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This e-mail originally came about due to a mistake in the solutions<br>
manual for a question (the 11th edition).<br>
<br>
<big><font size="2"><big>The publisher's solution to EOC problem
14.88 in the 11th edition is<br>
wrong. It </big></font></big><big><font size="2"><big><big><font
size="2"><big>erroneously states the half-lifes for both
first and second order<br>
reactions are constant over the course of the reaction.<br>
<br>
</big></font></big>This is EOC exercise 14.102 in the 12th
ed. and 14.96 in the 13th and<br>
14th eds. (although the solutions' manual has the correct
answer for<br>
these ed.).<br>
<br>
</big></font></big><big><font size="2"><big>This question deals
with half-lifes and how they depend on conc.<br>
(do they vary with conc and what happens to consecutive
half-lifes<br>
as the reaction proceeds). Remember, the half-life for a
1st-order<br>
reaction does NOT depend on conc. so consecutive half-lifes
are constant.<br>
Reactions which are other orders (zero, 2nd, etc.) have
half-lifes which<br>
depend on conc. and consecutive half-lifes change as the
reaction<br>
proceeds.<br>
<br>
For a zero-order reaction the half-life is proportional to the
initial conc.<br>
([A]o/2k) and consecutive half-lifes decrease (prove each one
is cut in<br>
half, e.g. 10 s, 5 s, 2.5 s, etc.).<br>
<br>
For a first-order </big></font></big><big><font size="2"><big>reaction
the half-life </big></font></big><big><font size="2"><big> is
constant and doesn't depend<br>
on conc (0.693/k) and consecutive half-lifes are constant (10
s, 10 s,<br>
etc.).<br>
<br>
For a second-order </big></font></big><big><font size="2"><big><big><font
size="2"><big>reaction the half-life is inversely
proportional to the<br>
initial conc. (1/k</big></font></big></big></font></big><big><font
size="2"><big><big><font size="2"><big><big><font size="2"><big><big><font
size="2"><big>[A]o</big></font></big></big></font></big>)
and consecutive half-lifes increase (prove each<br>
one doubles, e.g. 10 s, 20 s, 40 s, etc.).<br>
</big></font></big></big></font></big><br>
<big><font size="2"><big><big><font size="2"><big><big><font
size="2"><big>The only rate law for which the
half-life is constant and doesn't depend<br>
on conc. is first order. The half-life for all
other orders depends on conc.<br>
and thus changes as the reaction proceeds.<br>
</big></font></big> <br>
</big></font></big>If you find other mistakes please let
me know. Make sure you tell me<br>
which edition of the book.<br>
<br>
Dr. Zellmer</big></font></big><br>
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