Entropy The entropy of any system may be found, at least theoretically, using the relationship: S = (Boltzman Constant)*Ln(microstates) Where “microstates” measure the # of possible position and energy states of the particles making up the system. This is a probability. The book shows, for a volume change, ΔS = nRLn(Vf/Vi) & earlier we saw: qrev= nRTLn(Vf/Vi), so ΔS = qrev/T

Entropy ΔS = nRLn(Vf/Vi) qrev= nRTLn(Vf/Vi) ΔS = qrev/T &, at ΔP = 0 & ΔT >< 0 ΔS = nCPLn(Tf/Ti), or, if ΔV = 0 ΔS = nCVLn(Tf/Ti),

Entropy ΔS = qrev/T To melt one mole of a solid at its melting point: Qrev = ΔHfusion and T is the MP in K. The same relationship holds for any change of state. Therefore, ΔS = ΔHstate change T IF ΔE is used only to change S

Depends on magnitude of system vs. surroundings Entropy ΔS Spontaneous? sys sur univ + yes - No +/- -/+ ? Depends on magnitude of system vs. surroundings

Gibbs Free Energy, G ΔG = ΔH – TΔS ΔG = 0 for a system at equilibrium The Free Energy is the amount of energy available to/from a system. ΔG = ΔH – TΔS ΔG = 0 for a system at equilibrium ΔG > 0 for an endothermic process ΔG < 0 for an exothermic process

Gibbs Free Energy, G For the reaction: C(graphite)+ O2  CO2(g) ΔHo = -393.5kJ & ΔSo = 3.05J/K ΔGo = -393.5kJ – 298K*3.05J/K ΔGo = 394.4kJ

Gibbs Free Energy Maximum useful work, w = ΔG. If we combine this with what we know about ΔE, ΔH and ΔG ΔE = ΔH – PΔV, or ΔH = ΔE + PΔV and ΔG = ΔH – TΔS we could show: qP = ΔH if wusefull = 0, or qP = ΔS if wusefull  0

Gibbs Free Energy ΔG if ΔP  0 we can show: ΔG = ΔGo + RTLn(P), or, in general, ΔG = ΔGo + RTLn(Q) where “Q” is the mass expression. Q becomes K & ΔG = 0 at equilibrium, so: ΔGo = RTLn(K) (remember, “ΔG = 0” is the definition of a system at equilibrium.)