Given the following data, calculate the densities of a carbon-14 nucleus and a carbon-14 atom. Particle Mass Electron kg Proton
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Answer:
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:
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 . If we insert that into our equation we get:
That is the temperature at which the reaction's spontaneity will change, plugging in our values we find:
At that temperature we have .
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 , 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: . 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.