CK-12-Chemistry Intermediate

20.2. Spontaneous Reactions and Free Energy http://www.ck12.org

TABLE20.2:(continued)

∆H ∆S ∆G

−value (exothermic) −value (ordering) negative at lower temperatures

+ value (endothermic) −value (ordering) never negative

Keep in mind that the temperature in the Gibbs free energy equation is the Kelvin temperature, so it can only have
a positive value. When∆H is negative and∆S is positive, the sign of∆G will always be negative, and the reaction
will be spontaneous at all temperatures. This corresponds to both driving forces being in favor of product formation.
When∆H is positive and∆S is negative, the sign of∆G will always be positive, and the reaction can never be
spontaneous. This corresponds to both driving forces working against product formation.

When one driving force favors the reaction, but the other does not, it is the temperature that determines the sign
of∆G. Consider first an endothermic reaction (positive∆H) that also displays an increase in entropy (positive∆S).
It is the entropy term that favors the reaction. Therefore, as the temperature increases, the T∆S term in the Gibbs
free energy equation will begin to predominate and∆G will become negative. A common example of a process
which falls into this category is the melting of ice (Figure20.4). At a relatively low temperature (below 273 K),
the melting is not spontaneous because the positive∆H term “outweighs” the T∆S term. When the temperature rises
above 273 K, the process becomes spontaneous because the larger T value has tipped the sign of∆G over to being
negative.

FIGURE 20.4

Ice melts spontaneously only when the

temperature is above 0°C. The increase

in entropy is then able to drive the unfa-

vorable endothermic process.

When the reaction is exothermic (negative∆H) but undergoes a decrease in entropy (negative∆S), it is the enthalpy
term which favors the reaction. In this case, a spontaneous reaction is dependent upon the T∆S term being small
relative to the∆H term, so that∆G is negative. The freezing of water is an example of this type of process. It is
spontaneous only at a relatively low temperature. Above 273 K, the larger T∆S value causes the sign of∆G to be
positive, and freezing does not occur.

Sample Problem 20.1: Gibbs Free Energy

Methane gas reacts with water vapor to produce a mixture of carbon monoxide and hydrogen, according to the
balanced equation below.

CH 4 (g) + H 2 O(g)→CO(g) + 3H 2 (g)