At 300 K a gaseous reaction `A rarr B +C ` was found to follow first order kinetics . Starting with pure A the total pressure at the end of 20 minutes was 100 mm of Hg . The total pressure after the completion of the reactionn is 180 mm of Hg . The partial pressure of A ( in mm of Hg ) is :

Options

A. 100
B. 90
C. 180
D. 80

Answer

D

Explanation

`A to B + C`
On decomposition of 1 mole of A , 1 mole of B and 1 mole of C are produced . Thus the total pressure after completion of the reaction corresponds to 2 moles and initial pressure to 1 mole .
Initial pressure of A , (i.e, `p_(0) = (1)/(2) xx 180 = 90` mm Hg .... (1)
`{:(, A to " "B + C) , ("at t = 0" , p_(0) " "0 " "0) , ("after 20 min" , p_(0)-p " "p " " p):}`
After 20 minutes , the total pressure = 100 mm Hg .
`p_(0) - p + p + p = 100`
`p + p = 100`
from equation (1) `90 + p = 100`
`p = (100 - 90) = 10`mm Hg
So partial pressure of `A = p_(0) - p`
`= 90 - 10 = 80` mm Hg.