Question

The number of oxygen molecules in a cylinder of volume $1m^3$ at a temperature of ${27}^{o}C$ and pressure $13.8Pa$ is:(Boltzmaans constant $k=1.38\times {10}^{-23}J{K}^{-}1$:

• A. $6.23\times {10}^{26}$
• B. $0.33\times {10}^{28}$
• C. $3.3\times {10}^{21}$
• D. $Noneofthese$

Answer 1

The correct option is C $3.3\times {10}^{21}$

Given,

$\text{Pressure},P=13.8Pa$

$Temperature,T=(27+273.15)K$

$VolumeV=1m^3$

$Boltzmancons\tan t{k}_B=1.38\times {10}^{-23}J{K}^{-1}$

$R_{universal}=N_A{K}_B=(6.023\times {10}^{23})\times (1.38\times {10}^{-23})=8.314J/mol$

Apply Ideal gas equation

$PV=nRT$

$n=\frac{PV}{RT}=\frac{13.8\times 1}{8.314(27+273.15)}=5.53\times {10}^{-3}mol$

$x=n\times N_A=(5.53\times {10}^{-3})\times (6.023\times {10}^{+23})=3.33\times {10}^{21}molecules$

Number of molecules is $3.33\times {10}^{21}$