Question

Question #d46e8

Answer 1

See explanation.

Explanation:

For spontaneous processes, the change on the free energy `color(green)(DeltaG)` has to be negative.

The relationship between free energy `color(green)(DeltaG)` and the enthalpy `color(blue)(DeltaH)` is the following:

`color(green)(DeltaG)=color(blue)(DeltaH)-Tcolor(red)(DeltaS)`

For endothermic processes, `color(blue)(DeltaH)` is positive. Therefore, for the process to be spontaneous:
`color(green)(DeltaG)=color(blue)(DeltaH)-Tcolor(red)(DeltaS)<0`

`=>color(blue)(DeltaH)< Tcolor(red)(DeltaS)`

Since `color(blue)(DeltaH)>0`, for the term `Tcolor(red)(DeltaS)` to be greater than `color(blue)(DeltaH)`, the change on the entropy has to be positive as well (`color(red)(DeltaS)>0`).

`=>T > (color(blue)(DeltaH))/(color(red)(DeltaS))`

Therefore, we can say that endothermic processes can be spontaneous at high temperature.

Note that, endothermic reactions are never spontaneous if the change on entropy is negative.

`"If " color(blue)(DeltaH)>0 and color(red)(DeltaS)<0 =>color(green)(DeltaG)>0 " Always"`

You can follow this figure to predict the spontaneity of the reaction based on the signs of `color(blue)(DeltaH) and color(red)(DeltaS)`

Here is a video that further explains this topic:
Thermodynamics | Spontaneous Process & Entropy.