Page 173 - Essentials of physical chemistry

Basic Chemical Kinetics 135

a

time t 1=2 : ¼ a e k 1 t 1=2 so, canceling ‘‘a’’ we find (1=2) ¼ e k 1 t 1=2 and when we take the natural
2
log of the reciprocal of the whole equation we find that ln (2) ¼ k 1 t 1=2 ¼ 0:69314718. Most of the
0:693 0:693
. The
time this is rounded to (k 1 )(t 1=2 ) ¼ 0:693, so we also have k 1 ¼ as well as t 1=2 ¼
t 1=2 k 1
rounding to only 0.693 is left over from the days when that was sufficiently accurate for use with a
slide rule but you can use the more accurate value if you wish.

PROMETHIUM: AN INTRODUCTION TO NUCLEAR CHEMISTRY
We consider that one of the ‘‘essential’’ parts of physical chemistry is some awareness of nuclear
chemistry. While the periodic chart poses as a list of stable elements, there are hints of irregularity
by the absence of elements no. 43 (technetium, Tc) and no. 61 (promethium, Pm). Modern students
are also aware of unstable elements beyond no. 92 (uranium, U). Since nuclear reactions seem to
follow a sequence of first-order reactions, we take some time to mention a few of the mechanisms
that are occurring in the first-order processes.
Pm was long searched for, but not discovered until nuclear chemistry became a laboratory
science and small samples can now be prepared. Pm is elusive for several reasons. Although it
has some 44 known isotopes, not one of them is stable. However, it illustrates several aspects of
nuclear decay, even though all the processes are first order. The isotopes range from 128 Pm to 163 Pm
61
61
and the three most stable isotopes are 145 Pm (t 1=2 ¼ 17.7 years), 146 Pm (t 1=2 ¼ 5.53 years), and 147 Pm
61
61
61
(t 1=2 ¼ 2.623 years; data from Ref. [1]). We have ventured into this topic because of the simplicity of
first-order kinetics, which is so typical of the several forms of nuclear decay and because historically
the research of the Curies (Marie, Pierre, and their daughter, Irene) goes across the modern
boundaries of chemistry and physics and deserves mention in a ‘‘physical chemistry’’ text. How-
ever, even basic nuclear physics is beyond the scope of this text except to refer to Ref. [2], which
gives an overview of the main principles. The isotopes of Pm, all have sufficiently short half-lives so
that any that was present in primordial Earth has long since decayed but small amounts are present
due to decay of any one of several isotopes of Nd, which undergo beta decay (a neutron decays to a
proton and ejects an electron, thus increasing the atomic number by 1).
147 147 Pm þ b ; t 1=2 ¼ 10:98 days:

60 Nd ! 61
The main point here is that the case of Pm shows that while nuclear decay is usually thought of as
decreasing to a lower atomic number, some reactions (beta decay, a form of electron emission)
actually increase the atomic number of the elemental species. Note that in either case, we can use
first-order kinetics for a given single step.
In the 1800s, there were several other gaps in the known periodic chart such as for promethium
and technetium but while Pm is radioactive it is so scarce that it was not detected until 1944 at the
Oak Ridge National Laboratory by Jacob A. Marinsky, Lawrence E. Glendenin, and Charles D.
Coryell. Other radioactive elements are more plentiful in the crust of the Earth and Marie Curie was
interested in isolating such elements perhaps more because of their radioactivity than to describe a
new element. Thus, Madame Curie’s work went far beyond isolating two new elements. This
research opened up a new realization that a number of heavier elements have radioactive isotopes.
Marie Curie and her husband Pierre carried out a (laborious) chemical separation of two new
elements (polonium and radium) that are radioactive and you cannot separate the chemical signifi-
cance from the physical significance. Since the work of the Curies, we now know that there are
many possible isotopes, particularly of the heavier elements. The purpose of this short section is to
make undergraduates aware that natural nuclear chemistry is going on all the time. Nuclear reactions
are probably the source of heat within the core of the Earth and stars form heavier elements by
fusion reactions starting with hydrogen.