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Chapter 17: Problem 33

Predict the sign of \(\Delta S_{\text {surr }}\) for the following processes. a. \(\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g)\) b. \(\mathrm{I}_{2}(g) \longrightarrow \mathrm{I}_{2}(s)\)

Short Answer

Expert verified
For the given processes: a. H2O(l) → H2O(g): ΔSsurroundings is negative, as it's an endothermic process, removing heat from the surroundings. b. I2(g) → I2(s): ΔSsurroundings is positive, as it's an exothermic process, adding heat to the surroundings.

Step by step solution

01

Process a: H2O(l) → H2O(g)

This process depicts the phase change from liquid water to water vapor. During this process, energy is absorbed by water molecules in the form of heat, causing them to gain enough kinetic energy to enter the gas phase. Since energy is absorbed from the surroundings, the heat transfer is endothermic. An endothermic process removes heat from the surroundings, leading to a decrease in the entropy of the surroundings. Therefore, for this process, ΔSsurroundings will be negative.
02

Process b: I2(g) → I2(s)

This process represents the phase change from gaseous iodine to solid iodine. During this process, energy is released by the iodine molecules in the form of heat, causing them to lose kinetic energy and form a solid. Since energy is released into the surroundings, the heat transfer is exothermic. An exothermic process adds heat to the surroundings, resulting in an increase in the entropy of the surroundings. Therefore, for this process, ΔSsurroundings will be positive.

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Most popular questions from this chapter

In the text, the equation $$ \Delta G=\Delta G^{\circ}+R T \ln (Q) $$ was derived for gaseous reactions where the quantities in \(Q\) were expressed in units of pressure. We also can use units of \(\mathrm{mol} / \mathrm{L}\) for the quantities in \(Q\), specifically for aqueous reactions. With this in mind, consider the reaction $$ \mathrm{HF}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{F}^{-}(a q) $$ for which \(K_{\mathrm{a}}=7.2 \times 10^{-4}\) at \(25^{\circ} \mathrm{C} .\) Calculate \(\Delta G\) for the reaction under the following conditions at \(25^{\circ} \mathrm{C}\). a. \([\mathrm{HF}]=\left[\mathrm{H}^{+}\right]=\left[\mathrm{F}^{-}\right]=1.0 \mathrm{M}\) b. \([\mathrm{HF}]=0.98 M,\left[\mathrm{H}^{+}\right]=\left[\mathrm{F}^{-}\right]=2.7 \times 10^{-2} M\) c. \([\mathrm{HF}]=\left[\mathrm{H}^{+}\right]=\left[\mathrm{F}^{-}\right]=1.0 \times 10^{-5} \mathrm{M}\) d. \([\mathrm{HF}]=\left[\mathrm{F}^{-}\right]=0.27 M,\left[\mathrm{H}^{+}\right]=7.2 \times 10^{-4} M\) e. \([\mathrm{HF}]=0.52 M,\left[\mathrm{~F}^{-}\right]=0.67 M,\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-3} M\) Based on the calculated \(\Delta G\) values, in what direction will the reaction shift to reach equilibrium for each of the five sets of conditions?

You have a \(1.00\) - \(L\) sample of hot water \(\left(90.0^{\circ} \mathrm{C}\right)\) sitting open in a \(25.0^{\circ} \mathrm{C}\) room. Eventually the water cools to \(25.0^{\circ} \mathrm{C}\) while the temperature of the room remains unchanged. Calculate \(\Delta S_{\text {surr }}\) for this process. Assume the density of water is \(1.00 \mathrm{~g} / \mathrm{cm}^{3}\) over this temperature range, and the heat capacity of water is constant over this temperature range and equal to \(75.4 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}\).

Using the following data, calculate the value of \(K_{\mathrm{sp}}\) for \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\), one of the least soluble of the common nitrate salts. $$ \begin{array}{lc} \text { Species } & \Delta G_{\mathrm{f}}^{\circ} \\ \mathrm{Ba}^{2+}(a q) & -561 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{NO}_{3}^{-}(a q) & -109 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}(s) & -797 \mathrm{~kJ} / \mathrm{mol} \\ \hline \end{array} $$

For the reaction $$ \mathrm{SF}_{4}(g)+\mathrm{F}_{2}(g) \longrightarrow \mathrm{SF}_{6}(g) $$ the value of \(\Delta G^{\circ}\) is \(-374 \mathrm{~kJ}\). Use this value and data from Appendix 4 to calculate the value of \(\Delta G_{\mathrm{f}}^{\circ}\) for \(\mathrm{SF}_{4}(g)\).

The synthesis of glucose directly from \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) and the synthesis of proteins directly from amino acids are both nonspontaneous processes under standard conditions. Yet it is necessary for these to occur for life to exist. In light of the second law of thermodynamics, how can life exist?
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