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Chapter 19: Problem 87

Indicate whether each of the following statements is trueor false. If it is false, correct it. (a) The feasibility of manufacturing \(\mathrm{NH}_{3}\) from \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) depends entirely on the value of $\Delta H\( for the process \)\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) .$ (b) The reaction of \(\mathrm{Na}(s)\) with \(\mathrm{Cl}_{2}(g)\) to form \(\mathrm{NaCl}(s)\) is a spontaneous process. (c) A spontaneous process can in principle be conducted reversibly. (d) Spontaneous processes in general require that work be done to force them to proceed. (e) Spontaneous processes are those that are exothermic and that lead to a higher degree of order in the system.

Short Answer

Expert verified
False. The feasibility of manufacturing NH3 from N2 and H2 depends not only on the value of ΔH, but also on entropy change (ΔS) and temperature. True. The reaction of Na(s) with Cl2(g) to form NaCl(s) is a spontaneous process. False. Spontaneous processes may be irreversible, requiring external input to reverse them in the opposite direction. False. Spontaneous processes usually do not require any work or input from the surroundings in order for them to proceed. Partly true. Spontaneous processes may be exothermic and lead to an increase or decrease in order, but the key factor is the change in Gibbs free energy (ΔG).

Step by step solution

01

Statement a)

The feasibility of manufacturing NH3 from N2 and H2 depends entirely on the value of ΔH for the process N2(g) + 3 H2(g) → 2 NH3(g). This statement is false. While the value of ΔH is indeed an important factor, the feasibility of the reaction also depends on entropy change (ΔS) and temperature. The spontaneity of the reaction is determined by the Gibbs free energy (ΔG), which is given by the formula: ΔG = ΔH - TΔS. A reaction is spontaneous when ΔG is negative.
02

Statement b)

The reaction of Na(s) with Cl2(g) to form NaCl(s) is a spontaneous process. This statement is true. The reaction between sodium (Na) and chlorine (Cl2) to form sodium chloride (NaCl) is a spontaneous process because it is exothermic (releases energy) and leads to an increase in the stability of the products compared to the reactants.
03

Statement c)

A spontaneous process can in principle be conducted reversibly. This statement is false. A spontaneous process is, by definition, a process that occurs naturally and without any external input. In contrast, a reversible process is an idealization that can be reversed without any net change to the system or surroundings, which implies external work or other input. Spontaneous processes may be irreversible; a process can be spontaneous in one direction, but it requires external input (work, heat, or both) to reverse it in the opposite direction.
04

Statement d)

Spontaneous processes in general require that work be done to force them to proceed. This statement is false. Spontaneous processes usually do not require any work or input from the surroundings in order for them to proceed. They will occur naturally, often by releasing energy, due to a decrease in Gibbs free energy (ΔG). This characteristic is what differentiates spontaneous processes from non-spontaneous processes, which do require work or input to proceed.
05

Statement e)

Spontaneous processes are those that are exothermic and that lead to a higher degree of order in the system. This statement is partly true but not universally correct. Many spontaneous processes are indeed exothermic (releasing energy), but they may also lead to an increase or decrease in order (or entropy) within the system. The key factor determining whether a process is spontaneous or not is the change in Gibbs free energy (ΔG). If ΔG is negative, the process is spontaneous, whereas if ΔG is positive, the process is non-spontaneous. In some cases, a process may be endothermic but still spontaneous due to a larger increase in entropy.

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Most popular questions from this chapter

(a) Is the standard free-energy change, \(\Delta G^{\circ}\), always larger than \(\Delta G ?\) (b) For any process that occurs at constant temperature and pressure, what is the significance of \(\Delta G=0 ?\) (c) For a certain process, \(\Delta G\) is large and negative. Does this mean that the process necessarily has a low activation barrier?

Classify each of the following reactions as one of the four possible types summarized in Table 19.3: (i) spontanous at all temperatures; (ii) not spontaneous at any temperature; (iii) spontaneous at low \(T\) but not spontaneous at high \(T ;\) (iv) spontaneous at high T but not spontaneous at low \(T\). $$ \begin{array}{l} \text { (a) } \mathrm{N}_{2}(g)+3 \mathrm{~F}_{2}(g) \longrightarrow 2 \mathrm{NF}_{3}(g) \\ \Delta H^{\circ}=-249 \mathrm{~kJ} ; \Delta S^{\circ}=-278 \mathrm{~J} / \mathrm{K} \\ \text { (b) } \mathrm{N}_{2}(g)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NCl}_{3}(g) \\ \Delta H^{\circ}=460 \mathrm{~kJ} ; \Delta S^{\circ}=-275 \mathrm{~J} / \mathrm{K} \\ \text { (c) } \mathrm{N}_{2} \mathrm{~F}_{4}(g) \longrightarrow 2 \mathrm{NF}_{2}(g) \\ \Delta H^{\circ}=85 \mathrm{~kJ} ; \Delta S^{\circ}=198 \mathrm{~J} / \mathrm{K} \end{array} $$

The oxidation of glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\( in body tissue produces \)\mathrm{CO}_{2}$ and \(\mathrm{H}_{2} \mathrm{O} .\) In contrast, anaerobic decomposition, which occurs during fermentation, produces ethanol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\( and \)\mathrm{CO}_{2}$. (a) Using data given in Appendix \(\mathrm{C}\), compare the equilibrium constants for the following reactions: $$ \begin{array}{r} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \rightleftharpoons 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \\ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s) \rightleftharpoons 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(I)+2 \mathrm{CO}_{2}(g) \end{array} $$ (b) Compare the maximum work that can be obtained from these processes under standard conditions.

(a) What do you expect for the sign of \(\Delta S\) in a chemical reaction in which 3 mol of gaseous reactants are converted to 2 mol of gaseous products? (b) For which of the processes in Exercise 19.11 does the entropy of the system increase?

The \(K_{b}\) for methylamine \(\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)\) at \(25^{\circ} \mathrm{C}\) is given in Appendix \(D\). (a) Write the chemical equation for the equilibrium that corresponds to \(K_{b}\). (b) By using the value of \(K_{b}\), calculate \(\Delta G^{\circ}\) for the equilibrium in part (a). (c) What is the value of \(\Delta G\) at equilibrium? (d) What is the value of \(\Delta G\) when $\left[\mathrm{H}^{+}\right]=6.7 \times 10^{-9} \mathrm{M},\left[\mathrm{CH}_{3} \mathrm{NH}_{3}^{+}\right]=2.4 \times 10^{-3} \mathrm{M}$ and \(\left[\mathrm{CH}_{3} \mathrm{NH}_{2}\right]=0.098 \mathrm{M} ?\)
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