Page 175 - Essentials of physical chemistry

Basic Chemical Kinetics 137

Pm(147) decay ln-plot
3
2

1
0
ln(a(t)) –1 0 5 10 15 20 25 30

–2 y =–0.2642x +2.3026
2
R =1
–3
–4
–5
Years
FIGURE 7.2 A plot of ln (value of remaining Pm sample) vs. time in years.

the amount of the material which can decay. In many cases, the half-life is known more accurately
than here but Pm decays so fast that the small amounts that have been made limit the precision.
If the amounts of (a, t) are known for a number of points k 1 can be determined by plotting

a(t) 2
ln ¼ k 1 t or ln [a(t)] ¼ k 1 t þ ln (a 0 ) where the slope is ( k 1 ). Here, the R value is a
a 0
0:693
so we find
value of 1 indicating a perfect fit. The slope is 0.2642 and we know that k 1 ¼
t 1=2
0:693
¼ 2:623 years, which was the value we were given. Thus, if you
0:3013
from the plot that t 1=2 ¼
know data in the form of {a(t), t} values, you can find the value for k 1 and t 1=2 for a first-order rate
process. For those who are careful about units, we see that when concentration units of [x] are in
d[x]
mol=L, and then ¼ k t [a x] means that k t has units of reciprocal time (Figure 7.2).
dt
MADAME CURIE AND RADIOACTIVITY
While Pm was never found in nature, it has been made in modern nuclear reactors. However, there
were other holes in the periodic chart in the 1800s and Marie Sklodowska was a bright young
woman who came from Warsaw to study in Paris with Henri Becherel at the University of Paris.
There she met and married Pierre Curie who was studying magnetism. However, during isolation of
radioactive uranium from pitchblende ore, Marie was sure she had discovered another element in the
ore, which was much more radioactive than the uranium. Pierre was intrigued and joined Marie in
the laborious separation and isolation of polonium (Z ¼ 84) and then a second element, radium
(Z ¼ 88). Students of physical chemistry should note the combination of chemistry and physics in
this discovery. Radium was relatively easy to isolate but polonium is similar to bismuth in its
properties and there was also bismuth in the pitchblende ore, so a lengthy process of fractional
crystallization was carried out to separate polonium salts from bismuth salts.
The world press was initially captivated by the beautiful young Polish woman who shared the
1903 Nobel Prize in physics with Henri Becherel and Pierre Curie and she distributed the prize
money to acquaintances and students. She and Pierre did not realize the effect that the radioactivity
had on their health and in 1906 a weakened Pierre walked in front of a horse carriage and was killed.
The Curies had two daughters before Pierre died and one daughter, Irene Joliot-Curie, was also
awarded a Nobel Prize in chemistry in 1935 for discovering that aluminum became radioactive
when bombarded with alpha particles. Note that the decay of radium can provide energetic