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  • 50 mL of each gas A and gas B takes 150 and 200 seconds respectively for effusing through a pinhole under similar conditions. If the molecular mass of gas B is 36, the molecular mass of gas A will

50 mL of each gas A and gas B takes 150 and 200 seconds respectively for effusing through a pinhole under similar conditions. If the molecular mass of gas B is 36, the molecular mass of gas A will be :

Option: 1

96


Option: 2

128


Option: 3

20.25


Option: 4

64


Answers (1)

best_answer

 

Graham’s law of diffusion -The rate of diffusion of a gas is inversely proportional to the square root of the molar mass of gas at the same temperature and pressure. 

Rate = \frac{Amount\ of\ gas}{time}

For both gases amount of gas(volume) effused is the same. 

\dpi{100} r_{1}/r_{2}=\sqrt{M_{2}/M_{1}}  where r is the rate of diffusion of gas, and M is molar mass.

As per graham's law of diffusion 

\frac{r_{A}}{r_{B}}=\sqrt{}\frac{M_{B}}{M_{A}}\\ \\ r_{A}=\frac{50}{150}=1/3\\ \\r_{B}=\frac{50}{200}=1/4\\ \\ M_{B}=36

\frac{\frac{1}{3}}{\frac{1}{4}}=\sqrt{\frac{36}{M_{A}}}\\ \frac{4}{3}=\sqrt{\frac{36}{M_{A}}}\\ \\ \frac{4}{9}=\frac{9}{M_{A}}\\ \\ M_{A}=\frac{81}{4}=20.25\\

Molar Mass of the gas is 20.25 u.

Hence, the Correct answer is option 3.

Posted by

Rishabh

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