For a first order homogeneous gaseous reaction `Ato2B+C`, if the total pressure after time t was `P_(t)` and after a long time `(to to oo)` was `P_(oo)` then k in terms of `P_(t),P_(oo)` and t is

Options

A. `k=2.303/tlog((P_(oo))/(P_(oo)-P_(t)))`
B. `k=2.303/tlog((2P_(oo))/(P_(oo)-P_(t)))`
C. `2.303/tlog((2P_(oo))/(3(P_(oo)-P_(yt))))`
D. None of these

Answer

C

Explanation

`Ato2BC+C`
`P_(0)" "0" "0`
`(P_(0)-x)" "2x" "x`
`0" "2P_(0)" "P_(0)`
So `x=((3Pt-P_(alpha))/6),P_(0)=(P_(alpha))/3,K=2.303/txxlog((P_(0))/(P_(0)-x))=2.303/txxlog[(P_(alpha))/3xx6/(3(P_(alpha)-P_(t)))]`
`=2.303/txxlog[(2P_(alpha))/(3(P_(alpha)-P_(t)))]`