1.
2 (12) The following data was obtained for a decomposition of a drug D a.)Find the activation
energy and A b )If the decomposition follows first order kinetics (In [D]-+In [Do]), how long
will it take to decompose by 5% at 5°C? T(in °C) 25 35 45 /T k in days 0025 013 063 244
Ink
Solution
Arrhenius equation-Â Â Â Â Â k = A.e -E/RT
K = rate constant
A = pre-exponential factor
E = activation energy
T = temperature
So  lnk = lnA –(E/R).(1/T)
Hence a linear fitted plot between lnk vs 1/T will give a straight line with a slope of –E/R and
intercept lnA.
T(K)
k(days -1
)
1/T (K -1
)
lnk
298
0.0025
3.36×10 -3

2.
-5.99
308
0.013
3.25×10 -3
-4.34
318
0.063
3.14×10 -3
-2.76
328
0.244
3.05×10 -3
-1.41
Slope = -14728.78
Hence E = -(-14728.78×8.314) J/mol = 122.46 kJ/mol
Intercept = 43.51
Hence A = e 43.51
= 7.87 × 10 18
From graph lnk correspond to 278 K is -9.52. So k at 278 K is 7.34×10 -5
days -1
.
According to question [D]/[D 0 ] = 0.05
So t = 40814 days.
T(K) k(days -1
) 1/T (K -1
) lnk
298 0.0025 3.36×10 -3
-5.99
308 0.013 3.25×10 -3
-4.34
318 0.063 3.14×10 -3
-2.76
328 0.244 3.05×10 -3
-1.41