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Chapter 19: Problem 112

At room temperature and normal atmospheric pressure, is the entropy of the universe positive, negative, or zero for the transition of carbon dioxide solid to liquid?

Short Answer

Expert verified
The entropy of the universe for the transition of carbon dioxide from solid to liquid at room temperature and normal atmospheric pressure is positive.

Step by step solution

01

The Nature of the Process

We're dealing with a phase transition process, carbon dioxide going from solid state to liquid state. In this transition, the molecules' freedom of motion increases, leading to higher entropy.
02

The Second Law of Thermodynamics

According to the second law of thermodynamics, any spontaneous change in a closed system will always lead to either an increase or no change in the system's entropy.
03

Correlation with the Universe's Entropy

In this case, the question refers to the universe's entropy. The universe consists of the system (here, the carbon dioxide undergoing phase change) and the surroundings. The second law of thermodynamics applies to the universe too, meaning the total entropy of the universe can never decrease.
04

Entropy Change in the Given Process

Since the solid-to-liquid phase transition increases the system's entropy, and considering the overall entropy of the universe can't decrease, it’s logical to conclude that entropy of the universe must increase in this process.

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Most popular questions from this chapter

The following standard Gibbs energy changes are given for \(25^{\circ} \mathrm{C}\) (1) \(\mathrm{SO}_{2}(\mathrm{g})+3 \mathrm{CO}(\mathrm{g}) \longrightarrow \operatorname{COS}(\mathrm{g})+2 \mathrm{CO}_{2}(\mathrm{g})\) \(\Delta G^{\circ}=-246.4 \mathrm{kJ}\) (2) \(\mathrm{CS}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow \operatorname{COS}(\mathrm{g})+\mathrm{H}_{2} \mathrm{S}(\mathrm{g})\) \(\Delta G^{\circ}=-41.5 \mathrm{kJ}\) (3) \(\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{S}(\mathrm{g}) \longrightarrow \operatorname{COS}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g})\) \(\Delta G^{\circ}=+1.4 \mathrm{kJ}\) (4) \(\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g})\) \(\Delta G^{\circ}=-28.6 \mathrm{kJ}\) Combine the preceding equations, as necessary, to obtain \(\Delta G^{\circ}\) values for the following reactions. (a) \(\operatorname{COS}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow\) \(\begin{aligned} \mathrm{SO}_{2}(\mathrm{g})+\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{g}) & \Delta G^{\circ}=? \end{aligned}\) (b) \(\cos (g)+3 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow\) \(\mathrm{SO}_{2}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \quad \Delta G^{\circ}=?\) \(\left.+\quad \mathrm{H}_{\mathrm{O}} \mathrm{C}(\mathrm{d})=\mathrm{CO}_{-}^{\circ} \mathrm{G}\right)+\mathrm{H}_{-}^{-} \mathrm{S}(\mathrm{q})\) (c) \(\cos (\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{S}(\mathrm{g})\) \(\Delta G^{\circ}=?\) Of reactions (a), (b), and (c), which is spontaneous in the forward direction when reactants and products are present in their standard states?

\(\mathrm{H}_{2}(\mathrm{g})\) can be prepared by passing steam over hot iron: \(3 \mathrm{Fe}(\mathrm{s})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{Fe}_{3} \mathrm{O}_{4}(\mathrm{s})+4 \mathrm{H}_{2}(\mathrm{g})\) (a) Write an expression for the thermodynamic equilibrium constant for this reaction. (b) Explain why the partial pressure of \(\mathrm{H}_{2}(\mathrm{g})\) is independent of the amounts of \(\mathrm{Fe}(\mathrm{s})\) and \(\mathrm{Fe}_{3} \mathrm{O}_{4}(\mathrm{s})\) present. (c) Can we conclude that the production of \(\mathrm{H}_{2}(\mathrm{g})\) from \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) could be accomplished regardless of the proportions of \(\mathrm{Fe}(\mathrm{s})\) and \(\mathrm{Fe}_{3} \mathrm{O}_{4}(\mathrm{s})\) present? Explain.

The standard Gibbs energy change for the reaction \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightleftharpoons$$$ \mathrm{CH}_{3} \mathrm{CO}_{2}^{-}(\mathrm{aq})+\mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})$$is \)27.07 \mathrm{kJmol}^{-1}\( at 298 K. Use this thermodynamic quantity to decide in which direction the reaction is spontaneous when the concentrations of \)\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\mathrm{aq}), \mathrm{CH}_{3} \mathrm{CO}_{2}^{-}(\mathrm{aq}),\( and \)\mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})\( are \)0.10 \mathrm{M}, 1.0 \times 10^{-3} \mathrm{M},\( and \)1.0 \times 10^{-3} \mathrm{M},$ respectively.

Titanium is obtained by the reduction of \(\mathrm{TiCl}_{4}(1)\) which in turn is produced from the mineral rutile \(\left(\mathrm{TiO}_{2}\right)\) (a) With data from Appendix D, determine \(\Delta G^{\circ}\) at 298 K for this reaction. $$\mathrm{TiO}_{2}(\mathrm{s})+2 \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{TiCl}_{4}(1)+\mathrm{O}_{2}(\mathrm{g})$$ (b) Show that the conversion of \(\mathrm{TiO}_{2}(\mathrm{s})\) to \(\mathrm{TiCl}_{4}(1)\) with reactants and products in their standard states, is spontaneous at \(298 \mathrm{K}\) if the reaction in (a) is coupled with the reaction $$2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{g})$$

At \(298 \mathrm{K},\) for the reaction \(2 \mathrm{H}^{+}(\mathrm{aq})+2 \mathrm{Br}^{-}(\mathrm{aq})+\) \(2 \mathrm{NO}_{2}(\mathrm{g}) \longrightarrow \mathrm{Br}_{2}(1)+2 \mathrm{HNO}_{2}(\mathrm{aq}), \Delta H^{\circ}=-61.6 \mathrm{kJ}\) and the standard molar entropies are \(\mathrm{H}^{+}(\mathrm{aq}), 0 \mathrm{JK}^{-1}\) \(\mathrm{Br}^{-}(\mathrm{aq}), 82.4 \mathrm{JK}^{-1} ; \mathrm{NO}_{2}(\mathrm{g}), 240.1 \mathrm{JK}^{-1} ; \mathrm{Br}_{2}(1), 152.2\) \(\mathrm{J} \mathrm{K}^{-1} ; \mathrm{HNO}_{2}(\mathrm{aq}), 135.6 \mathrm{JK}^{-1} .\) Determine (a) \(\Delta G^{\circ}\) at 298 K and (b) whether the reaction proceeds spontaneously in the forward or the reverse direction when reactants and products are in their standard states.
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