Questions: Classify each of the following reactions as one of the four possible types summarized in the lecture slides as: (1) spontaneous at all temperatures; (ii) not spontaneous at any temperature; (iii) spontaneous at low T but not spontaneous at high T; (iv) spontaneous a high T but not spontaneous at low T. a. N2(g)+3 F2(g) → 2 NF3(g) ΔHrxn°=-249 kJ ; ΔSrxn°=-278 J / K ΔHrxn°=460 kJ ; ΔSrxn°=-275 J / K ΔHrxn°=85 kJ ; ΔSrxn°=198 J / K

Solution Steps

We need to classify the reaction: \[ \mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{~F}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{NF}_{3}(\mathrm{~g}) \] Given data: \[ \Delta \mathrm{H}_{\mathrm{rxn}}^{\circ}=-249 \mathrm{~kJ} ; \Delta \mathrm{S}_{\mathrm{rxn}}^{\circ}=-278 \mathrm{~J} / \mathrm{K} \]

The Gibbs free energy change (\(\Delta G\)) is given by: \[ \Delta G = \Delta H - T \Delta S \] For spontaneity:

• If \(\Delta G < 0\), the reaction is spontaneous.
• If \(\Delta G > 0\), the reaction is non-spontaneous.

• \(\Delta H_{\mathrm{rxn}}^{\circ} = -249 \mathrm{~kJ}\) (negative, exothermic)
• \(\Delta S_{\mathrm{rxn}}^{\circ} = -278 \mathrm{~J} / \mathrm{K}\) (negative, decrease in entropy)

Since both \(\Delta H\) and \(\Delta S\) are negative:

• At low temperatures, the \(-T \Delta S\) term is small, so \(\Delta G\) is likely negative (spontaneous).
• At high temperatures, the \(-T \Delta S\) term becomes large and positive, making \(\Delta G\) positive (non-spontaneous).

Final Answer