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A2 litre vessel is filled with air at 50...

A2 litre vessel is filled with air at `50^(@)C` and pressure of 3 atm. The temperature is now raised to `200^(@)C` A valve is now opened so that the pressure inside drops to one atm What fraction of the total number of moles, inside escaped on openig the valve ? Assume no change in the volume of the container .

A

`7.7`

B

`9.9`

C

`8.9`

D

`0.77`

Text Solution

Verified by Experts

The correct Answer is:
D
Given that, `V = 2 L, T_(1)=50+273=323 K, P_(1)=3` atm
On heating `V=2L, T_(2)=200+273=473, P_(2)= ?`
Using P-T law, `(P_(1))/(T_(1))=(P_(2))/(T_(2))`
`P_(2)=(3xx473)/(323)=4.39` atm
and `n=(PV)/(RT)=(3xx2)/(0.0821xx323)=0.226`
Now valve is opened till the pressure is maintained at 1 atm. Thus, at constant V and T, `P prop n`
`therefore P_(2) prop n`
`therefore 1 prop n_("left")`
`therefore (P_(2))/(1)=(n)/(n_("left"))`
`therefore n_("left")=(0.226)/(4.39)=0.052`
`therefore` Moles escaped out `=0.226-0.052=0.174`
`therefore` Fraction of moles escaped out `=(0.174)/(0.226)=0.77`
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