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A sample of an ideal gas occupies a volu...

A sample of an ideal gas occupies a volume V at pressure P and absolute temperature T. The masss of each molecule is m, then the density of the gas is

A

p/(Kt)

B

pm/(kT)

C

p/(kTV)

D

mkT

Text Solution

Verified by Experts

The correct Answer is:
B
Pressure, `p=1/3,(nm)/(V)v_(rms)^(2)`
`therefore` nm = mass of the gas, V= volume of the gas
`therefore (mn)/(V)=` density of the gas. Thus.
`p=1/3pv_(rms)^(2)=1/3p(3RT)/(M_(o))=(pRT)/(M_(o))" "(thereforev_(rms)=sqrt((3RT)/(M_(o))))`
`p=(pM_(o))/(RT)=(p mN_(A))/(kN_(A)T)" "(therefore R =N_(A)and M_(o)=mN_(A))`
`p=(p m)/(kT)`
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