Question

How does temperature affect spontaneity of a reaction?

Answer 1

We know that in thermodynamics, Gibbs free energy is known as thermodynamic potential. Moreover, this potential is used to calculate reversible work by one thermodynamic system that can perform at constant pressure and temperature. The unit of Gibbs Free Energy is Joules and by using Gibbs Free Energy, we can determine the temperature affecting the spontaneity of a reaction.

Complete step-by-step answer:
Here basic thing to know for determining the effect of spontaneity we should know that, spontaneity depends on the sign of $\Delta G$ ,likewise $\Delta G$ depends on the temperature of the system.
The value of ∆G is given by:

$\Delta G\text{ }=\text{ }\Delta H\text{ }-\text{ }T\Delta S$

Here, $T$ is the temperature of the system or reaction.
$\Delta G$ is Gibbs Free Energy and Spontaneity of reaction.
$\Delta H$ is Enthalpy of a reaction.
$\Delta S$ is Entropy of a reaction.

There are three possible situations:
If $\Delta G\text{ }<\text{ }0~$ , the reaction is spontaneous in forward direction.
If $\Delta G\text{ }=\text{ }0$ , the reaction is at equilibrium.
If $\Delta G\text{ }>\text{ }0$ , the reaction is not spontaneous in forward direction, and it's also spontaneous in reverse direction.

Now, by that we have four possible situation by which we have depending on signs of $\Delta H$ and $\Delta S$ and the tabular form is given by:

$\Delta H$	$\Delta S$	High Temperature	Low Temperature
$+$	$+$	$\Delta G-$ ; Spontaneous	$\Delta G+$ ; Non Spontaneous
$+$	$-$	$\Delta G+$ ; Non Spontaneous	$\Delta G+$ ; Non Spontaneous
$-$	$+$	$\Delta G-$ ; Spontaneous	$\Delta G-$ ; Spontaneous
$-$	$-$-	$\Delta G+$ ; Non Spontaneous	$\Delta G-$ ; Spontaneous

A reaction will continue to stay spontaneous at constant pressure and temperature if following two conditions are:
i) It's exothermic reaction that is $\Delta {{H}_{reaction}}\text{ }<\text{ }0$
ii) Also the entropy of chemical system increase which is $\Delta {{S}_{reaction}}\text{ }>\text{ }0$
The temperature is in kelvin for chemical system will always greater than $0\text{ }\left( T\text{ }>\text{ }0 \right)$

Note: The only executional case here which we should note that is a sign of $\Delta {{G}_{reaction}}$ does not change with changes in temperature if sign of the $\Delta H$ is opposite of sign of $\Delta S:$
i) $\Delta H\text{ }<\text{ }0$ and $\Delta S\text{ }>\text{ }0$ then $\Delta G\text{ }<\text{ }0$ and reaction is a spontaneous at any given temperature.
ii) $\Delta H\text{ }>\text{ }0$ and $\Delta S\text{ }<\text{ }0$ then $\Delta G\text{ }>\text{ }0$ and reaction is a non-spontaneous at any given temperature.