Chapter 19: Problem 91
Ammonium nitrate dissolves spontaneously and endothermally in water at room temperature. What can you deduce about the sign of \(\Delta S\) for this solution process?
Chapter 19: Problem 91
Ammonium nitrate dissolves spontaneously and endothermally in water at room temperature. What can you deduce about the sign of \(\Delta S\) for this solution process?
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Get started for freeFor each of the following pairs, predict which substance possesses the larger entropy per mole: (a) 1 1 mol of \(\mathrm{O}_{2}(g)\) at \(300^{\circ} \mathrm{C}, 0.01\) atm, or 1 \(\mathrm{mol}\) of \(\mathrm{O}_{3}(g)\) at \(300^{\circ} \mathrm{C}, 0.01\) atm; (b) 1 \(\mathrm{mol}\) of \(\mathrm{H}_{2} \mathrm{O}(g)\) at \(100^{\circ} \mathrm{C}, 1 \mathrm{atm},\) or 1 \(\mathrm{mol}\) of \(\mathrm{H}_{2} \mathrm{O}(l)\) at \(100^{\circ} \mathrm{C}, 1\) atm; \((\mathbf{c}) 0.5 \mathrm{mol}\) of \(\mathrm{N}_{2}(g)\) at \(298 \mathrm{K}, 20 \mathrm{-L}\) volume, or 0.5 \(\mathrm{mol} \mathrm{CH}_{4}(g)\) at \(298 \mathrm{K}, 20-\mathrm{volume} ;(\mathbf{d}) 100 \mathrm{g} \mathrm{Na}_{2} \mathrm{SO}_{4}(s)\) at \(30^{\circ} \mathrm{C}\) or 100 \(\mathrm{g} \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)\) at \(30^{\circ} \mathrm{C} .\)
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 \(T .\) $$ \begin{array}{c}{\text { (a) } \mathrm{N}_{2}(g)+3 \mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{NF}_{3}(g)} \\ {\Delta H^{\circ}=-249 \mathrm{kJ} ; \Delta S^{\circ}=-278 \mathrm{J} / \mathrm{K}}\\\\{\text { (b) } \mathrm{N}_{2}(g)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NCl}_{3}(g)} \\\ {\Delta H^{\circ}=460 \mathrm{kJ} ; \Delta S^{\circ}=-275 \mathrm{J} / \mathrm{K}} \\ {\text { (c) } \mathrm{N}_{2} \mathrm{F}_{4}(g) \longrightarrow 2 \mathrm{NF}_{2}(g)} \\ {\Delta H^{\circ}=85 \mathrm{kJ} ; \Delta S^{\circ}=198 \mathrm{J} / \mathrm{K}}\end{array} $$
Using data from Appendix \(\mathrm{C}\) , calculate \(\Delta G^{\circ}\) for the following reactions. Indicate whether each reaction is spontaneous at 298 \(\mathrm{K}\) under standard conditions. (a) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) (b) \(\mathrm{NO}_{2}(g)+\mathrm{N}_{2} \mathrm{O}(g) \longrightarrow 3 \mathrm{NO}(g)\) (c) \(6 \mathrm{Cl}_{2}(g)+2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \rightarrow 4 \mathrm{FeCl}_{3}(s)+3 \mathrm{O}_{2}(g)\) (d) \(\mathrm{SO}_{2}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{S}(s)+2 \mathrm{H}_{2} \mathrm{O}(g)\)
(a) What sign for \(\Delta S\) do you expect when the volume of 0.200 mol of an ideal gas at \(27^{\circ} \mathrm{Cis}\) increased isothermally from an initial volume of 10.0 \(\mathrm{L} ?(\mathbf{b})\) If the final volume is 18.5 \(\mathrm{L}\) , calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change?
Which of the following processes are spontaneous: (a) the melting of ice cubes at \(-10^{\circ} \mathrm{C}\) and 1 atm pressure; (b) separating a mixture of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) into two separate samples, one that is pure \(\mathrm{N}_{2}\) and one that is pure \(\mathrm{O}_{2}\);(c) alignment of iron filings in a magnetic field; (d) the reaction of hydrogen gas with oxygen gas to form water vapor at room temperature; (e) the dissolution of HCl(g) in water to form concentrated hydrochloric acid?
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