A fiven sample of an ideal gas occupise a volume V at a pressure p and sbsoulte temperature T.The mass of each molecule of the gas is m. Which of the following fives the dinsity of the gas ?

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)`