For first order reaction time required for 99.9%completion is 100 min find rate constant
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Explanation:
For first order reaction,
t=
k
2.303
log
a−x
a
Given that:-
x=99.9a for t
99.9%
x=0.5a for t
50%
∴
t
50%
t
99.9%
=
k
2.303
log
a−0.5a
a
k
2.303
log
a−0.999a
a
⇒
t
50%
t
99.9%
=
log
0.5
1
log
0.001
1
⇒
t
50%
t
99.9%
=
log2
−log0.001
⇒
t
50%
t
99.9%
=
0.3010
−(−3)
⇒t
99.9%
=10×t
50%
Hence proved.
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