Chemistry

Problem

A student uses tabulated

\Delta H^{\circ}

and

\Delta S^{\circ}

values to predict that dissolving

\mathrm{KNO_3(s)}

in water at

25\,^{\circ}\!\text{C}

should be spontaneous, yet experimentally the process is nearly at equilibrium. Which of the following most likely accounts for the discrepancy? a) The student did not include the

RT\ln Q

term; the experiment used a nearly saturated solution (large

Q

), so

\Delta G

is close to zero even if

\Delta G^{\circ}

is negative. b) The tabulated entropy values ignore the ordering of water molecules in the hydration shells of

\mathrm{K^+}

and

\mathrm{NO_3^-}

, so

\Delta S^{\circ}_{\text{diss}}

was overestimated. c) The student failed to convert

\Delta S^{\circ}

from

\mathrm{J\,mol^{-1}K^{-1}}

\mathrm{kJ\,mol^{-1}K^{-1}}

, exaggerating the magnitude of

T\Delta S^{\circ}

. d) The student treated the lattice energy as negative instead of positive, making

\Delta H^{\circ}_{\text{diss}}

appear much smaller and the process seem strongly exergonic.

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