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Chapter 52: Problem 12

Is \(\Delta S\) for the following process positive or negative? Why? \(\mathrm{C}_{4} \mathrm{H}_{8}(\mathrm{~g} ; 298 \mathrm{~K} ; 1 \mathrm{~atm}) \rightleftharpoons \mathrm{C}_{4} \mathrm{H}_{8}(\mathrm{~g} ; 298 \mathrm{~K} ; 0.5 \mathrm{~atm})\)

Short Answer

Expert verified
\(\Delta S\) for the given process is positive because the system is moving from a state of higher pressure to lower pressure, which increases the randomness or disorder of the gas molecules.

Step by step solution

01

Identify the initial and final states

Identify the initial and final states of the system. Here, the initial state is \(C_4H_8(g)\) at 298 K and 1 atm, and the final state is \(C_4H_8(g)\) at 298 K and 0.5 atm.
02

Compare the pressure conditions

Compare the pressure of the initial and final states. The initial state has higher pressure (1 atm) compared to the final state (0.5 atm).
03

Analyze the entropy change

As the system moves from a state of higher pressure to lower pressure, the disorder or randomness of the gas molecules increases because they have more space to move around. Therefore, the entropy change, \(\Delta S\), is positive.

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Most popular questions from this chapter

Rank the following in order of increasing entropy: \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) ; \mathrm{H}_{2} \mathrm{O}(\boldsymbol{\ell}) ; \mathrm{H}_{2} \mathrm{O}(\mathrm{s}) .\) In general, how are the entropy of the solid, liquid, and gaseous phases of a particular compound related? Explain your reasoning.

Is \(\Delta S\) for the following process positive or negative? Why? \(\mathrm{C}_{4} \mathrm{H}_{8}(\mathrm{~g} ; 298 \mathrm{~K} ; 1 \mathrm{~atm}) \rightleftarrows \mathrm{C}_{4} \mathrm{H}_{8}(\mathrm{~g} ; 398 \mathrm{~K} ; 1 \mathrm{~atm})\)

Is it possible to determine whether a process will occur naturally solely by examining the sign of \(\Delta H\) for the process? Explain.

A ball tends to roll down a hill. a) Which is the lower energy state: the ball at the top of the hill or the ball at the bottom of the hill? b) Is the change in the potential energy for this process, \(V_{\mathrm{f}}-V_{\mathrm{i}}\), positive, negative, or zero? c) Why doesn't the ball roll up the hill?

Write a chemical equation that describes the melting of ice, and indicate whether \(\Delta H\) for the process is positive, negative, or zero. Under what temperature conditions does this process naturally occur?
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