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  • Please help! A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas?

A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas?

  • Option 1)

    {P \mathord{\left/ {\vphantom {P {\left( {kT} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {kT} \right)}}

  • Option 2)

    {Pm \mathord{\left/ {\vphantom {P {\left( {kT} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {kT} \right)}}

  • Option 3)

    {P \mathord{\left/ {\vphantom {P {\left( {kT} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {kTV} \right)}}

  • Option 4)

    mkT

 

Answers (1)

 

Ideal gas equation -

PV = nRT
 

 

- wherein

T= Temprature

P= pressure of ideal gas

V= volume

n= numbers of mole

R = universal gas constant

 

 From equation of ideal gas

PM = \rhoRT

Or pm =  \rhoKT -(1)

m = mass of a molecule.

 \rho = density of gas.

K = Boltzmann's constant

=>  \rho = \rho \frac{pm}{kt}

 


Option 1)

{P \mathord{\left/ {\vphantom {P {\left( {kT} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {kT} \right)}}

this is the incorrect option

Option 2)

{Pm \mathord{\left/ {\vphantom {P {\left( {kT} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {kT} \right)}}

this is the correct option

Option 3)

{P \mathord{\left/ {\vphantom {P {\left( {kT} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {kTV} \right)}}

this is the incorrect option

Option 4)

mkT

this is the incorrect option

Posted by

Sabhrant Ambastha

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