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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 process: (a) photodissociation of \(\mathrm{O}_{2}(g),(\mathbf{b})\) formation of 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
(a) The entropy of the system increases during the photodissociation of O₂(g), as the number of particles and possible configurations increase. (b) Entropy decreases during the formation of ozone, as the total number of particles decreases and the system becomes more ordered. (c) Entropy increases in the diffusion of CFCs into the stratosphere, as the particles become more dispersed and the number of possible configurations increases. (d) In the desalination of water by reverse osmosis, entropy decreases as the system becomes more ordered and the number of possible configurations decreases.

Step by step solution

01

Process (a): Photodissociation of O₂(g)

When O₂(g) undergoes photodissociation, it breaks down into two individual oxygen atoms. This process results in an increase in the number of particles, leading to an increase in the number of possible configurations or microstates of the system. As a result, the entropy of the system increases.
02

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

In this process, we have a reaction between an oxygen molecule (O₂) and an oxygen atom (O) to form ozone (O₃). The total number of particles in the system decreases, as three particles combine to form one particle. As the number of particles decreases, the number of possible configurations or microstates also decreases, leading to a decrease in the system's entropy.
03

Process (c): Diffusion of CFCs into the stratosphere

During the diffusion process, CFCs move from a region of higher concentration to a region of lower concentration. As the CFCs spread out, the number of possible configurations or microstates of the system increases because the particles are more dispersed. Therefore, the entropy of the system increases in this process.
04

Process (d): Desalination of water by reverse osmosis

In reverse osmosis, water is forced through a semipermeable membrane, separating the water from dissolved salts. As a result, the system becomes more ordered as the separated water has a lower concentration of dissolved salts. The number of possible configurations or microstates decreases because the particles are not as dispersed as they were before the process. Therefore, the entropy of the system decreases during desalination by reverse osmosis.

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Most popular questions from this chapter

Consider the following reaction between oxides of nitrogen: $$ \mathrm{NO}_{2}(g)+\mathrm{N}_{2} \mathrm{O}(g) \longrightarrow 3 \mathrm{NO}(g) $$ (a) Use data in Appendix \(C\) to predict how \(\Delta G\) for the reaction varies with increasing temperature. (b) Calculate \(\Delta G\) at \(800 \mathrm{~K}\), assuming that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not change with temperature. Under standard conditions is the reaction spontaneous at $800 \mathrm{~K} ?\( (c) Calculate \)\Delta G\( at \)1000 \mathrm{~K}$. Is the reaction spontaneous under standard conditions at this temperature?

Using the data in Appendix \(C\) and given the pressures listed, calculate \(K_{\mathrm{p}}\) and \(\Delta G\) for each of the following reactions: $$ \begin{array}{l} \text { (a) } \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) \\ \quad R_{\mathrm{N}_{2}}=263.4 \mathrm{kPa}, P_{\mathrm{H}_{2}}=597.8 \mathrm{kPa}, P_{\mathrm{NH}_{3}}=101.3 \mathrm{kPa} \\ \text { (b) } 2 \mathrm{~N}_{2} \mathrm{H}_{4}(g)+2 \mathrm{NO}_{2}(g) \longrightarrow 3 \mathrm{~N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g) \end{array} $$ \(P_{\mathrm{N}_{2} \mathrm{H}_{4}}=P_{\mathrm{NO}_{2}}=5.07 \mathrm{kPa}\) $$ \begin{array}{l} \quad R_{\mathrm{N}_{2}}=50.7 \mathrm{kPa}, P_{\mathrm{H}_{2} \mathrm{O}}=30.4 \mathrm{kPa} \\ \text { (c) } \mathrm{N}_{2} \mathrm{H}_{4}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2}(g) \\ P_{\mathrm{N}_{2} \mathrm{H}_{4}}=101.3 \mathrm{kPa}, P_{\mathrm{N}_{2}}=152.0 \mathrm{kPa}, P_{\mathrm{H}_{2}}=253.3 \mathrm{kPa} \end{array} $$

The potassium-ion concentration in blood plasma is about $5.0 \times 10^{-3} \mathrm{M}$, 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 \(\mathrm{K}^{+} ?\)

Does the entropy of the system increase, decrease, or stay the same when (a) the temperature of the system increases, (b) the volume of a gas increases, (c) equal volumes of ethanol and water are mixed to form a solution?

Predict the sign of the entropy change of the system for each of the following reactions: (a) $\mathrm{CO}(g)+\mathrm{H}_{2}(g) \longrightarrow C(s)+\mathrm{H}_{2} \mathrm{O}(g)$ (b) $2 \mathrm{O}_{2}(g)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$ (c) $\mathrm{NH}_{4} \mathrm{Cl}(s) \longrightarrow \mathrm{HCl}(g)+\mathrm{NH}_{3}(g)$ (d) $2 \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}(g)$
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