A reaction is non-spontaneous at any temperature when

A reaction is non-spontaneous at any temperature when the Gibbs free energy > 0.

Explanation:

There is a state function, that determines if a reaction is sponaneous or non spontaneous:

ΔG = Gibbs free energy

A reaction is non spontaneous when it does require energy to produce that reaction. It will be spontaneous, when the reaction does not require energy to be occured.

The formula is: ΔG = ΔH - T.ΔS

ΔH → Enthalpy → Energy gained or realeased as heat.

ΔH < 0 → Exothermic reaction. Spontaneity is favored

T → Temperature

ΔS → Entropy → Degree of disorder of a system.

When the system has a considered disorder ΔS > 0, disorder increases.

When the system is more ordered, ΔS < 0, disorder decreases.

The reaction will be non spontaneous if, the enthalpy is positive (endothermic reaction) and the ΔS < 0 (disorder decreases). It will not occur if we do not give energy.

ΔG < 0 → Spontaneous reaction

ΔG > 0 → Non spontaneous reaction

ΔG = 0 → System in equilibrium