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Chapter 17: Problem 2

For a liquid, which would you expect to be larger, $\Delta S_{\text { fusion }}\( or \)\Delta S_{\text { evaporation }} ?$ Why?

Short Answer

Expert verified
For a liquid, we would expect the entropy change during evaporation (\(\Delta S_{\text { evaporation }}\)) to be larger than the entropy change during fusion (\(\Delta S_{\text { fusion }}\)). This is because evaporation involves a much larger increase in disorder compared to fusion, as the substance transitions from a liquid phase to a gaseous phase, which has a significantly higher level of randomness than the liquid phase or solid phases.

Step by step solution

01

1. Understanding Fusion and Evaporation Processes

Fusion is the process where a substance changes from its solid state to its liquid state. Evaporation is the process where a substance changes from its liquid state to its gaseous state. During both these processes, the substance gains energy and undergoes a phase transition.
02

2. Defining Entropy Change

Entropy (S) is a thermodynamic property that measures the degree of disorder or randomness in a system. The entropy change (ΔS) during a process (such as fusion or evaporation) is the difference between the final entropy of the system and the initial entropy of the system.
03

3. Entropy Change during Fusion

During the fusion process, a solid absorbs heat and changes into a liquid. As the substance changes from a more ordered solid phase to a more disordered liquid phase, the entropy of the system increases. The entropy change during fusion (ΔS_fusion) can be calculated using the following formula: \[\Delta S_{\text{fusion}} = \frac{q_{\text{fusion}}}{T_{\text{fusion}}}\] where - \(q_{\text{fusion}}\) is the heat absorbed during fusion - \(T_{\text{fusion}}\) is the temperature at which fusion occurs
04

4. Entropy Change during Evaporation

During the evaporation process, a liquid absorbs heat and changes into a gas. As the substance changes from a more ordered liquid phase to a more disordered gaseous phase, the entropy of the system increases. The entropy change during evaporation (ΔS_evaporation) can be calculated using the following formula: \[\Delta S_{\text{evaporation}} = \frac{q_{\text{evaporation}}}{T_{\text{evaporation}}}\] where - \(q_{\text{evaporation}}\) is the heat absorbed during evaporation - \(T_{\text{evaporation}}\) is the temperature at which evaporation occurs
05

5. Comparing Entropy Changes

When comparing the two processes, evaporation involves a much larger increase in disorder compared to fusion. In the evaporation process, the substance changes from the liquid phase to the gaseous phase, a state with a significantly higher level of randomness compared to the liquid phase. On the other hand, in fusion, the substance merely changes from the solid phase to the liquid phase, which though is more disordered than the solid phase, is still more ordered than the gaseous phase.
06

6. Conclusion

Therefore, the entropy change during evaporation (ΔS_evaporation) is larger than the entropy change during fusion (ΔS_fusion) for a liquid. This is because the degree of disorder or randomness is much higher in the gaseous phase compared to the liquid or solid phases.

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Most popular questions from this chapter

Is \(\Delta S_{\text { surt }}\) favorable or unfavorable for exothermic reactions? Endothermic reactions? Explain.

Predict the sign of \(\Delta S\) for each of the following and explain. a. the evaporation of alcohol b. the freezing of water c. compressing an ideal gas at constant temperature d. dissolving NaCl in water

Monochloroethane \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\right)\) can be produced by the direct reaction of ethane gas $\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)$ with chlorine gas or by the reaction of ethylene gas \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)\) with hydrogen chloride gas. The second reaction gives almost a 100\(\%\) yield of pure $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}$ at a rapid rate without catalysis. The first method requires light as an energy source or the reaction would not occur. Yet \(\Delta G^{\circ}\) for the first reaction is considerably more negative than \(\Delta G^{\circ}\) for the second reaction. Explain how this can be so.

Consider the following energy levels, each capable of holding two particles: $$\begin{array}{l}{E=2 \mathrm{kJ}} \\ {E=1 \mathrm{kJ}} \\ {E=0 \quad \underline{X X}}\end{array}$$ Draw all the possible arrangements of the two identical particles (represented by X) in the three energy levels. What total energy is most likely, that is, occurs the greatest number of times? Assume that the particles are indistinguishable from each other.

Which of the following processes are spontaneous? a. Salt dissolves in \(\mathrm{H}_{2} \mathrm{O}\) . b. A clear solution becomes a uniform color after a few drops of dye are added. c. Iron rusts. d. You clean your bedroom.
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