Answer: The rate of diffusion of methane is 100 cc.
Explanation:
Graham's law states that the rate of diffusion of a gas is inversely proportional to the square root of the molar mass of the gas. The equation for this follows:
[tex]\text{Rate}=\frac{1}{\sqrt{M}}[/tex] .....(1)
where M is the molar mass of the gas
We are given:
[tex]Rate_{X}=50cc[/tex]
[tex]M_{X}=4\times M_{CH_4}[/tex]
Since the molar mass of methane = 16 g/mol
Using equation 1:
[tex]\frac{Rate_{CH_4}}{Rate_{X}}=\sqrt{\frac{M_X}{M_{CH_4}}}[/tex]
Putting values in above equation, we get:
[tex]\frac{Rate_{CH_4}}{50cc}=\sqrt{\frac{(4\times 16)}{16}}\\\\Rate_{CH_4}=50\times \sqrt{4}\\\\Rate_{CH_4}=50times 2=100cc[/tex]
Hence, the rate of diffusion of methane is 100 cc.
