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Problem 46

20.46 Given that $\Delta G_{\mathrm{sys}}=-T \Delta S_{\text { univ }},$ explain how the sign of $\Delta G_{\mathrm{sys}}$ correlates with reaction spontaneity.

Answer

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## Discussion

## Video Transcript

We know that this equation represents the relationship between the changing Gibbs free energy of a system, the temperature of that system and the change in entropy of the universe. And we want to use this relationship in order to explain how Delta G correlates with the spontaneity of a reaction. Remember that if a reaction is spontaneous, then that means that Delta s universe is greater than zero and he has a positive sign in. Conversely, if it's non spontaneous, then the opposite is true. That is, Delta s universe is less than zero and has a negative sign. So we want to determine than whether Delta G should have a positive or negative sign to denote whether the reaction is spontaneous or non spontaneous. And we can use this this to help us determine this. This information So for spontaneous process, is you know that Delta's universes positive we know the temperature is is measured in absolute units of Kelvin the lowest. It can possibly be a zero, and it can never be negative. So the temperature is positive when we want apply these two positive values together. But we have a negative sign in front then that comes out to a negative value. And so the temperature again is always positive. That won't change. Delta s universe is positive or spontaneous reactions. So if he reaction is spontaneous, we have this negative of two positive values multiplied together, which is a negative value. So that means that when we have a spontaneous reaction, Delta s universes positive. That means that Delta G of the system is negative. So therefore, for a spontaneous reaction in terms of changing Gibbs free energy this time, if the reaction is spontaneous than the change in Gibbs, free energy of the system is negative, less than zero. And if it's known of its non spontaneous again, the opposite is true. Delta G of the system is greater than zero or positive because again, for non spontaneous Delta s universe would be negative this time and multiplied by the always positive temperature that would come out to a negative value. But we subtract a negative. So we added to make a positive. So Delta G sign of Delta G in relation to spontaneity is the opposite of the relationship between Delta