If we calculate gibbs energy change from the cycle pattern
according to hess's law and then by the relation G = H -TS, will it
give the same value ??
If you intend to apply Hess' Law to Gibbs free energy cycle, note
that all steps in the cycle must all be in terms of Gibbs free
energy (and not some steps inolving enthalpy, some entropy and some
Gibbs free energy).
Provided it's for the *same* reaction under the exact *same*
conditions (ie. temperature, pressure, solvent, etc), then you
should get the same value, whether you calculate the Gibbs free
energy change for a particular reaction by applying Hess' Law (and
given Gibbs free energy change values for several *different* but
related equations in a cycle), or by applying delta G = delta H - T
x delta S (and given the enthalpy change and entropy change values
for the exact *same* reaction as what you're calculating Gibbs free
energy change for).