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Chapter 52: Problem 13

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

Short Answer

Expert verified
The \(\Delta S\) for the given process is positive because the entropy of the system increases due to the increase in temperature.

Step by step solution

01

Preliminary Understanding

First, it's crucial to understand the concept of entropy. It is a measure of the disorder or randomness of the particles in a system. In a particular system, when the temperature, volume, or the number of particles increases, the randomness, and thus the entropy, generally increases, while the reverse leads to a decrease in entropy.
02

Analyzing the given condition

The given process is moving from a state (298 K) to another state (398 K). Here, the number of particles and volume are constant, and only the temperature is changing. The temperature is increasing from 298 K to 398 K.
03

Determine the Change in Entropy

When the temperature of a system increases, the particles of the system move around more freely, and hence there is more disorder in the system. Therefore, the entropy increases. When entropy increases, the change in entropy (\(\Delta S\)) is positive.

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Most popular questions from this chapter

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

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 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?

Is \(\Delta S\) for the following process positive or negative? Why? \(\mathrm{C}_{4} \mathrm{H}_{8}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})\)
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