Correct Answer - Option 1 :
\(\dfrac{1}{\sqrt{m}}\)
Concept:
Graham’s law of diffusion states that at a constant temperature and pressure, the rate of diffusion of a gas is inversely proportional to the square root of its density.
\(\frac{r_{A}}{r_{B}}=\sqrt{\frac{d_{A}}{d_{B}}}\) or \(\frac{r_{A}}{r_{B}}=\sqrt{\frac{M_{B}}{M_{A}}}\)
Where rA and rB are rates of diffusions of A and B, dA and dB are densities and MA and MB are molecular masses of A and B respectively.
Explanation:
- The rate at which a gas diffuses is inversely proportional to the density of the gas.
- The movement of gas molecules from one place to the other along the concentration gradient is called diffusion.
\(\frac{r_{A}}{r_{B}}=\sqrt{\frac{d_{A}}{d_{B}}}\)
Since the vapor density is M/2 (molar mass).
\(\frac{r_{A}}{r_{B}}=\sqrt{\frac{M_{B}}{M_{A}}}\)
So, The coefficient of diffusion of any gas is proportional to \(\dfrac{1}{\sqrt{m}}\).
