The pressure of a gas in a 100 mL container is 200 kPa and the average translation kinetic energy of each gas particle is 6 - 10-21- Find the number of gas particles in the container- How many moles are there in the container -

The total translational kinetic energy is given by E= 3 2 nRT= 3 2 PV Also, since energy of one particle is e , let the total number of particles b ...

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Standard XII

Physics

Temperature

The pressure ...

Question

The pressure of a gas in a 100 mL container is 200 kPa and the average translation kinetic energy of each gas particle is $6 \times 10^{- 21}$ . Find the number of gas particles in the container. How many moles are there in the container ?

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Solution

The total translational kinetic energy is given by

$E = \frac{3}{2} n R T = \frac{3}{2} P V$

Also, since energy of one particle is $e$ , let the total number of particles be N. Then

$E = N e$

Hence,

$N e = \frac{3}{2} P V$

$N = \frac{3}{2 e} P V$

$N = \frac{3 (2 X 10^{5}) (0.1 X 10^{- 3})}{2 (6 X 10^{- 21})} = 5 X 10^{21}$ particles.

Also, number of moles will be

$n = \frac{N}{N_{A}} = \frac{5 X 10^{21}}{6.023 X 10^{23}} = 8.3 X 10^{- 3}$ mol.

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The pressure of a gas in a 100 mL container is 200 kPa and the average translation kinetic energy of each gas particle is 6×10−21. Find the number of gas particles in the container. How many moles are there in the container ?

The total translational kinetic energy is given byE=32nRT=32PVAlso, since energy of one particle is e, let the total number of particles be N. ThenE=NeHence, Ne=32PVN=32ePVN=3(2X105)(0.1X10−3)2(6X10−21)=5X1021 particles.Also, number of moles will ben=NNA=5X10216.023X1023=8.3X10−3 mol.

The pressure of a gas in a 100 mL container is 200 kPa and the average translation kinetic energy of each gas particle is $6 \times 10^{- 21}$ . Find the number of gas particles in the container. How many moles are there in the container ?