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Chapter 19: Problem 2

As shown here, one type of computer keyboard cleaner contains liquefied 1,1 -difluoroethane \(\left(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{~F}_{2}\right),\) which is a gas at atmospheric pressure. When the nozzle is squeezed, the 1,1 -difluoroethane vaporizes out of the nozzle at high pressure, blowing dust out of objects. (a) Based on your experience, is the vaporization a spontaneous process at room temperature? (b) Defining the 1,1 -difluoroethane as the system, do you expect \(q_{\mathrm{sys}}\) for the process to be positive or negative? Explain. (c) Predict whether \(\Delta S\) is positive or negative for this process. (d) Given your answers to (a), (b), and (c), do you think the operation of this product depends more on heat flow or more on entropy change?

Short Answer

Expert verified
The vaporization of 1,1-difluoroethane in a keyboard cleaner is a spontaneous process at room temperature. The heat exchange, \(q_{\text{sys}}\), for this process is positive as the gas absorbs heat from its surroundings. The entropy change, \(\Delta S\), is positive since the gas moves from a more ordered liquid state to a less ordered gaseous state. The operation of this product depends more on the entropy change than heat flow, as vaporization occurs without the need for an external heat source and the increase in disorder drives the process.

Step by step solution

01

(a) Spontaneity

If you have used a computer keyboard cleaner or similar products, you would have observed that the gas from the nozzle comes out without the need for additional energy input (i.e., just by squeezing the nozzle). When the cleaner is at room temperature, it vaporizes, which suggests that the vaporization is a spontaneous process at room temperature.
02

(b) Heat Exchange \(q_{\text{sys}}\)

When 1,1-difluoroethane vaporizes from the nozzle, the gas absorbs heat from its surroundings in order to turn from liquid to gas. As heat is being absorbed by the system (1,1-difluoroethane), its \(q_{\text{sys}}\) for the process should be positive.
03

(c) Entropy Change \(\Delta S\)

Entropy is a measure of the disorder of a system. During the vaporization process, the 1,1-difluoroethane changes from a more ordered liquid state to a less ordered gaseous state. Therefore, the overall entropy of the system increases, making \(\Delta S\) positive.
04

(d) Heat Flow vs. Entropy Change

Considering the spontaneous vaporization at room temperature, we can conclude that the operation of the keyboard cleaner depends mainly on the entropy change rather than heat flow. This is because vaporization occurs without the need for an external heat source, and the increase in entropy (disorder) drives the process. Thus, \(\Delta S\) is the dominant factor in the operation of this product.

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Most popular questions from this chapter

(a) Which of the thermodynamic quantities \(T, E, q, w,\) and \(S\) are state functions? (b) Which depend on the path taken from one state to another? (c) How many reversible paths are there between two states of a system? (d) For a reversible isothermal process, write an expression for \(\Delta E\) in terms of \(q\) and \(w\) and an expression for \(\Delta S\) in terms of \(q\) and \(T\).

For the isothermal expansion of a gas into a vacuum, \(\Delta E=0, q=0\), and \(w=0\). (a) Is this a spontaneous process? (b) Explain why no work is done by the system during this process. (c) In thermodynamics, what is the "driving force" for the expansion of the gas?

Acetylene gas, \(\mathrm{C}_{2} \mathrm{H}_{2}(g),\) is used in welding. (a) Write a balanced equation for the combustion of acetylene gas to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\). (b) How much heat is produced in burning \(1 \mathrm{~mol}\) of \(\mathrm{C}_{2} \mathrm{H}_{2}\) under standard conditions if both reactants and products are brought to \(298 \mathrm{~K}\) ? (c) What is the maximum amount of useful work that can be accomplished under standard conditions by this reaction?

(a) Using data in Appendix \(C\), estimate the temperature at which the free- energy change for the transformation from \(\mathrm{I}_{2}(s)\) to \(\mathrm{I}_{2}(g)\) is zero. What assumptions must you make in arriving at this estimate? (b) Use a reference source, such as Web Elements (www.webelements.com), to find the experimental melting and boiling points of \(\mathrm{I}_{2} .\) (c) Which of the values in part (b) is closer to the value you obtained in part (a)? Can you explain why this is so?

For each of the following pairs, choose the substance with the higher entropy per mole at a given temperature: (a) \(\operatorname{Ar}(l)\) or \(\mathrm{Ar}(g),\) (b) \(\mathrm{He}(g)\) at 3 atm pressure or \(\mathrm{He}(g)\) at 1.5 atm pressure, (c) \(1 \mathrm{~mol}\) of \(\mathrm{Ne}(g)\) in \(15.0 \mathrm{~L}\) or \(1 \mathrm{~mol}\) of \(\mathrm{Ne}(g)\) in \(1.50 \mathrm{~L}\), (d) \(\mathrm{CO}_{2}(g)\) or \(\mathrm{CO}_{2}(s)\).
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