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

Options

A. p/(Kt)
B. pm/(kT)
C. p/(kTV)
D. mkT

Answer

B

Explanation

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)`