Predict the spontaneity of a reaction (and the temperature dependence of the spontaneity) for each possible combination of signs for? H and? S (for the system).

1) ΔH negative, ΔS positive

2) ΔH positive, ΔS negative

3) ΔH negative, ΔS negative

4) ΔH positive, ΔS positive

a) The reaction will be nonspontaneous at low temperature, but spontaneous at high temperature.

b) The reaction will be spontaneous at all temperatures.

c) The reaction will be nonspontaneous at all temperatures.

d) The reaction will be spontaneous at low temperature, but nonspontaneous at high temperature.

Answer and Explanation:

At constant pressure and constant temperature, the Gibbs free energy of a process is given by the following equation:

ΔG = ΔH - T ΔS

The process is spontaneous when ΔG<0. For this, there are four alternatives depending on the signs of ΔH and ΔS and the temperature (T):

1) ΔH negative, ΔS positive ⇒ b) The reaction will be spontaneous at all temperatures.

ΔG = (-H) - T (+S) ⇒ ΔG<0 always

2) ΔH positive, ΔS negative ⇒ c) The reaction will be nonspontaneous at all temperatures.

ΔG = (+H) - T (-S) ⇒ ΔG>0 always

3) ΔH negative, ΔS negative ⇒ d) The reaction will be spontaneous at low temperature, but nonspontaneous at high temperature.

ΔG = (-H) - T (-S) ⇒ ΔG<0 if TΔS is lower than ΔH, because is the positive term

4) ΔH positive, ΔS positive ⇒ a) The reaction will be nonspontaneous at low temperature, but spontaneous at high temperature.

ΔG = (+H) - T (+S) ⇒ ΔG<0 if TΔS higher than ΔH because is the negative term