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Chapter 18: Problem 57

Predict whether the entropy change is positive or negative for each of these reactions: (a) \(\mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g)\) (b) \(\mathrm{O}(g)+\mathrm{O}(g) \longrightarrow \mathrm{O}_{2}(g)\) (c) \(\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \longrightarrow \mathrm{N}_{2} \mathrm{O}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\) (d) \(2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)\)

Short Answer

Expert verified
The entropy change is positive for reactions (a) and (c), and negative for reactions (b) and (d).

Step by step solution

01

Reaction (a)

In the reaction \(Zn(s)+2 HCl(aq) \rightarrow ZnCl_2(aq)+H_2(g)\), Zn(s) reacts with 2 molecules of HCl(aq) to give ZnCl2(aq) and a molecule of H2(g). The number of molecules doesn't change on both sides of the reaction, but there is a transformation from solid (less randomized) to gas (more randomized). So the entropy change for this reaction is positive.
02

Reaction (b)

In the reaction \(O(g)+O(g) \rightarrow O2(g)\), two atoms of gaseous oxygen combine to form a single molecule of gaseous oxygen. Here, the number of molecules decreases, indicating a decrease in randomness. So, the entropy change for this reaction is negative.
03

Reaction (c)

In the reaction \(NH_4 NO_3(s) \rightarrow N_2O(g)+2 H_2O(g)\), solid ammonium nitrate decomposes into three molecules of gases which increases the randomness. Therefore, the entropy change for this reaction is positive.
04

Reaction (d)

In the reaction \(2H_2O_2(l) \rightarrow 2H_2O(l)+O_2(g)\), two molecules of liquid hydrogen peroxide decompose to form two molecules of liquid water and a molecule of gaseous oxygen. Here, even though the number of molecules increases, the transformation from liquid (a more randomized state) to gas (a less randomized state) leads to a decrease in randomness. Hence, the entropy change for this reaction is negative.

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Most popular questions from this chapter

From the values of \(\Delta H\) and \(\Delta S,\) predict which of the following reactions would be spontaneous at \(25^{\circ} \mathrm{C}\) : Reaction \(\mathrm{A}: \Delta H=10.5 \mathrm{~kJ} / \mathrm{mol}, \Delta S=30 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}\) reaction \(\mathrm{B}: \Delta H=1.8 \mathrm{~kJ} / \mathrm{mol}, \Delta S=-113 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}\). If either of the reactions is nonspontaneous at \(25^{\circ} \mathrm{C}\), at what temperature might it become spontaneous?

Find the temperatures at which reactions with the following \(\Delta H\) and \(\Delta S\) values would become spontaneous: (a) \(\Delta H=-126 \mathrm{~kJ} / \mathrm{mol}, \Delta S=84 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}\) (b) \(\Delta H=-11.7 \mathrm{~kJ} / \mathrm{mol}, \Delta S=-105 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}\).

For the autoionization of water at \(25^{\circ} \mathrm{C}\), $$ \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q) $$ \(K_{\mathrm{w}}\) is \(1.0 \times 10^{-14}\). What is \(\Delta G^{\circ}\) for the process?

Calculate \(\Delta G^{\circ}\) for the following reactions at \(25^{\circ} \mathrm{C}\) : (a) \(2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s)\) (b) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) (c) \(2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)\) See Appendix 2 for thermodynamic data.

(a) Over the years there have been numerous claims about "perpetual motion machines," machines that will produce useful work with no input of energy. Explain why the first law of thermodynamics prohibits the possibility of such a machine existing. (b) Another kind of machine, sometimes called a “perpetual motion of the second kind," operates as follows. Suppose an ocean liner sails by scooping up water from the ocean and then extracting heat from the water, converting the heat to electric power to run the ship, and dumping the water back into the ocean. This process does not violate the first law of thermodynamics, for no energy is created-energy from the ocean is just converted to electrical energy. Show that the second law of thermodynamics prohibits the existence of such a machine.
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