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Chapter 17: Problem 25

Which of the following processes are spontaneous? a. Salt dissolves in \(\mathrm{H}_{2} \mathrm{O}\). b. A clear solution becomes a uniform color after a few drops of dye are added. c. Iron rusts. d. You clean your bedroom.

Short Answer

Expert verified
Processes a, b, and c are spontaneous. Salt dissolving in \(H_2O\), a clear solution becoming a uniform color after adding dye, and iron rusting are all natural processes that occur without external input. Process d, cleaning your bedroom, is not spontaneous as it requires energy and effort from you.

Step by step solution

01

Process a: Salt dissolves in H2O

This process is spontaneous. When salt is added to water, the ions present in salt interact with water molecules and, as a result, dissolve. This process occurs naturally and does not require any external input.
02

Process b: A clear solution becomes a uniform color after a few drops of dye are added

This process is spontaneous. When dye is added to a clear solution, the dye molecules spread throughout the solution and create a uniform color. This process, known as diffusion, occurs naturally without any external input.
03

Process c: Iron rusts

This process is spontaneous. Rusting of iron is a chemical reaction that occurs when iron comes into contact with oxygen and water (or air moisture). This reaction happens naturally over time and does not require any external input.
04

Process d: You clean your bedroom

This process is not spontaneous. Cleaning your bedroom requires energy and effort from you. It does not occur naturally or without any external input, thus, it is considered a non-spontaneous process.

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Most popular questions from this chapter

Using Appendix 4 and the following data, determine \(S^{\circ}\) for \(\mathrm{Fe}(\mathrm{CO})_{5}(g)\) $$ \begin{aligned} \mathrm{Fe}(s)+5 \mathrm{CO}(g) & \longrightarrow \mathrm{Fe}(\mathrm{CO})_{5}(g) & & \Delta S^{\circ}=? \\ \mathrm{Fe}(\mathrm{CO})_{5}(l) & \longrightarrow \mathrm{Fe}(\mathrm{CO})_{5}(g) & & \Delta S^{\circ}=107 \mathrm{~J} / \mathrm{K} \\ \mathrm{Fe}(s)+5 \mathrm{CO}(g) & \longrightarrow \mathrm{Fe}(\mathrm{CO})_{5}(l) & & \Delta S^{\circ}=-677 \mathrm{~J} / \mathrm{K} \end{aligned} $$

Predict the sign of \(\Delta S^{\circ}\) and then calculate \(\Delta S^{\circ}\) for each of the following reactions. a. \(\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)\) b. \(2 \mathrm{CH}_{3} \mathrm{OH}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)\) c. \(\mathrm{HCl}(g) \longrightarrow \mathrm{H}^{+}(a q)+\mathrm{Cl}^{-}(a q)\)

The Ostwald process for the commercial production of nitric acid involves three steps: $$ \begin{array}{l} 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \underset{825^{\circ} \mathrm{C}}{\longrightarrow} 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) \\\ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) \\ 3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HNO}_{3}(l)+\mathrm{NO}(g) \end{array} $$ a. Calculate \(\Delta H^{\circ}, \Delta S^{\circ}, \Delta G^{\circ}\), and \(K\) (at \(\left.298 \mathrm{~K}\right)\) for each of the three steps in the Ostwald process (see Appendix 4). b. Calculate the equilibrium constant for the first step at \(825^{\circ} \mathrm{C}\), assuming \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not depend on temperature. c. Is there a thermodynamic reason for the high temperature in the first step, assuming standard conditions?

Human DNA contains almost twice as much information as is needed to code for all the substances produced in the body. Likewise, the digital data sent from Voyager II contained one redundant bit out of every two bits of information. The Hubble space telescope transmits three redundant bits for every bit of information. How is entropy related to the transmission of information? What do you think is accomplished by having so many redundant bits of information in both DNA and the space probes?

The following reaction occurs in pure water: $$ \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{OH}^{-}(a q) $$ which is often abbreviated as $$ \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q) $$ For this reaction, \(\Delta G^{\circ}=79.9 \mathrm{~kJ} / \mathrm{mol}\) at \(25^{\circ} \mathrm{C}\). Calculate the value of \(\Delta G\) for this reaction at \(25^{\circ} \mathrm{C}\) when \(\left[\mathrm{OH}^{-}\right]=0.15 \mathrm{M}\) and \(\left[\mathrm{H}^{+}\right]=0.71 M\).
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