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For a first order homogenous gaseous re...

For a first order homogenous gaseous reaction `A rarr2B +C` if the total pressure after time `t` was `p_(t)` and after long time `(t rarr infty)` was `p_(infty)` then k in terms of `p_(t), p_(infty)` and `t` is

A

`k = (2.303)/(t)log((P_(oo))/(p_(oo) - P_(t)))`

B

`k = (2.303)/(t) log((2P)/(P_(oo) - P_(t)))`

C

`k = (2.303)/(t)log((2P_(oo))/(3(P_(oo) - P_(1))))`

D

`k = (2.303)/(t) log((P_(oo))/(P_(oo) + P_(t)))`

Text Solution

Verified by Experts

`{:(,A,rarr,2B,+,C),(t = 0,p_(i),,0,,0),(t,P_(i-x),,0,,0),(t rarr oo,0,,2P_(i),,P_(i)):}`
`P_(oo) = 3P_(i)` or `P_(i) = (P_(oo))/(3), P_(i) + 2x = P_(t), x = (P_(t) - P_(i))/(2)`
As we know `k = (2.303)/(t) log((P_(i))/(P_(i)-x))` so `k = (2.303)/(t)log((2P_(oo))/(3(P_(oo) - P_(t))))`
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