Which of these is spontaneous at low temperatures?*A system with ΔHᵒ>0; ΔSᵒ<0A system with ΔHᵒ<0; ΔSᵒ<0A system with ΔHᵒ<0; ΔSᵒ>0A system with ΔHᵒ>0; ΔSᵒ>0

The spontaneity of a reaction can be determined using the Gibbs Free Energy equation: ΔG = ΔH - TΔS.

A reaction is spontaneous if ΔG < 0.

Let's analyze each option:

1. A system with ΔHᵒ>0; ΔSᵒ<0: In this case, ΔG = ΔH - TΔS will be positive because both terms are positive (ΔH is positive and -TΔS is also positive because ΔS is negative). So, this reaction is not spontaneous at any temperature.

2. A system with ΔHᵒ<0; ΔSᵒ<0: In this case, ΔG = ΔH - TΔS will be negative at low temperatures because ΔH is negative and -TΔS is less negative (because ΔS is negative and T is low). So, this reaction is spontaneous at low temperatures.

3. A system with ΔHᵒ<0; ΔSᵒ>0: In this case, ΔG = ΔH - TΔS will always be negative because both terms are negative (ΔH is negative and -TΔS is also negative because ΔS is positive). So, this reaction is spontaneous at all temperatures.

4. A system with ΔHᵒ>0; ΔSᵒ>0: In this case, ΔG = ΔH - TΔS will be negative at high temperatures because ΔH is positive and -TΔS is negative but becomes more negative as T increases (because ΔS is positive). So, this reaction is spontaneous at high temperatures.

So, the answer is: A system with ΔHᵒ<0; ΔSᵒ<0 is spontaneous at low temperatures.