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2X(g) rarr 3Y(g)+2Z(g) {:("Time (in mi...

`2X(g) rarr 3Y(g)+2Z(g)`
`{:("Time (in min)",0,100,200,):}`
`|{:("Partial pressure of X (mm Hg)",800,400,200,),("Assuming ideal gas condition, calculate",,,,):}|`
(a) Order of reaction
(b) Rate constant
( c) Time taken for `75%` completion of reaction
(d) Total pressure when `p_(x) = 700 mm`

Text Solution

Verified by Experts

(i) As pressure of X is changing with time, it cannot be a zero order reaction. Let us now check it for 1st order.
`{:("At",,,t=100" min,",,,k=(2.303)/(100)log""(P_(0))/(P_(t))=(2.303)/(100)log""(800)/(400)=6.932xx10^(-3)"min"^(-1)),("At",,,t=200" min,",,,k=(2.303)/(200)log""(800)/(200)=(2.303)/(800)log4=6.932xx10^(-3)"min"^(-1)):}`
As k comes out to be constant, hence it is a reaction of 1st order.
(ii) `t_(75%)=(2.303)/(k)log""(100)/(100-75)=(2.303)/(6.932xx10^(-3)"min"^(-1))log4=200" min".`
(iii) `2X(g) to 3" Y"(g)+2" Z"(g)`
`{:("Initial Pressure",,,800" mm",,,0,,,0),("Pressure after time t",,,800-2" p",,,3" p",,,2" p"):}`
When pressure of X is 700 mm, `800-2" p"=700" or "p=50" mm"`
Total pressure `=(800-2" p")+3" p"+2" p"=800+3" p"=800+3xx50=950" mm"`
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