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The decompoistion of Cl(2)O(7) at 400 K ...

The decompoistion of `Cl_(2)O_(7)` at `400 K` in gas phase to `Cl_(2)` and `O_(2)` is a first order reaction.
a. After `55 s` at `400 K`, the pressure of `Cl_(2)O_(7)` falls form `0.062` to `0.044 atm`. Calculate `k`.
b. Calculate the pressure of `Cl_(2)O_(7)` after `100 s` of decompoistion.

Text Solution

Verified by Experts

As pressuer `prop` concentration,
`k=(2.303)/(t)"log"_(10)(P_(i)("initial pressure"))/(P_(t)("pressure after time t"))`
`=(2.303)/(55)"log"_(10)(0.062)/(0.044)=6.2xx10^(-3)s^(-1)`
(ii) Again applying the first order kinetic eqution,
`k=(2.303)/(t)"log"_(10)(P_(i)("intial pressure"))/(P_(t)("pressure after time t"))`
`6.2xx10^(-3)=(2.303)/(100)"log"_(10)(0.062)/(P_(t)`
`or(6.2xx10^(-3)xx100)/(2.303)="log"0.062-log_(10)(P_(t))`
`or 0.2692=log_(10)0.062-0.2692`
`or log_(10)(P_(t))=log_(10)0.062-0.2692`
`=(bar(2).7924-0.2692)`
`P_(t) =0.033` atmoshpere
Pressure after 100 sec =0.033 atm
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