Answer: The molar mass of A is one fourth that of B
Explanation:
To calculate the rate of diffusion of gas, we use Graham's Law.
This law states that the rate of diffusion of gas is inversely proportional to the square root of the molar mass of the gas. The equation given by this law follows the equation:
[tex]\text{Rate of diffusion}\propto \frac{1}{\sqrt{\text{Molar mass of the gas}}}[/tex]
So,
[tex]\frac{\text{Rate}_A}{\text{Rate}_{B}}=\sqrt{\frac{M_{B}}{M_{A}}}[/tex]
We are given:
Rate of diffusion of A = [tex]2\times[/tex] Rate of diffusion of B
Putting values in above equation, we get:
[tex]2=\sqrt{\frac{M_{B}}{M_{A}}}[/tex]
[tex]4={\frac{M_{B}}{M_{A}}}[/tex]
[tex]M_{A}={\frac{M_{B}}{4}[/tex]
Thus the molar mass of A is one fourth that of B
