Question

One might be tempted to say that exothermic processes are always spontaneous since the system is emitting energy (heat) in order to reach a (preferred) lower energy state. However, as we have just investigated, the spontaneous process for polymers is endothermic. This reveals that we must consider entropy changes when determining the nature of spontaneity. The most probable configuration of a system and its surroundings, naturally, is the one that will be observed. The condition for spontaneity can be recast using the concept of the free energy of the system, where a change in free energy results both from changes in the enthalpy (which includes internal potential and kinetic energies) and the entropy (the number of states accessible to the system). Δ G = Δ H − T Δ S.
An unknown chemical reaction undergoes an enthalpy change of Δ H =17 kJ/mol while the entropy increases by Δ S =50 J/(mol * K).

Above what temperature (in Kelvin) does this reaction occur spontaneously?

Answer 1

Answer : This reaction occur spontaneously at temperature above in kelvins is, 340 K

Explanation : Given,

$\Delta H$ = 17 KJ/mole = 17000 J/mole

$\Delta S$ = 50 J/mole.K

Gibbs–Helmholtz equation is :

$\Delta G=\Delta H-T\Delta S$

As per question the reaction is spontaneous that means the value of $\Delta G$ is negative or we can say that the value of $\Delta G$ is less than zero.

$\Delta G$

The above expression will be:

$0>\Delta H-T\Delta S$

$T\Delta S>\Delta H$

$T>\frac{\Delta H}{\Delta S}$

Now put all the given values in this expression, we get :

$T>\frac{17000J/mole}{50J/mole.K}$

$T>340K$

Therefore, this reaction occur spontaneously at temperature above in kelvins is, 340 K