Thermodynamic Stability: Free Energy and ... - McGill University

Free Energy -6- Chemistry 2232.1. Coupled ReactionsIn some cases, the direct formation of a certain compound by direct reaction is thermodynamicallyforbidden. An example is the formation of titanium tetrachloride 1from common TiO 2 ore; i.e.,TiO 2 (s) + 2Cl 2 (g) → TiCl 4 (l) + O 2 (g).It turns out that ∆G =+152. 3kJ/mole. Nonetheless, we can make the reaction go by coupling itto one which pulls it along. For example, suppose we use the produced oxygen to burn carbon;i.e.,C(s, graphite) + O 2 (g) → CO 2 (g),where here ∆G =−394. 36kJ/mole. The free energy change for the coupled processes is -394.36+152.3 = -242.1 kJ/mole, and thus the coupled reaction can proceed. The burning carbon suppliesthe needed free energy to make the desired reaction work.2.2. General Tr endsFor this discussion, we will consider systems were the reactions take place at a fixed temperatureand pressure; as such, the direction of change is determined by∆G =∆H − T ∆S,where ∆H and ∆S are the enthalpy and entropy change for the process, at the actual temperatureand pressure. As we have said, for constant pressure and temperature processes, ∆G