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Calculate the half life of the first-ord...

Calculate the half life of the first-order reaction:
`C_(2)H_(4)O(g) rarr CH_(4)(g)+CO(g)`
The initial pressure of `C_(2)H_(4)O(g)` is `80 mm` and the total pressure at the end of `20 min` is `120 mm`.

A

`40 min`

B

`120 min`

C

`20 min`

D

`80 min`

Text Solution

Verified by Experts

The correct Answer is:
C
`{:(,C_(2)H_(4)O(g) ,rarr,CH_(4)(g)+,CO(g)),(t=0,P_(0),,0,0),(t=t,P_(0)-x,,x,2x):}`
Total pressure `(P_(t)) = P_(0) - x + x + x = P_(0) + x`
`P_(0) = 80 mm`
`P_(0) + x = 120 mm`
`:. x = 120 - 80 = 40 mm`
`k = (2.203)/(20)log.(P_(0))/(P_(0)-x) = (2.3)/(20)log.(80)/(80-40)`
`k = (2.3 xx 0.3)/(20) rArr t_(1//2) = (0.69)/(k) = (0.69 xx 20)/(0.69) = 20 min`
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