At constant temperature and pressure, if ΔH is positive and ΔS is negative, what is the sign of ΔG?

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Q: At constant temperature and pressure, if ΔH is positive and ΔS is negative, what is the sign of ΔG?

Solution: If ΔH is positive and ΔS is negative, ΔG will always be positive.

Steps: 8

Step 1: Understand the symbols. ΔH represents the change in enthalpy (heat content), ΔS represents the change in entropy (disorder), and ΔG represents the change in Gibbs free energy.
Step 2: Identify the conditions given in the question. We have ΔH > 0 (positive) and ΔS < 0 (negative).
Step 3: Recall the formula for Gibbs free energy: ΔG = ΔH - TΔS, where T is the temperature in Kelvin.
Step 4: Since ΔH is positive, this means that the system is absorbing heat.
Step 5: Since ΔS is negative, this means that the disorder of the system is decreasing.
Step 6: When you multiply T (a positive value) by ΔS (which is negative), the result is negative. So, TΔS < 0.
Step 7: Now, substitute the values into the Gibbs free energy formula: ΔG = ΔH - TΔS. Since ΔH is positive and TΔS is negative, ΔG will be positive - positive minus a negative is positive.
Step 8: Therefore, if ΔH is positive and ΔS is negative, ΔG will always be positive.