Geology Reference
In-Depth Information
Exercises
increased by 10°C. Calculate the activation energy
for a reaction that exactly conforms to this relation-
ship. (Gas constant
R
= 8.3143 J K
−
1
mol
−
1
.)
3.3
Use the viscosity measurements given below to
verify that the Arrhenius equation is applicable to
the flow of a silicate melt, and determine the acti-
vation energy. (
Hint
: viscosity is the
resistance
to
flow, to which flow rate is inversely proportional.)
3.1
The table below gives the Geiger counter count-rate
at various times during an experiment on radioac-
tive iodine-131 (
131
I). Treating the decay of
131
I as a
chemical reaction in which the count rate may be
taken as being a measure of the concentration of
131
I,
confirm that the reaction is first-order and determ-
ine the decay constant. From the linear graph you
have drawn, calculate the half-life of
131
I (Box 3.2).
Temperature
(°C)
Viscosity of rhyolite
melt (N s m
−
2
)
1325
2042
Time (hours)
Counts (sec
−1
)
1345
1585
0
18,032
1374
1097
25
16,410
1405
741
50
15,061
100
12,590
(Gas constant as given in Exercise 3.2.)
3.4
Calculate the half-life of
87
Rb (λ
87
200
8789
Rb
=×. year
−
1
).
What percentage of the
87
Rb incorporated in the
Earth 4.6 × 10
9
years ago has now decayed to
87
Sr?
3.5
Demonstrate that the units of diffusion coefficient
D
i
in Equation 3.11 are m
2
s
−
1
, when concentration
c
i
is expressed in mol m
−3
and the net flux
f
i
is expressed
in mol m
−
2
s
−
1
.
14210
11
300
6144
400
4281
500
3002
3.2
There is a rule of thumb that says that the rate
of many room-temperature chemical reactions
approximately doubles when the temperature is
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