Answer

Verified

405.3k+ views

**Hint:**To find the number of gas particles in the container, we must know the number of moles of gas present in it. We have been given the pressure and the volume for the gas and we know the value of the universal gas constant, so we can use the ideal gas equation to find the number of moles and then proceed to find the no. of gas particles.

**Formula Used:**

\[KE=\dfrac{3}{2}KT\]

\[PV=nRT\]

\[N=n\times {{N}_{A}}\]

**Complete step by step answer:**

To use the ideal gas equation, we must be aware of the temperature of the gas system. To this end, we have been given the average translational kinetic energy of each gas particle.

We know that average kinetic energy for gas particles is given as \[KE=\dfrac{3}{2}KT\] where \[K\] is the Boltzmann’s constant, and \[T\] is the temperature of the gas.

Hence we can say that \[T=\dfrac{2\times KE}{3\times K}\]

From the ideal gas equation, we can say that \[PV=nRT\]

Substituting the expression of temperature in the above equation, we get \[PV=nR\times \dfrac{2\times KE}{3\times K}\]

By transposing the terms to the left-hand side, we get that \[n=\dfrac{3}{2}\times \dfrac{P\times V\times K}{R\times KE}\]

Substituting the values of Boltzmann constant, the pressure, the volume, the average kinetic energy and the gas constant in the above obtained equation, we get

\[\begin{align}

& n=\dfrac{3\times (200\times {{10}^{3}})\times (100\times {{10}^{-6}})\times (1.38\times {{10}^{-23}})}{2\times 8.314\times 6\times {{10}^{-21}}}\left( \because 1mL={{10}^{-6}}{{m}^{3}} \right) \\

& \Rightarrow n=\dfrac{6\times 1.38\times {{10}^{-22}}}{2\times 8.314\times 6\times {{10}^{-21}}} \\

& \Rightarrow n=8.3\times {{10}^{-3}}mol \\

\end{align}\]

We have thus obtained the number of moles of the gas. Now using Avogadro’s number we can easily find the number of particles of the gas

Number of particles of the gas \[(N)=n\times {{N}_{A}}\] where \[{{N}_{A}}\] is Avogadro's number.

\[\begin{align}

& \Rightarrow N=8.3\times {{10}^{-3}}\times 6.023\times {{10}^{23}} \\

& \Rightarrow N=5\times {{10}^{21}} \\

\end{align}\]

**Note:**We can use the relation between the total translational kinetic energy of the gas and the pressure and volume of the gas to find the number of particles of the gas. We would have to use the energy of one particle given to us and multiply it by the total number of particles to find the total energy.

\[E=\dfrac{3}{2}nRT=\dfrac{3}{2}PV\] and \[E=Ne\] are the two alternate relations that we can use to obtain our answer.

Recently Updated Pages

Cryolite and fluorspar are mixed with Al2O3 during class 11 chemistry CBSE

Select the smallest atom A F B Cl C Br D I class 11 chemistry CBSE

The best reagent to convert pent 3 en 2 ol and pent class 11 chemistry CBSE

Reverse process of sublimation is aFusion bCondensation class 11 chemistry CBSE

The best and latest technique for isolation purification class 11 chemistry CBSE

Hydrochloric acid is a Strong acid b Weak acid c Strong class 11 chemistry CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Name 10 Living and Non living things class 9 biology CBSE

The Buddhist universities of Nalanda and Vikramshila class 7 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE