Given that${\mathbf{\Delta G}}_{\mathbf{sys}}\mathbf{}\mathbf{=}\mathbf{-}{\mathbf{T\Delta S}}_{\mathbf{univ}}$, explain how the sign of${\mathbf{\Delta G}}_{\mathbf{sys}}$correlates with reaction spontaneity.

Gibbs free energy, also known as Gibbs function, Gibbs energy, or free enthalpy, is a term used to measure the highest amount of work done in a thermodynamic system when temperature and pressure remain constant.

It is well known that ${\mathrm{\Delta S}}_{\mathrm{univ}}>0$describes the spontaneous reaction or activity. For Gibb's free energy, whereas the reaction/process is considered spontaneous if ${\mathrm{\Delta G}}_{\mathrm{sys}}<0$.

The temperature is expressed in Kelvin using SI units. Since the energy of atoms and molecules is measured by temperature, the temperature scale should always be positive because atoms cannot have negative energy. The absolute zero temperature is known as $\text{0K}$. Thus, the $\text{T}$term (measured in Kelvin) is always positive.

It is given that –

${\mathrm{\Delta G}}_{\mathrm{sys}}=-\mathrm{T}·{\mathrm{\Delta S}}_{\mathrm{univ}}$

Where$\text{T>0}$and ${\mathrm{\Delta S}}_{\mathrm{univ}}>0$.

Therefore, ${\mathrm{\Delta G}}_{\mathrm{sys}}<0$ is always negative, thus corresponding to the reaction spontaneity as supposed.