Mistake in solutions' manual for EOCE 19.34(b)

[Zellmer, Robert]

EOCE 19.34(b) asks you how the enropy changes for the processes
in  19.12.  The mistake is for 19.12(e).

19.12(e) is HCl(g) dissolving to give HCl(aq).  The solutions' manual
states the entropy for this process increases due to more motional
freedom (the HCl ionizes and you get ions).  This is incorrect.

It is true the HCl ionizes to give ions.  That process itself would have
a positive entropy change.  However, the HCl(g) dissolving in water
has a negative entropy change.  I've pointed out several times how
the entropy change for a gas dissolving in a liquid is negative. This
is a pretty large negative entropy change.  Also, while ions are
formed (you get 2 ions for every one HCl molecule) and that would
lead to more disorder, those ions attract water molecules which
surround the ions leading to a decrease in disorder of the water
molecules. That's because some of the water molecules are
now more ordered around the ions than they were as "free" water
molecules.  These negative entropy changes are enough to
outweigh the positive entropy change of the HCl ionizing to form
ions.  You can calculate the entropy change using the standard
entropy values in the back of the book (Appendix C, at 25.00 C,
298.15 K).

            HCl (g)  ---->     H+ (aq)   +   Cl- (aq)

S           186.69             0                    56.5

del(S) = [ 1 (0)  +  1 (56.5)] - 1 (186.69) = -130.2 J/K

This reaction is very spontaneous (at 25 C) even with this rather large
negative entropy change because it is very exothermic, del(H) = -74.9 kJ
and del(G) = -35.9 kJ (both calculated using the values in the table
in Appendix C).

Dr. Zellmer
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