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Chapter 19: Problem 12

Which of the following processes are spontaneous: (a) the melting of ice cubes at \(-10^{\circ} \mathrm{C}\) and 1 atm pressure; (b) separating a mixture of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) into two separate samples, one that is pure \(\mathrm{N}_{2}\) and one that is pure \(\mathrm{O}_{2} ;\) (c) alignment of iron filings in a magnetic field; (d) the reaction of hydrogen gas with oxygen gas to form water vapor; (e) the dissolution of \(\mathrm{HCl}(g)\) in water to form concentrated hydrochloric acid?

Short Answer

Expert verified
In summary, the following processes are spontaneous: (c) alignment of iron filings in a magnetic field, (d) the reaction of hydrogen gas with oxygen gas to form water vapor, and (e) the dissolution of HCl(g) in water to form concentrated hydrochloric acid. The other processes, (a) the melting of ice cubes at -10°C and 1 atm pressure and (b) separating a mixture of N2 and O2 into pure samples, are not spontaneous.

Step by step solution

01

(a) Melting of ice cubes at -10°C and 1 atm pressure

Ice normally melts at 0°C when the surrounding temperature is above the melting point. In this case, the temperature is below the melting point (-10°C), which means that the process is not favored thermodynamically. Therefore, the melting of ice cubes at -10°C and 1 atm pressure is not a spontaneous process.
02

(b) Separating a mixture of N2 and O2 into pure samples

Separation of a mixture of gases into pure samples requires energy input to overcome intermolecular interactions. Moreover, this process would decrease the entropy of the system, which also requires energy input. As no external energy source is specified in the exercise, we can assume that this separation process is not spontaneous.
03

(c) Alignment of iron filings in a magnetic field

When iron filings are exposed to a magnetic field, they align along the field lines due to their magnetic properties. This alignment process happens when the magnetic energy within the system is minimized. Therefore, we can conclude that the alignment of iron filings in a magnetic field is a spontaneous process.
04

(d) Reaction of hydrogen gas with oxygen gas to form water vapor

The reaction of hydrogen gas (e.g. 2H2) with oxygen gas (O2) to form water vapor (2H2O) is an exothermic reaction, meaning it releases energy in the form of heat. This reaction has a negative Gibbs free energy change, indicating that it is a spontaneous process under standard conditions.
05

(e) Dissolution of HCl(g) in water to form concentrated hydrochloric acid

The dissolution of HCl(g) in water to form concentrated hydrochloric acid is an exothermic process, as energy is released when the HCl molecules interact with water molecules. The process leads to an increase in entropy as the ordered gas molecules are dispersed in the more random liquid state. Given that both entropy and enthalpy favor spontaneity, we can conclude that the dissolution of HCl(g) in water is a spontaneous process.

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Most popular questions from this chapter

The crystalline hydrate \(\mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2} \cdot 4 \mathrm{H}_{2} \mathrm{O}(s)\) loses water when placed in a large, closed, dry vessel: $$ \mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2} \cdot 4 \mathrm{H}_{2} \mathrm{O}(s) \longrightarrow \mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2}(s)+4 \mathrm{H}_{2} \mathrm{O}(g) $$ This process is spontaneous and \(\Delta H\) is positive. Is this process an exception to Bertholet's generalization that all spontaneous changes are exothermic? Explain.

(a) For a process that occurs at constant temperature, express the change in Gibbs free energy in terms of changes in the enthalpy and entropy of the system. (b) For a certain process that occurs at constant \(T\) and \(P,\) the value of \(\Delta G\) is positive. What can you conclude? (c) What is the relationship between \(\Delta G\) for a process and the rate at which it occurs?

The normal boiling point of \(\mathrm{Br}_{2}(l)\) is \(58.8{ }^{\circ} \mathrm{C},\) and its molar enthalpy of vaporization is \(\Delta H_{\text {vap }}=29.6 \mathrm{~kJ} /\) mol. (a) When \(\mathrm{Br}_{2}(l)\) boils at its normal boiling point, does its entropy increase or decrease? (b) Calculate the value of \(\Delta S\) when \(1.00 \mathrm{~mol}\) of \(\mathrm{Br}_{2}(l)\) is vaporized at \(58.8{ }^{\circ} \mathrm{C}\).

(a) Express the second law of thermodynamics as a mathematical equation. (b) In a particular spontaneous process the entropy of the system decreases. What can you conclude about the sign and magnitude of \(\Delta S_{\text {surr }} ?\) (c) During a certain reversible process, the surroundings undergo an entropy change, \(\Delta S_{\text {surr }}=-78 \mathrm{~J} / \mathrm{K}\). What is the entropy change of the system for this process?

Which of the following processes are spontaneous and which are nonspontaneous: (a) the ripening of a banana, (b) dissolution of sugar in a cup of hot coffee, \((\mathrm{c})\) the reaction of nitrogen atoms to form \(\mathrm{N}_{2}\) molecules at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm},\) (d) lightning, (e) formation of \(\mathrm{CH}_{4}\) and \(\mathrm{O}_{2}\) molecules from \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) at room temperature and 1 atm of pressure?
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