Question

Rate of effusion of a gas depends upon:
A. Size of pinhole
B. Pressure
C. Temperature
D. Molecular mass

Answer 1

Hint: We know that gas particles have steady random motion and gas particles have kinetic energy thus tend to go through diffusion. As we know when a gas is made to pass through a fine hole made in the wall of the container under a difference of pressure, it is termed as effusion.

 Complete step by step answer:
As we know from graham’s law that at a constant temperature and for constant pressure gradients the rates of effusion of diffusion gases are inversely proportional to the square root of their densities. Rate of effusion depends on density, temperature of the gas and pressure gradient. Mathematically it can be indicated as,
\[{\text{r}} \propto {\text{P}}\] Here P is pressure and r is rate of diffusion.
                …… (1)
\[{\text{r}} \propto \dfrac{1}{{\sqrt {\text{M}} }}\] Here M is the number of moles.
                …… (2)
Now equation (1) and (2) together can be written is as follows:
\[{\text{r}} \propto \dfrac{{\text{P}}}{{\sqrt {\text{M}} }}\]
Or, \[\dfrac{{{{\text{r}}_{\text{1}}}}}{{{{\text{r}}_{\text{2}}}}}{\text{ = }}\dfrac{{{{\text{P}}_{\text{1}}}}}{{{{\text{P}}_{\text{2}}}}}\sqrt {\dfrac{{{{\text{M}}_{\text{2}}}}}{{{{\text{M}}_{\text{1}}}}}} \]
Thus all options are correct.

Additional Information:
We know that diffusion is a process which involves the migration of a component in solution down a gradient of its own concentration, i.e., from a part of higher to a part of lower concentration.
Gas molecules consist of a large number of minute particles. Gas molecules are so tiny that we can neglect their actual volume fraction of the total volume which is occupied by gas.

Note:
Graham’s law is very useful for us. Because this law is used to calculate molecular weight, density, etc. of gases. However it should be noted Graham’s law is true only for gases diffusing under low pressure gradients.