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Chapter 17: Problem 38

Predict the sign of \(\Delta S^{\circ}\) for each of the following changes. a. \(\mathrm{Na}(s)+\frac{1}{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NaCl}(s)\) b. \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{~g})\) c. \(\mathrm{NaCl}(s) \longrightarrow \mathrm{Na}^{+}(a q)+\mathrm{Cl}^{-}(a q)\) d. \(\mathrm{NaCl}(s) \longrightarrow \mathrm{NaCl}(l)\)

Short Answer

Expert verified
a. \(\Delta S^{\circ} < 0\) b. \(\Delta S^{\circ} < 0\) c. \(\Delta S^{\circ} > 0\) d. \(\Delta S^{\circ} > 0\)

Step by step solution

01

Reaction a:

In this reaction, a solid sodium \(\mathrm{(Na)}\) reacts with gaseous chlorine \(\frac{1}{2}\mathrm{Cl}_2\) to form solid sodium chloride \(\mathrm{(NaCl)}\). The products have a lower entropy than the reactants, because a gas is involved in the reactants and both products are solids. Therefore, the sign of \(\Delta S^{\circ}\) is negative.
02

Reaction b:

In this reaction, gaseous nitrogen \(\mathrm{(N_{2})}\) reacts with gaseous hydrogen \(\mathrm{(3H_{2})}\) to produce gaseous ammonia \(\mathrm{(2NH_{3})}\). We have 4 moles of gas in the reactants and 2 moles of gas in the products. The decrease in the number of gas moles results in a decrease in entropy. Therefore, the sign of \(\Delta S^{\circ}\) is negative.
03

Reaction c:

In this reaction, solid sodium chloride \(\mathrm{(NaCl)}\) dissociates into aqueous ions \(\mathrm{Na}^{+}\) and \(\mathrm{Cl}^{-}\). The dissociation of the solid into separate ions in solution increases the entropy as there is an increase in the number of particles and their freedom of movement. Therefore, the sign of \(\Delta S^{\circ}\) is positive.
04

Reaction d:

In this reaction, solid sodium chloride \(\mathrm{(NaCl)}\) changes its state to a liquid \(\mathrm{(NaCl(l))}\). A change from a solid to a liquid results in higher entropy, as the particles have more freedom to move and rearrange in the liquid state compared to the solid state. Therefore, the sign of \(\Delta S^{\circ}\) is positive.

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Most popular questions from this chapter

a. Using the free energy profile for a simple one-step reaction, show that at equilibrium \(K=k_{\mathrm{f}} / k_{\mathrm{r}}\), where \(k_{\mathrm{f}}\) and \(k_{\mathrm{r}}\) are the rate constants for the forward and reverse reactions. Hint: Use the relationship \(\Delta G^{\circ}=-R T \ln (K)\) and represent \(k_{\mathrm{f}}\) and \(k_{\mathrm{r}}\) using the Arrhenius equation \(\left(k=A e^{-E_{2} / R T}\right)\). b. Why is the following statement false? "A catalyst can increase the rate of a forward reaction but not the rate of the reverse reaction."

For a liquid, which would you expect to be larger, \(\Delta S_{\text {fusion }}\) or \(\Delta S_{\text {evaporation }}\) ? Why?

Many biochemical reactions that occur in cells require relatively high concentrations of potassium ion \(\left(\mathrm{K}^{+}\right)\). The concentration of \(\mathrm{K}^{+}\) in muscle cells is about \(0.15 M\). The concentration of \(\mathrm{K}^{+}\) in blood plasma is about \(0.0050 M .\) The high internal concentration in cells is maintained by pumping \(\mathrm{K}^{+}\) from the plasma. How much work must be done to transport \(1.0 \mathrm{~mol} \mathrm{~K}^{+}\) from the blood to the inside of a muscle cell at \(37^{\circ} \mathrm{C}\), normal body temperature? When \(1.0 \mathrm{~mol} \mathrm{~K}^{+}\) is transferred from blood to the cells, do any other ions have to be transported? Why or why not?

Cells use the hydrolysis of adenosine triphosphate, abbreviated as ATP, as a source of energy. Symbolically, this reaction can be written as $$\mathrm{ATP}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{ADP}(a q)+\mathrm{H}_{2} \mathrm{PO}_{4}^{-}(a q)$$ where ADP represents adenosine diphosphate. For this reaction, \(\Delta G^{\circ}=-30.5 \mathrm{~kJ} / \mathrm{mol}\) a. Calculate \(K\) at \(25^{\circ} \mathrm{C}\). b. If all the free energy from the metabolism of glucose $$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)$$ goes into forming ATP from ADP, how many ATP molecules can be produced for every molecule of glucose? c. Much of the ATP formed from metabolic processes is used to provide energy for transport of cellular components. What amount (mol) of ATP must be hydrolyzed to provide the energy for the transport of \(1.0 \mathrm{~mol} \mathrm{~K}^{+}\) from the blood to the inside of a muscle cell at \(37^{\circ} \mathrm{C}\) as described in Exercise \(78 ?\)

Calculate \(\Delta G^{\circ}\) for \(\mathrm{H}_{2} \mathrm{O}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}_{2}(g)\) at \(600 . \mathrm{K}\) using the following data: \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(g) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}_{2}(g) \quad K=2.3 \times 10^{6}\) at \(600 . \mathrm{K}\) \(2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}(g) \quad K=1.8 \times 10^{37}\) at 600. \(\mathrm{K}\)
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