KEY2CHEM

Predicting if a Process is Thermodynamically Favored

A process is thermodynamically favored (favors formation of the products; $$K > 1$$) if $$\Delta G ^{\circ} < 0$$. Since $$\Delta G^\circ = \Delta H^\circ -T\Delta S^\circ$$$$\Delta G^\circ < 0$$ if $$\Delta H^\circ < 0$$ and $$\Delta S^\circ > 0$$. Conversely, a process is not thermodynamically favored if $$\Delta G^\circ > 0$$, which occurs if $$\Delta H ^\circ> 0$$ and $$\Delta S^\circ < 0$$. If the values of $$\Delta H^\circ$$ and $$\Delta S^\circ$$ are either both $$> 0$$ or $$<0$$, then the magnitude of temperature (in Kelvin) determines whether the process is thermodynamically favored, since the magnitude of $$T$$ will determine whether $$\Delta G ^\circ> 0$$ or $$\Delta G^\circ < 0$$.

Example 1.

Liquid octane is combusted to form gaseous products, heat, and light. Which statement about this process is true?

A. It is thermodynamically favored.

B. It is not thermodynamically favored.

C. It is thermodynamically favored at low temperatures only.

Solution

A. It is thermodynamically favored.

The process releases heat ($$\Delta H ^\circ< 0$$) and generates gaseous products from a liquid starting material ($$\Delta S^\circ > 0$$) so the process is thermodynamically favored.

Example 2.

What is $$\Delta G^\circ$$ if the $$\Delta H^\circ = 214 \text{ kJ}$$and $$\Delta S^\circ = 150 \text{ J/K}$$ at$$298 \text{ K}$$?

A. $$64 \text{ kJ}$$

B. $$169 \text{ kJ}$$

C. $$-4.45 \times 10^ 4 \text{ kJ}$$

Solution

B. $$169 \text{ kJ}$$

$$\Delta G^\circ = \Delta H^\circ – T\Delta S^\circ = 214 \text{ kJ} – (298 \text { K})(0.150 \text{ kJ/K}) = 169 \text{ kJ}$$

Example 3.

A process is spontaneous at low temperatures but nonspontaneous at high temperatures. What is true about the process?

A. $$\Delta H^\circ > 0, \Delta S ^\circ> 0$$

B. $$\Delta H^\circ > 0, \Delta S^\circ < 0$$

C.$$\Delta H^\circ < 0, \Delta S ^\circ< 0$$

Solution

C. $$\Delta H^\circ < 0, \Delta S^\circ < 0$$

When the $$T$$ value is small in magnitude, the $$T\Delta S^\circ$$ term is a smaller magnitude than the $$\Delta H^\circ$$ term, and the process with be thermodynamically favored with $$\Delta G^\circ < 0$$.