A process will be spontaneous at all temperatures if:

CONCEPT:

Gibbs Free Energy (ΔG)

• Gibbs Free Energy (ΔG) determines the spontaneity of a process.
• The relationship between ΔG, enthalpy (ΔH), and entropy (ΔS) is given by the equation:

  ΔG = ΔH - TΔS

• A process is spontaneous if ΔG < 0.
• For a process to be spontaneous at all temperatures, ΔG must always be negative regardless of the temperature (T).

EXPLANATION:

• To determine when ΔG is always negative:
  • ΔG = ΔH - TΔS
  • For ΔG to be negative at all temperatures, ΔH must be negative and ΔS must be positive.
  • This is because:
    • If ΔH < 0 and ΔS > 0, then -TΔS is always negative, making ΔG negative.
    • If ΔH > 0 and ΔS < 0, then both terms would be positive, making ΔG positive.
    • If ΔH < 0 and ΔS < 0, the sign of ΔG would depend on the temperature.
    • If ΔH > 0 and ΔS > 0, the sign of ΔG would again depend on the temperature.

Therefore, the correct answer is option 3: ΔH < 0 and ΔS > 0.