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Chapter 19: Problem 106

The following processes were all discussed in Chapter 18 "Chemistry of the Environment." Estimate whether the entropy of the system increases or decreases during each ozone from oxygen molecules and oxygen atoms, (c) diffusion of CFCs into the stratosphere, (d) desalination of water by reverse osmosis.

Short Answer

Expert verified
In summary, during the formation of ozone from oxygen molecules and oxygen atoms, the entropy of the system decreases. When CFCs diffuse into the stratosphere, the entropy of the system increases. Lastly, during the desalination of water by reverse osmosis, the entropy of the system decreases.

Step by step solution

01

Process (a): Formation of ozone from oxygen molecules and oxygen atoms

When ozone (O₃) forms from oxygen molecules (O₂) and oxygen atoms (O), the process can be represented as follows: \(O₂ + O \rightarrow O₃ \). In this process, two particles are combining to form a single particle. As a result, the number of available microstates for the system decreases, which means the entropy of the system decreases. Therefore, during the formation of ozone, the entropy of the system decreases.
02

Process (b): Diffusion of CFCs into the stratosphere

During the diffusion of chlorofluorocarbons (CFCs) into the stratosphere, the CFC molecules spread out and disperse within the stratosphere. This increases the number of available microstates and the randomness of the system. Therefore, the entropy of the system increases during the diffusion of CFCs into the stratosphere.
03

Process (c): Desalination of water by reverse osmosis

In the desalination process by reverse osmosis, a high pressure is applied to the salty water, forcing the water molecules to pass through a semipermeable membrane, leaving the salt ions and other impurities behind. In this process, the water molecules become more ordered as they are separated from the salt ions, resulting in a decrease of available microstates for the system. Therefore, the entropy of the system decreases during desalination of water by reverse osmosis. To summarize, the entropy changes for each process are: 1. Formation of ozone: Entropy decreases. 2. Diffusion of CFCs: Entropy increases. 3. Desalination by reverse osmosis: Entropy decreases.

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Most popular questions from this chapter

For each of the following pairs, predict which substance possesses the larger entropy per mole: (a) 1 1 mol of \(\mathrm{O}_{2}(g)\) at \(300^{\circ} \mathrm{C}, 0.01\) atm, or 1 \(\mathrm{mol}\) of \(\mathrm{O}_{3}(g)\) at \(300^{\circ} \mathrm{C}, 0.01\) atm; (b) 1 \(\mathrm{mol}\) of \(\mathrm{H}_{2} \mathrm{O}(g)\) at \(100^{\circ} \mathrm{C}, 1 \mathrm{atm},\) or 1 \(\mathrm{mol}\) of \(\mathrm{H}_{2} \mathrm{O}(l)\) at \(100^{\circ} \mathrm{C}, 1\) atm; \((\mathbf{c}) 0.5 \mathrm{mol}\) of \(\mathrm{N}_{2}(g)\) at \(298 \mathrm{K}, 20 \mathrm{-L}\) volume, or 0.5 \(\mathrm{mol} \mathrm{CH}_{4}(g)\) at \(298 \mathrm{K}, 20-\mathrm{volume} ;(\mathbf{d}) 100 \mathrm{g} \mathrm{Na}_{2} \mathrm{SO}_{4}(s)\) at \(30^{\circ} \mathrm{C}\) or 100 \(\mathrm{g} \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)\) at \(30^{\circ} \mathrm{C} .\)

The value of \(K_{a}\) for nitrous acid \(\left(\mathrm{HNO}_{2}\right)\) at \(25^{\circ} \mathrm{C}\) is given in Appendix D. (a) Write the chemical equation for the equilibrium that corresponds to \(K_{a \cdot}\) (b) By using the value of \(K_{a},\) calculate \(\Delta G^{\circ}\) for the dissociation of nitrous acid in aqueous solution. (c) What is the value of \(\Delta G\) at equilibrium? (d) What is the value of \(\Delta G\) when \(\left[\mathrm{H}^{+}\right]=5.0 \times 10^{-2} M\) \(\left[\mathrm{NO}_{2}^{-}\right]=6.0 \times 10^{-4} M,\) and \(\left[\mathrm{HNO}_{2}\right]=0.20 \mathrm{M} ?\)

Consider the reaction 2 \(\mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g) .(\mathbf{a})\) Using data from Appendix \(\mathrm{C},\) calculate \(\Delta G^{\circ}\) at 298 \(\mathrm{K}\) . (b) Calculate \(\Delta G\) at 298 \(\mathrm{K}\) if the partial pressures of \(\mathrm{NO}_{2}\) and \(\mathrm{N}_{2} \mathrm{O}_{4}\) are 0.40 atm and 1.60 atm, respectively.

The potassium-ion concentration in blood plasma is about \(5.0 \times 10^{-3} M,\) whereas the concentration in muscle-cell fluid is much greater \((0.15 \mathrm{M}) .\) The plasma and intracellular fluid are separated by the cell membrane, which we assume is permeable only to \(\mathrm{K}^{+} .\) (a) What is \(\Delta G\) for the transfer of 1 \(\mathrm{mol}\) of \(\mathrm{K}^{+}\) from blood plasma to the cellular fluid at body temperature \(37^{\circ} \mathrm{C} ?\) (b) What is the minimum amount of work that must be used to transfer this \(\mathrm{K}^{+} ?\)

Predict the sign of the entropy change of the system for each of the following reactions: $$\begin{array}{l}{\text { (a) } \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)} \\ {\text { (b) } \mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)} \\ {\text { (c) } 3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{6}(g)} \\ {\text { (d) } \mathrm{Al}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{Al}(s)+3 \mathrm{H}_{2} \mathrm{O}(g)}\end{array}$$
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