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Chapter 6: Problem 23

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) \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})\)

Short Answer

Expert verified
Option (c) has 螖S掳 greater than zero.

Step by step solution

01

Understanding Entropy and 螖S掳

Entropy ( abla S) is a measure of the disorder or randomness in a system. A positive abla S^{ ext{o}} indicates that the disorder has increased in the reaction. We can generally predict the sign of abla S^{ ext{o}} by considering changes in the state of matter and the number of molecules or ions in the reaction.
02

Analyzing Each Option

Let's analyze the reactions to determine the sign of abla S^{ ext{o}}. (a) abla S^{ ext{o}} < 0 because gaseous molecules are combining to form a solid, decreasing disorder. (b) abla S^{ ext{o}} < 0 as it involves the crystallization, going from dissolved ions (aq) to a solid (s). (c) abla S^{ ext{o}} > 0 because a solid is dissolving into ions in solution, increasing disorder. (d) abla S^{ ext{o}} < 0 because multiple gas molecules are combining to form fewer gas molecules, decreasing disorder.
03

Identifying the Reaction with 螖S掳 > 0

From the analysis, only reaction (c) ( ext{NaNO}_3(s) ightleftharpoons ext{Na}^+(aq) + ext{NO}_3^-(aq)), where a solid dissolves into ions, has an increase in disorder, resulting in abla S^{ ext{o}} > 0.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Entropy Change
Entropy, denoted as \( \Delta S \), is a fundamental concept in thermodynamics representing the degree of disorder or randomness in a system. In chemical reactions, the change in entropy \( \Delta S^{\circ} \) helps us understand how the disorder of the system changes as the reaction proceeds.

To determine \( \Delta S^{\circ} \), consider the states of the reactants and products:
  • Gases generally have higher entropy than liquids, which in turn have higher entropy than solids.
  • An increase in the number of gas molecules typically indicates an increase in entropy.
  • Dissolution of solids into ions tends to increase entropy due to the greater distribution and movement of particles.
By evaluating the initial and final states of a reaction, entropy changes can help predict whether the abla S^{\circ} will be positive or negative, thus indicating an increase or decrease in disorder.
Reaction Entropy
Reaction entropy specifically refers to the change in entropy (\( \Delta S \)) that occurs during a chemical reaction. During a reaction, the arrangement and movement of atoms and molecules change, which then influences the system's entropy.

Consider the following when analyzing reaction entropy:
  • If reactants combine to form a product with fewer molecules or a more ordered arrangement, \( \Delta S^{\circ} \) is likely negative.
  • If products are formed from a greater number of reactant molecules, or if components dissolve forming a larger number of ions, \( \Delta S^{\circ} \) tends to be positive.
  • The phase of each component in the reaction (solid, liquid, or gas) significantly affects the system's entropy.
This understanding of reaction entropy allows us to anticipate how the entropy of a system will change when a chemical reaction takes place, which can influence the feasibility and spontaneity of reactions.
Sign of Delta S
The sign of \( \Delta S^{\circ} \) is crucial in predicting the behavior of a chemical reaction. It informs us whether a process results in increased or decreased randomness in the system. Recognizing the signs of \( \Delta S \) helps students understand broader thermodynamic principles.

Here are key points to decide the sign of \( \Delta S^{\circ} \):
  • Reactions where solid substances dissolve into ions or gases usually have \( \Delta S^{\circ} > 0 \), as they lead to more dispersed and free-moving particles.
  • Conversely, reactions that produce fewer gas molecules from more gaseous reactants typically result in \( \Delta S^{\circ} < 0 \), indicating a decrease in disorder.
  • The process of crystallization or condensing gases into solids often decreases entropy.
Ultimately, the sign of \( \Delta S \) guides us in determining the spontaneity of the reaction under certain conditions, aiding us in predicting whether the reaction will occur naturally.

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Most popular questions from this chapter

The enthalpy of vaporization of a liquid is \(30 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and entropy of vaporization is \(5 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}\). The boiling point of the liquid at 1 atm is: (a) \(250 \mathrm{~K}\) (b) \(400 \mathrm{~K}\) (c) \(450 \mathrm{~K}\) (d) \(600 \mathrm{~K}\)

The enthalpies of solution of \(\mathrm{BaCl}_{2}\) (s) and \(\mathrm{BaCl}_{2} .2 \mathrm{H}_{2} \mathrm{O}\) (s) are \(-20.6\) and \(8.8 \mathrm{~kJ} \mathrm{~mol}^{2}\) respectively. The enthalpy change for the hydration of \(\mathrm{BaCl}_{2}(\mathrm{~s})\) is: (a) \(29.8 \mathrm{~kJ}\) (b) \(-11.8 \mathrm{~kJ}\) (c) \(-20.6 \mathrm{~kJ}\) (d) \(-29.4 \mathrm{~kJ}\).

10 mole of an ideal gas expand isothermally and reversibly from a pressure of 10 atm to 1 atm at \(27^{\circ} \mathrm{C}\). What will be the largest mass that be lifted through a height of 100 metre? (a) \(5.855 \mathrm{Kg}\) (b) \(58.55 \mathrm{Kg}\) (c) \(585.5 \mathrm{Kg}\) (d) \(29.28 \mathrm{Kg}\)

The internal energy change when a system goes from state \(\mathrm{A}\) to \(\mathrm{B}\) is \(40 \mathrm{~kJ} / \mathrm{mol}\). If the system goes from \(\mathrm{A}\) to \(B\) by a reversible path and returns to state \(A\) by an irreversible path what would be the net change in internal energy? (a) \(40 \mathrm{~kJ}\) (b) \(>40 \mathrm{~kJ}\) (c) \(<40 \mathrm{~kJ}\) (d) zero

Calculate \(Q\) and \(W\) for the isothermal reversible expansion of one mole of an ideal gas from an initial pressure of \(1.0\) bar to a final pressure of \(0.1\) bar at a constant temperature of \(273 \mathrm{~K}\). (a) \(5.22 \mathrm{~kJ},-5.22 \mathrm{~kJ}\) (b) \(-27.3 \mathrm{~kJ}, 27.3 \mathrm{~kJ}\) (c) \(27.3 \mathrm{~kJ},-27.3 \mathrm{~kJ}\) (d) \(-5.22 \mathrm{~kJ}, 5.22 \mathrm{~kJ}\)
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