CHAPTER 19 SECTION 6 FREE ENERGY AND TEMPERATURE

ΔG = ΔH - TΔS = ΔH + (-TΔS) Enthalpy Entropy Notice that the expression for ΔG is a sum of two contributions, an enthalpy term (ΔH) and an entropy term (-TΔS). Because the value of -TΔS depends directly on the absolute temperature T, ΔG will vary with temperature. T is a positive value at all temperatures (Kelvin!). Enthalpy (ΔH) can be positive or negative. Entropy (-TΔS) can also be positive or negative.

When ΔS is positive, which means the final state has greater disorder (a greater number of microstates) than the initial state, the term -TΔS is negative. When ΔS is negative, the term -TΔS is positive. The sign of ΔG, which tells us whether a process is spontaneous, will depend on the signs and magnitudes of ΔH and -TΔS. When both ΔH and -TΔS are negative, ΔG will always be negative and the process will be spontaneous at all temperatures (exothermic).

Likewise, when both ΔH and -TΔS are positive, ΔG will always be positive and the process will be nonspontaneous at all temperatures. When ΔH and -TΔS have opposite signs, the sign of ΔG will depend on the magnitudes of the two terms. Generally, ΔH and ΔS change very little with temperature. However, the value of T directly affects the magnitude of -TΔS which increases with an increase in temperature and becomes more important in determining the sign and magnitude of ΔG.

Let’s consider once more the melting of ice to liquid water at 1 atm pressure: H 2 O (s)  H 2 O (l) ΔH > 0, ΔS > 0 This process is endothermic, which means ΔH is positive. We also know that entropy increases during this process, so ΔS is positive and -TΔS is negative. At temperatures below 0 o C the magnitude of ΔH is greater than that of -TΔS. Hence, the positive enthalpy term dominates, leading to a positive value for ΔG.

The positive value of ΔG means that the melting of ice is not spontaneous at T < 0 o C, rather, the reverse process, the freezing of liquid water into ice, is spontaneous at these temperatures. As the temperature increases, the magnitude of the entropy term -TΔS increases. When T > 0 o C, the magnitude of -TΔS is greater than ΔH. At these temperatures the negative entropy term dominates, which leads to a negative value for ΔG.

The negative value of ΔG tells us that the melting of ice is spontaneous at T > 0 o C. At the normal melting point of water, T = 0 o C, the two phases are at equilibrium. Recall that ΔG = 0 at equilibrium; at T = 0 o C, ΔH and -TΔS, are equal in magnitude and opposite in sign, so they cancel one another and give ΔG = 0. See Table 19.4 for a summary

ΔH ΔS -T ΔS ΔG = ΔH - TΔS Reaction Characteristics _ + _ _ Spontaneous at all temp’s. + _ + + Non-spont. at all temp’s. _ _ + + or - Spont. at low T Non-spont. at high T + + _ + or - Spont. at high T Non-spont. at low T