Tell whether reactions with the following values of ΔH and ΔS are spontaneous or nonspontaneous and whether they are exothermic or endothermic. (a) ΔH = -128 kJ; ΔS = 35 J/K at 500 K (b) ΔH = +67 kJ; ΔS = -140 J/K at 250 K (c) ΔH = +75 kJ; ΔS = 95 J/K at 800 K

Verified step by step guidance

1. Step 1: Understand the relationship between spontaneity, enthalpy (ΔH), and entropy (ΔS) using the Gibbs free energy equation: ΔG = ΔH - TΔS, where T is the temperature in Kelvin.
2. Step 2: Convert the entropy change (ΔS) from J/K to kJ/K by dividing by 1000, since ΔH is given in kJ.
3. Step 3: Calculate the Gibbs free energy change (ΔG) for each reaction using the equation ΔG = ΔH - TΔS, substituting the given values for ΔH, ΔS, and T.
4. Step 4: Determine spontaneity: If ΔG < 0, the reaction is spontaneous; if ΔG > 0, the reaction is nonspontaneous.
5. Step 5: Determine if the reaction is exothermic or endothermic: If ΔH < 0, the reaction is exothermic; if ΔH > 0, the reaction is endothermic.