Chapter 12.1, Problem 9SSC

Interpretation Introduction

Interpretation:

The effect of mass of gas particles on the rate of effusion and diffusion needs to be explained.

Concept introduction:

Gas is one of the physical states of matter in which the particles are located away from each other.

The particles of gas have high kinetic energy and exhibit different characteristics compare to liquid and solids.

Answer to Problem 9SSC

$\frac{\text{Rate of effusion/diffusion of gas 1}}{\text{Rate of effusion/diffusion of gas 2}}\text{=}\sqrt{\frac{\text{M2}}{\text{M1}}}$

Explanation of Solution

Due to high kinetic energy, gases can diffuse and effuse. The diffusion of gases is the dispersion of particles throughout a container whereas effusion occurs through an opening. The relation of effusion and diffusion of gases can explain with the help of Graham’s law.

According to the Graham’s law of effusion/diffusion, rate of effusion/diffusionof any gas is always inversely proportional to the square root of the mass of gaseous particles. The mathematical expression for this law is:

$\frac{\text{Rate of effusion/diffusion of gas 1}}{\text{Rate of effusion/diffusion of gas 2}}\text{=}\sqrt{\frac{\text{M2}}{\text{M1}}}$

In terms of time for gases; we can write as:

$\frac{\text{Effusion time of gas 1}}{\text{Effusion time of gas 2}}\text{=}\sqrt{\frac{\text{M1}}{\text{M2}}}$

Conclusion

Thus,

$\frac{\text{Rate of effusion/diffusion of gas 1}}{\text{Rate of effusion/diffusion of gas 2}}\text{=}\sqrt{\frac{\text{M2}}{\text{M1}}}$