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

Question

Which one of the following has \(\Delta S^{\circ}\) 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

The reaction \( \mathrm{NaNO}_{3} (\mathrm{~s}) \rightleftharpoons \mathrm{Na}^{+} (\mathrm{aq}) + \mathrm{NO}_{3}^{-} (\mathrm{aq}) \) has \( \Delta S^{\circ} > 0 \).

Step 1: Analyze Reaction (a)

The reaction is \( \mathrm{CaO} (\mathrm{s}) + \mathrm{CO}_{2} (\mathrm{~g}) \rightleftharpoons \mathrm{CaCO}_{3} (\mathrm{~s}) \). In this process, a gas and a solid react to form a solid. Generally, the entropy decreases when gases are involved as reactants and form solids, implying \( \Delta S^{\circ} < 0 \).

Step 2: Analyze Reaction (b)

The reaction is \( \mathrm{NaCl} (\mathrm{aq}) \rightleftharpoons \mathrm{NaCl} (\mathrm{s}) \). Dissolved ions in solution have higher entropy compared to ions in a solid crystal lattice. Hence, forming a solid from an aqueous solution results in a decrease in entropy, \( \Delta S^{\circ} < 0 \).

Step 3: Analyze Reaction (c)

The reaction is \( \mathrm{NaNO}_{3} (\mathrm{~s}) \rightleftharpoons \mathrm{Na}^{+} (\mathrm{aq}) + \mathrm{NO}_{3}^{-} (\mathrm{aq}) \). This process involves dissolving a solid in water to form aqueous ions, which increases the system's entropy due to the greater disorder in the dissolved state. Therefore, \( \Delta S^{\circ} > 0 \).

Step 4: Analyze Reaction (d)

The reaction is \( \mathrm{N}_{2} (\mathrm{~g}) + 3 \mathrm{H}_{2} (\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3} (\mathrm{~g}) \). Here, four moles of gases are being converted into two moles of gas, reducing the entropy of the system. Hence, \( \Delta S^{\circ} < 0 \).

Step 5: Conclusion: Identify Reaction with Positive Entropy Change

Among the four reactions analyzed, Reaction (c) has \( \Delta S^{\circ} > 0 \) because it involves the dissolution of a solid into ions in solution, which increases entropy.

Key Concepts

Chemical Reactions

Chemical reactions are the processes where substances convert into new products with different chemical identities. A key aspect that characterizes these reactions involves changes in energy and disorder, often measured by changes in entropy and enthalpy.

When analyzing a chemical reaction, one must consider how molecules interact and transform. For example, reactions involving gases or changes in states, like solid dissolving into liquid, often involve significant changes in entropy. Understanding these processes helps in predicting the products and feasibility of a reaction.

In the given exercise, the reaction turning a solid \(\mathrm{NaNO}_3(\mathrm{~s})\) into its aqueous ionic form \(\mathrm{Na}^+(\mathrm{aq})\) and \(\mathrm{NO}_3^-(\mathrm{aq})\) is a prime example of a chemical reaction that increases entropy. As ions move freely in solution, the disorder of the system increases, making this process energetically favorable due to higher entropy.

Thermodynamics

Thermodynamics is the branch of physical science that deals with the relations between heat and other forms of energy. It plays a crucial role in understanding how chemical reactions proceed and their energy requirements or releases.
A central concept in thermodynamics related to chemical reactions is entropy (\(\Delta S^{\circ}\)), a measure of disorder. The Second Law of Thermodynamics states that for any spontaneous process, the total entropy of a system and its surroundings always increases.
In our exercise, analyzing reactions through the lens of thermodynamics involves understanding how the structure and phases of reactants and products affect entropy. For example, gases generally have higher entropy compared to liquids and solids. This is evident in reaction (c) from the exercise, where a solid dissolves into ions, increasing the system's overall entropy, thereby aligning with the thermodynamic principle that spontaneous reactions tend to increase disorder.

Equilibrium

Equilibrium in chemistry refers to a state in which both the forward and reverse reactions occur at the same rate, leading to stable concentrations of reactants and products over time.

Chemical equilibrium is closely tied to the concept of free energy and entropy. For instance, at equilibrium, the free energy change (\(\Delta G\)) is zero, meaning that the reaction doesn't gain or lose energy. However, changes in conditions like pressure or temperature can disrupt this state.
The exercise's reactions explore how changes in state, like dissolving solids or forming gases, impact entropy. For example, when \(\mathrm{NaCl}(\mathrm{aq})\) turns into a solid, the entropy decreases, impacting equilibrium position and potentially favoring reactants. Conversely, the dissolution of \(\mathrm{NaNO}_3(\mathrm{~s})\) increases entropy and partially shifts equilibrium toward product formation.