Chapter U3.63, Problem 4E

Interpretation Introduction

Interpretation :

The effect of change in the number of gas particles on the gas pressure in the container must be explained with the help of kinetic theory of gases.

Concept Introduction :

Kinetic theory of gas considers that gas molecules are always moving in zigzag motion and they are colliding with themselves as well as with the container.

Answer to Problem 4E

If the number of gas particles in a container is increased then pressure also increases.

Explanation of Solution

According to kinetic theory of gas

$\text{P=}\frac{\text{1}}{\text{3}}{\text{ρc}}^{\text{2}}$ Here, $\text{P, ρ, c}$ are pressure, density and root means square velocity of the gas.

  $\begin{array}{l}\text{Or,PV=}\frac{\text{1}}{\text{3}}{\text{ρVc}}^{\text{2}}\text{=}\frac{\text{1}}{\text{3}}{\text{mc}}^{\text{2}}\text{=}\frac{\text{2}}{\text{3}}\text{×}\frac{\text{1}}{\text{2}}{\text{mc}}^{\text{2}}\\ \text{Or,PV=}\frac{\text{2}}{\text{3}}\text{RT}\\ \text{Or,PV=nRT}\end{array}$

  $\text{ρV=m}$ where V and m are volume and mass, R is universal gas constant.

Kinetic energy $\frac{\text{1}}{\text{2}}{\text{mc}}^{\text{2}}$ is proportional to temperature T.

Thus, $\text{P=}\frac{\text{nRT}}{\text{V}}$

So at a particular temperature and volume, if n (number of moles of gas which is equal to ${\text{n×N}}_{\text{A}}$ , N_A is Avogadro’s number) is increased, then pressure will increase.

Conclusion

Number of gas molecules present in container is proportional to the gas pressure in the container.