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Three ideal gas samples in separate equa...

Three ideal gas samples in separate equal volume containers are taken and following data is given :
`{:(" ","Pressure","Temperature","Mean free paths","Mol.wt."),("Gas A",1atm,1600K,0.16nm,20),("Gas B",2atm,200K,0.16nm,40),("Gas C",4atm,400K,0.04nm,80):}`
Calculate number of collision by one molecule per sec `(Z_(1))`.
(a)`4:1:4`
(b)`1:4:4`
(c)`4:3:2`
(d)`1:2:4`

A

`4:1:4`

B

`1:4:4`

C

`4:3:2`

D

`1:2:4`

Text Solution

Verified by Experts

The correct Answer is:
a
(a) Let `sigma_(A),sigma_(B)` and `sigma_(C)` be collision diameters of A,B and C
`lambda=(kT)/(sqrt(2)pilsigma^(2)P),i.e.,sigmapropsqrt((T)/(lambdaP))`
`:. " "sigma_(A):sigma_(B):sigma_(C)`
`=sqrt((1600)/(0.16xx1)):sqrt((200)/(0.16xx2)):sqrt((400)/(0.04xx4))`
`=4:1:2`
`Z_(1)prop((sigma^(2))P)/(sqrt(MT))`
`impliesA:B:C=(0.6xx1)/(sqrt(20xx1600)):(1xx2)/(sqrt(40xx200)):(4xx4)/(sqrt(80xx400))`
`=4:1:4`
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