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Question

At 380oC, the half-life period for the first order decomposition of H2O2 is 360 min. The energy of activation of the reaction is 200kJmol1. The time required for 25% decomposition at 450oC in minutes (nearest integer) is :

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Solution

Lower temeperature T1=380+273=653K

Higher temperature T2=450+273=723K
Ea=200kJmol1

Rate constant at T1=k1=0.693t1/2=0.693360=1.925×103

Rate constant at T2=k2=?

Activation Energy Ea=2.303×R×T1×T2(T2T1)×logk2k1

On solving we get k2=6.81×102min1

When 25% decomposition takes place at 723K

For first order reaction
k2=2.303t×logNoNt

Nt=0.75No

We get t=4.22
t=4 (nearest integer value)

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