Considering the form of the Gibb's Free Energy and the condition about it that some process be spontaneous, if some system has the following properties, what would be the result?

A) Always Spontaneous.

B) Spontaneous at lower temperatures.

C) Spontaneous at higher temperatures.

D) Never Spontaneous.

Explanation:

The change in Gibb's free energy for a process, ΔG, is given by

ΔG = ΔH - TΔS

where ΔH is the change in enthalpy for the process

T = absolute temperature in Kelvin of the process

ΔS = change in enthalpy of the process.

And for a process to be spontaneous, its change in Gibb's free energy must be negative.

If it is positive, then the reaction isn't spontaneous.

So, we consider the conditions given one by one.

A) The enthalpy change is negative and the entropy change is positive.

ΔH = -ve, ΔS = +ve

ΔG = ΔH - TΔS = (negative number) - T(positive number) = (negative number - negative number) = negative number (since T isn't negative for these processes.)

Hence, the process with these conditions is always spontaneous.

B) The enthalpy change is negative and the entropy change is negative.

ΔH = negative, ΔS = negative

ΔG = ΔH - TΔS

For this relation, ΔG can only be positive if the numerical value of the ΔH (without the sign) is greater than TΔS.

This will happen mostly at low temperatures as low T, helps to reduce the numerical value of TΔS, thereby making ΔH (without the negative sign) the bigger number and subsequently makethe overall expression negative and the process, spontaneous.

C) The enthalpy change is positive and the entropy change is positive.

ΔH = positive, ΔS = positive.

ΔG = ΔH - TΔS

For this to be spontaneous,

TΔS > ΔH

And the one thing that favours this is high temperatures for the process.

At high temperatures, TΔS gives a much larger number which would drive the overall expression towards the negative sign, thereby making the process spontaneous.

D) The enthalpy change is positive and the entropy change is negative.

ΔH = positive, ΔS = negative.

ΔG = ΔH - TΔS

The signs on these state functions mean that the change in Gibb's free energy will always be positive for this set of conditions (since the temperature can't go as low as being negative).

A process with these conditions, is never spontaneous.

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