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Chapter 1: Problem 17

In which of the following reactions is entropy increasing? (A) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{SO}_{3}(g)\) (B) \(\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)\) (C) \(\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{HCl}(g)\) (D) \(2 \mathrm{NO}_{2}(g) \rightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)\)

Short Answer

Expert verified
The reaction in which entropy is increasing as per above mentioned criteria is (D) \(2 \mathrm{NO}_{2}(g) \rightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)\)

Step by step solution

01

Analyze Reaction (A)

\[2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{SO}_{3}(g)\] \nHere there are 3 mole of gas molecules on the reactants side and 2 mole of gas molecules on the products side. This means the number of gas molecules is decreasing in this reaction, hence entropy is not increasing.
02

Analyze Reaction (B)

\[\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow\mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)\] \nFor this reaction, the number of gas molecules on both the reactants side and the products side are 2. This means there is no change in the number of gas molecules, thus entropy is not increasing.
03

Analyze Reaction (C)

\[\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{HCl}(g)\] \nInspecting this reaction, the number of gas molecules are 2 on the reactants side and 2 on the products side as well. Therefore, no increase in the number of gas molecules in this reaction implies that the entropy is not increasing.
04

Analyze Reaction (D)

\[2 \mathrm{NO}_{2}(g) \rightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)\] \nIn this reaction, there are 2 mole of gas molecules on the reactants side and 3 mole of gas molecules on the products side. This indicates that the number of gas molecules is increasing and consequently, entropy is also increasing.

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Key Concepts

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

Entropy Change
Entropy can be thought of as a measure of disorder or randomness in a system. During a chemical reaction, the entropy can either increase, decrease, or stay the same, depending on the changes that occur in the arrangement of atoms and molecules. When analyzing reactions for entropy change, consider whether the system becomes more or less ordered.

In the context of chemical reactions, higher entropy implies a greater degree of randomness. An increase in entropy usually happens when substances move from a solid or liquid state to a gas state, or when the number of particles increases during a reaction. Hence, entropy change is a crucial factor in determining the spontaneity of a reaction. It can help predict whether a reaction might occur without external intervention.
Number of Gas Molecules
The number of gas molecules plays a significant role in determining entropy changes in reactions. More gas molecules often mean greater disorder because gases have more freedom of movement compared to solids and liquids. Therefore, reactions that increase the number of gas molecules typically result in a higher entropy.
  • Reactions with more gas molecules on the product side than the reactant side generally indicate an increase in entropy.
  • If the number of gas molecules decreases, it usually suggests a decrease in entropy.
In Reaction (D) from our exercise, for example, moving from 2 moles of NO extsubscript{2}(g) to a total of 3 moles (2 moles of NO(g) + 1 mole of O extsubscript{2}(g)) leads to an increase in entropy due to a rise in gas molecules.
Reaction Analysis
Analyzing reactions for entropy involves checking the number of reactants and products, especially focusing on their physical states and molecular complexity. Reactions that generate small, dispersed particles such as gases usually increase disorder and thus entropy.
  • For Reaction (A), a decrease in the total gas molecules from 3 to 2 indicates a decline in entropy.
  • Reaction (B) maintains the same number of gas molecules, and Reaction (C) also exhibits no change in gas molecules, leading to unchanged entropy levels.
Understanding these analyses can help better grasp why certain reactions increase in entropy while others may not. This insight aids in predicting whether reactions will proceed spontaneously based on entropy considerations.
Predicting Entropy Changes
Predicting whether entropy increases or decreases during a reaction involves considering both the physical state changes and the number of molecules. Gases play a pivotal role here due to their high entropy levels compared to liquids and solids.
  • When predicting entropy changes, reactions involving a change from solid or liquid to gas usually signify an increase in entropy.
  • A reaction leading to more gaseous products than reactants likely results in more disorder and higher entropy.
In the original exercise, Reaction (D) demonstrates this principle clearly by increasing the number of gas molecules, therefore resulting in a net increase in entropy. Being able to predict entropy changes not only aids in understanding chemical processes but also aligns with thermodynamics principles, which describe the natural tendency towards disorder.

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Most popular questions from this chapter

Use the following information to answer questions 25-28. A voltaic cell is created using the following half-cells: \(\begin{array}{ll}{\mathrm{Cr}^{3+}+3 e \rightarrow \mathrm{Cr}(s)} & {E^{\circ}=-0.41 \mathrm{V}} \\ {\mathrm{Pb}^{2+}+2 e \rightarrow \mathrm{Pb}(s)} & {E^{\circ}=-0.12 \mathrm{V}}\end{array}\) The concentrations of the solutions in each half-cell are 1.0 M. Which of the following best describes the activity in the salt bridge as the reaction progresses? (A) Electrons flow through the salt bridge from the \(\mathrm{Pb} / \mathrm{Pb}^{2+}\) half-cell to the \(\mathrm{Cr} / \mathrm{Cr}^{3+}\) half-cell. (B) \(\quad \mathrm{Pb}^{2+}\) flows to the \(\mathrm{Cr} / \mathrm{Cr}^{3+}\) flows to the \(\mathrm{Pb} / \mathrm{Pb}^{2+}\) half-cell. (C) \(\mathrm{Na}^{+}\) flows to the \(\mathrm{Cr} / \mathrm{Cr}^{3+}\) half-cell, and \(\mathrm{Cl}^{-}\) flows to the \(\mathrm{Pb} / \mathrm{Pb}^{2+}\) half- cell. (D) \(\quad \mathrm{Na}^{+}\) flows to the \(\mathrm{Pb} / \mathrm{Pb}^{2}\) half- cell, and \(\mathrm{Cl}^{-}\) flows to the \(\mathrm{Cr} / \mathrm{Cr}^{3+}\) half- cell.

A sealed, rigid container contains three gases: 28.0 \(\mathrm{g}\) of nitrogen, 40.0 \(\mathrm{g}\) of argon, and 36.0 g of water vapor. If the total pressure exerted by the gases is \(2.0 \mathrm{atm},\) what is the partial pressure of the nitrogen? (A) 0.33 atm (B) 0.40 atm (C) 0.50 \(\mathrm{atm}\) (D) 2.0 \(\mathrm{atm}\)

Use the following information to answer questions 14-16 The radius of atoms and ions is typically measured in Angstroms \((A),\) which is equivalent to \(1 * 10^{-10} \mathrm{m} .\) Below is a table of information for three different elements. TABLE NOT AVAILABLE The phosphorus ion is larger than a neutral phosphorus atom, yet a zinc ion is smaller than a neutral zinc atom. Which of the following statements best explains why? (A) The zinc atom has more protons than the phosphorus atom. (B) The phosphorus atom is paramagnetic, but the zinc atom is diamagnetic. (C) Phosphorus gains electrons when forming an ion, but zinc loses them. (D) The valence electrons in zinc are further from the nucleus than those in phosphorus.

When calcium chloride \(\left(\mathrm{CaCl}_{2}\right)\) dissolves in water, the temperature of the water increases dramatically. During this reaction, heat transfers from (A) the reactants to the products (B) the reactants to the system (C) the system to the surroundings (D) the products to the surroundings

Which gas exerts the greatest pressure? (A) He (B) Ne (C) NO (D) All gases exert the same amount of pressure.
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