A 1st order reaction is 50% complete in 40min at 300K and in 20min at 320K. Calculate the activation energy.
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Answer:
Explanation:
When a first order reaction is 50% completed, the time is equal to half life period.
A first order reaction is 50% completed in 40 minutes at 300K and in 20 minutes at 320 K.
t
1/2
=40 minutes
t
1/2
′
=20 minutes
The Arrhenius equation and temperature variation is given by the expression.
log(
k
k
′
)=
2.303R
E
a
[
TT
′
T
′
−T
]
Also, t
1/2
=
k
0.693
or t
1/2
∝
k
1
Hence, log(
t
1/2
′
t
1/2
)=
2.303R
E
a
[
TT
′
T
′
−T
]
log(
20
40
)=
2.303×8.314J/mol/K
E
a
[
300K×320K
320K−300K
]
0.3010=
19.147J/mol/K
E
a
[0.0002083/K]
E
a
=27664J/mol
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