Final answer:
For a reaction with positive enthalpy and negative entropy, Gibbs free energy will always be positive, and the reaction is non-spontaneous at all temperatures.
Step-by-step explanation:
If a reaction has a positive enthalpy (ΔH > 0) and a negative entropy (ΔS < 0), the reaction can never be spontaneous under any temperature conditions. This is because, according to the Gibbs free energy equation (ΔG = ΔH - TΔS), both the enthalpy and entropy terms contribute unfavorably to the value of Gibbs free energy (ΔG). As the temperature (T) can only be positive in the Kelvin scale, the TΔS term will reduce the total Gibbs free energy due to the negative entropy (ΔS), but not enough to overcome the positive enthalpy (ΔH) contribution.
Therefore, in this situation, the value of Gibbs free energy (ΔG) will always be positive, indicating that the reaction is non-spontaneous. The positive ΔG signifies that the driving forces are working against product formation. In order to proceed, such a reaction would require an input of energy from an external source.