Answer:
[tex]T=533.49\, K[/tex]
For temperatures higher than 533.49 K we will see a spontaneous reaction, and for temperatures lower than that the reaction will not be spontaneous.
Explanation:
When are chemical reactions spontaneous? To find out we need to look at the reaction's change in Gibbs Free energy:
[tex]\Delta G=\Delta H-T\Delta S[/tex]
When this is greater than zero, the reaction isn't spontaneous, when it is less than zero, we have a spontaneous reaction. The reaction must then change from spontaneous to non spontaneous when [tex]\Delta G=0[/tex]. If we insert that into our equation we get:
[tex]0=\Delta H-T\Delta S\\\\T=\frac{\Delta H}{\Delta S}[/tex]
That is the temperature at which the reaction's spontaneity will change, plugging in our values we find:
[tex]T=533.49\, K[/tex]
At that temperature we have [tex]\Delta G=0[/tex].
Now, at a temperature greater than this one, the entropy term in our equation for the Gibbs' free energy of reaction will take over, and make [tex]\Delta G<0[/tex], thus the reaction will be spontaneous.
On the other hand, if we lower the temperature, we will have a smaller entropy term, and we will have: [tex]\Delta G>0[/tex]. That is, the reaction will not be spontaneous. Therefore for temperatures higher than 533.49 K we will see a spontaneous reaction, and for temperatures lower than that the reaction will not be spontaneous.
