a measure of disorder or randomness in a system. In chemical reactions, the symbol \( \Delta \mathrm{S} \) denotes the change in entropy. When \( \Delta \mathrm{S}^{\circ} \) is greater than zero, it indicates that the system has become more disordered after the reaction.
This increase in disorder is often associated with processes where solids dissolve into ions or when the number of gaseous species increases. For instance, when a solid substance like \( \mathrm{NaNO}_3 \) dissociates into ions in an aqueous solution, the organized solid lattice dissolves into randomly moving ions, resulting in a positive entropy change. Understanding this concept is crucial for predicting the direction of chemical reactions, especially in understanding which reactions are thermodynamically favorable, when paired with the system's enthalpy change. It provides insights into the energy distribution within molecules and is a key factor in determining whether a reaction happens spontaneously under constant temperature and pressure.

Thermodynamics in JEE

Thermodynamics is a vital subject in the Indian Joint Entrance Exam (JEE), focusing on energy changes during chemical reactions. Students need to grasp not just entropy, but also concepts like enthalpy and Gibbs free energy to excel.
In thermodynamics, entropy contributes to understanding the feasibility of a reaction. For JEE, it's essential to remember that the total entropy change \( \Delta S_{\text{universe}} = \Delta S_{\text{system}} + \Delta S_{\text{surroundings}} \) must be greater than zero for a spontaneous process.

• Spontaneity: A reaction is spontaneous if the overall entropy of the universe increases.
• Gibbs Free Energy: Combines enthalpy and entropy to predict spontaneity: \( \Delta G = \Delta H - T\Delta S \). A negative \( \Delta G \) indicates spontaneity.
• JEE Application: Questions often explore the temperature dependence of these properties, emphasizing calculations involving equilibria and phase changes.

Mastering these areas will mean students can tackle complex problems that involve predictions of reaction courses and deducing whether reactions absorb or release energy.

Chemical reactions and entropy

In chemistry, understanding how chemical reactions influence entropy is key to predicting reaction behavior. Entropy is essentially a factor in determining the spontaneity of reactions, alongside enthalpy, the measure of heat content.

• Solid to Molecules: Consider reactions where a solid turns into ions or gas molecules. Since the latter are usually more disordered than solids, these reactions typically increase entropy.
• Gaseous Reactions: The number of gas molecules before and after a reaction heavily influences entropy change. More molecules generally mean more disorder, as seen in the reaction converting one solid species into multiple gaseous ions.
• Practical Examples: Dissolution processes often involve an increase in disorder as structured ionic compounds break down to freely moving ions, enhancing entropy.

Understanding how these processes impact entropy helps chemists control reactions. By controlling disorder through measures like temperature, chemists can influence reaction rates and equilibrium positions, crucial for industrial and laboratory processes.