Burdge/Overby, Chemistry: Atoms First, 2e Ch14 | Page 14

SEC TION 14.4 ? Entropy Changes in the Universe

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the system and corresponding temperature decrease cause a decrease in the entropy of the
system, the increased temperature of the surrounding air causes an increase in the entropy
of the surroundings.
?Ssys is negative.
?Ssurr is positive.
Thus, it is not just the entropy of the system that determines if a process is spontaneous, the entropy
of the surroundings is also important. There are also examples of spontaneous processes in which
?Ssys and ?Ssurr are both positive. The decomposition of hydrogen peroxide produces water and
oxygen gas, 2H2O2(l)
2H2O(l) + O2(g). Because the reaction results in an increase in the
number of gas molecules, we know that there is an increase in the entropy of the system. However,
this is an exothermic reaction, meaning that it also gives off heat to the surroundings. An increase
in temperature of the surroundings causes an increase in the entropy of the surroundings as well.
(Note that there are no spontaneous processes in which ?Ssys and ?Ssurr are both negative, which
will become clear shortly.)

Calculating ????Ssurr
When an exothermic process takes place, the heat transferred from the system to the surroundings increases the temperature of the molecules in the surroundings. Consequently, there is an
increase in the number of energy levels accessible to the molecules in the surroundings and the
entropy of the surroundings increases. Conversely, in an endothermic process, heat is transferred
from the surroundings to the system, decreasing the entropy of the surroundings. Remember that
for constant-pressure processes, the heat released or absorbed, q, is equal to the enthalpy change
of the system, ?Hsys [9 Section 10.3]. The change in entropy for the surroundings, ?Ssurr, is
directly proportional to ?Hsys:
?Ssurr ? –?Hsys
The minus sign indicates that a negative enthalpy change in the system (an exothermic process)
corresponds to a positive entropy change in the surroundings. For an endothermic process, the
enthalpy change in the system is a positive number and corresponds to a negative entropy change
in the surroundings.
In addition to being directly proportional to ?Hsys, ?Ssurr is inversely proportional to
temperature:
1
?Ssurr ? __?
?? ??
T
Combining the two expressions gives
–?Hsys
??
?
?Ssurr = ______?
??

T

Equation 14.7

The Second Law of Thermodynamics
We have seen that both the system and surroundings can undergo changes in entropy during a
process. The sum of the entropy changes for the system and the surroundings is the entropy change
for the universe overall:

?Suniv = ?Ssys + ?Ssurr

Equation 14.8

The second law of thermodynamics says that for a process to be spontaneous as written (in the forward direction), ?Suniv must be positive. Therefore, the system may undergo a decrease in entropy,
as long as the surroundings undergoes a larger increase in entropy, and vice versa. A process for
which ?Suniv is negative is not spontaneous as written.
In some cases, ?Suniv is neither positive nor negative but is equal to zero. This happens when
the entropy changes of the system and surroundings are equal in magnitude and opposite in sign

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