1"t Example: Order Rate Law
2N2O5
Question
l:
-+
+ 02
4NO2
.
Is this a First-Order Reaction?
Question 2: What is the rate constant?
Answer: We can't tell without an experiment!
+
Half-life of lst Order Reactions
.
Measure how concentration varies with time:
0.10
Rat" =
0.00
-
dlNzo'l
dt
=
t[N,o,l
hard to tell from [NzOr] vs Time
How to determine fr?
0.04
aA -+ products
Rate=
...if it's fust order
0lr
Definition: Half-life
Half-life : time taken for concentration to
fall to half its original value.
#=urot
\
Therefore^ hrfl l
hr[a]= -frt+kr[A]o
and
r wi)=o'
0.o2
ofr
l0
20
T:@(s)
when
Plot: ln[NrOr] vs Time
First order:
-3.()
ln[NrOr]
d
i
a {.m
Straight line?
-5.0
So,kr[2]:ktyz-ffi
: -h + order
= ln[NrOr]o
.g
,r[#)=0,,,
rAr=ry
l't sloPe:
-k
l(.
5
m
3m ,(!
Tnc(s)
Half Lives: Radioactivity
Half Life or a.Qj,brder
--Reaction
. Example: Decay of Polonium
210Po
2N2O5+4NO2+02
-+
206Pb
+ aHe (alpha radiation)
. Radioactive Decay: First Order process
t
r,r(ztoP o)
:
I3
. Minimum lethal dose
lN,o,L-o
o,$o
. Excreted in -30
o.(xD
ogrfl)
-
8.376 days
- I pg for 80 kg person
50 days
Former KGB agent Alexander Litvinenko
o_lm
] lxgL-o.oco
i:. t
Dose: l0 pg (@ $l million per pg)
'oo-
Before
0.o3n
hiro'L4 o,o:(n
After
E;ot--*r,
50
,t:
0
L50 :tI)
a50
f!:
lv=
3$
,150
100
Tm(sl
4L.--100s
. Compare with
. Half life
:
238U'
238U
4.5 billion years
=
-)
234Th + 4He
much lower toxicity