Question

volume 2 pressure and an P are mass a is mi If the temperature of idea V. P and I respectively. gas the of molecule is Boltzmann's constant R constant, then the number of molecules în this m, k the is the universal gas is.​

Answer 1

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Class 11

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>>States of Matter

>>Ideal Gas Equation

>>If m is the mass of a molecule, k is

Question



If m is the mass of a molecule, k is the Boltzmann constant,P is the pressure and T is the absolute temperature, then the density of the gas is given by:

A

PmkT

B

kmPT

C

kTPm

D

TmPk

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Solution



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Correct option is C)

The ideal gas law is given by PV=nRT, where n is the number of moles of a gas.

n = mass of the gas/molecular weight of the gas.

Density (d) = mass of the gas/volume of the gas.

So, the ideal gas law can also be written as PM=dRT, where, M is the molecular mass of the gas. 

d=RTPM 

⟹d=(NR)TPm, where k=NR, m is the mass of one molecule and N is the Avogadro's number.

Answer 2

option c is correct PV=nRT

n=m/M

PV=(m/M)RT

d=m/v

PM=dRT

d=kTPm

d=(NR)TPm=NR=k

so

d=kTPm