250
Chemical Kinetics
PROBLEMS B
15 The radioactivity of an isotope is studied, and the following counts per minute
(cpm) are obtained at five-minute intervals, starting with t = 0 4500, 3703,
2895, 2304, 1507, 1198, 970, 752, 603, 496, 400, 309, 250, 199 Determine the
half-life of this isotope
16 You buy a 250 mg sample of radioactive Na 3 PO 4 in order to carry out some
experiments with the radioactive
32
P, but unforeseen problems delay the initiation of the experiments for 60 days What percentage of the original sample
remains active for your use if the half-life of
V P is 14 3 days
9
17 Free, isolated neutrons have a half-life of 12 8 mm If you produce 10
4 neu
Irons in a pulsed nuclear target experiment, how long will you have to wait
until only 10 neutrons remain (statistically)
9
18 A piece of wood from the doorway of a Mayan temple is subjected to radioactive carbon dating techniques and found to have 12 7 cpm per gram of carbon
The living trees from which the wood came had 15 3 cpm per gram of carbon
How old must this temple be, knowing that the half-life of
14
C is 5730 yr
9
19 Benzene diazomum chloride (B) decomposes in water according to the equation
C 6 H 5 N 2 C1 -» C 6 H 5 C1 + N 2
It is possible to follow the rate of the reaction by measuring the volume V of
N 2 produced at a given temperature and pressure The following data are
obtained at 50 0°C using 35 0 ml of a 0 0672 M solution of B The N 2 gas is
collected over water in a gas buret where the temperature is 14 0°C The
barometric pressure is 745 torr From these data, determine the order of the
reaction and rate constant
t (mm)
V (ml)
0
00
60
20 2
70
22 6
80
25 4
90
27 8
100
299
120
33 6
130
35 4
170
41 0
190
43 1
21 0
45 0
230
465
20 Acetaldehyde (A) decomposes in the gas phase according to the equation
CH 3 CHO -> CH 4 + CO
The rate of decomposition can be measured by observing the rate of change of
gas pressure at a given volume and temperature, because one gaseous mole is
converted to two gaseous moles The change in total pressure at any given
time interval will be equal to the partial pressure of A used up in that time In
the accompanying set of data obtained at 518 0°C, the total pressure of the gas
mixture is given as a function of time Determine the order of the reaction and
the rate constant Use pressure in torr as a measure of concentration, not
moles/liter
Chemical Kinetics
PROBLEMS B
15 The radioactivity of an isotope is studied, and the following counts per minute
(cpm) are obtained at five-minute intervals, starting with t = 0 4500, 3703,
2895, 2304, 1507, 1198, 970, 752, 603, 496, 400, 309, 250, 199 Determine the
half-life of this isotope
16 You buy a 250 mg sample of radioactive Na 3 PO 4 in order to carry out some
experiments with the radioactive
32
P, but unforeseen problems delay the initiation of the experiments for 60 days What percentage of the original sample
remains active for your use if the half-life of
V P is 14 3 days
9
17 Free, isolated neutrons have a half-life of 12 8 mm If you produce 10
4 neu
Irons in a pulsed nuclear target experiment, how long will you have to wait
until only 10 neutrons remain (statistically)
9
18 A piece of wood from the doorway of a Mayan temple is subjected to radioactive carbon dating techniques and found to have 12 7 cpm per gram of carbon
The living trees from which the wood came had 15 3 cpm per gram of carbon
How old must this temple be, knowing that the half-life of
14
C is 5730 yr
9
19 Benzene diazomum chloride (B) decomposes in water according to the equation
C 6 H 5 N 2 C1 -» C 6 H 5 C1 + N 2
It is possible to follow the rate of the reaction by measuring the volume V of
N 2 produced at a given temperature and pressure The following data are
obtained at 50 0°C using 35 0 ml of a 0 0672 M solution of B The N 2 gas is
collected over water in a gas buret where the temperature is 14 0°C The
barometric pressure is 745 torr From these data, determine the order of the
reaction and rate constant
t (mm)
V (ml)
0
00
60
20 2
70
22 6
80
25 4
90
27 8
100
299
120
33 6
130
35 4
170
41 0
190
43 1
21 0
45 0
230
465
20 Acetaldehyde (A) decomposes in the gas phase according to the equation
CH 3 CHO -> CH 4 + CO
The rate of decomposition can be measured by observing the rate of change of
gas pressure at a given volume and temperature, because one gaseous mole is
converted to two gaseous moles The change in total pressure at any given
time interval will be equal to the partial pressure of A used up in that time In
the accompanying set of data obtained at 518 0°C, the total pressure of the gas
mixture is given as a function of time Determine the order of the reaction and
the rate constant Use pressure in torr as a measure of concentration, not
moles/liter