Question

I was looking at the enthalpy change for water-splitting reaction:

ΔHoR=[ΔH0H2(g)+12ΔH0O2(g)]−ΔH0H2O(l)=285.83kJ/mol

According to the book Thermal physicsby Schroeder; at constant T and P; if there are no other forms of work on the system besides compression/expansion, then ΔHoR=Q
. However, when there are other forms of work being done we then have ΔGºR≤Wother
and ΔHoR=Q+Wother
. The value for the Gibbs free energy in this case is ΔGºR=237kJ/mol
. We can relate ΔG
and ΔH
by ΔG=ΔH−TΔS
.

My confusion arises first from reading that the gibbs free energy is the work we need to drive the reaction, say electrical work. However, the enthalpy change shows that the energy required could be done via heat and/or another form of work is higher than that of the Gibbs free energy? My guess so far is that we can take some energy from the environment for free, but what happens when we drive this reaction only via heat, such that ΔH=Q
, would ΔG=0
?

Answer 1

Enthalpy change (ΔH) includes heat and non-expansion work at constant pressure, while Gibbs free energy (ΔG) represents maximum non-expansion work obtainable from a reaction and can differ from ΔH due to entropy contribution.

Step-by-step explanation:

The confusion about enthalpy change (ΔH) and Gibbs free energy (ΔG) can be clarified by noting that ΔH represents the total heat energy change in a reaction at constant pressure and includes both heat exchanged with the environment (ΔQ) and any other forms of work (ΔWother) besides expansion/compression. The enthalpy change when 1 mole of hydrogen and half mole of oxygen reacts to form 1 mole of liquid water is -286 kJ/mol. If the reaction only produces gaseous water, this value changes to -242 kJ/mol since the physical state of the products affects the enthalpy.

On the other hand, Gibbs free energy change (ΔG) represents the maximum amount of non-expansion work that can be obtained from a chemical reaction at constant temperature and pressure. It is calculated by ΔG = ΔH - TΔS, where T is the temperature and ΔS is the change in entropy. So, even if ΔH is provided purely by heat (ΔQ), ΔG can still differ due to the entropy term TΔS.