Answer: Argon
Explanation:
To find the <em>amount of an unknown noble gas that requires 157 seconds fo effuse from a container from which a same amount of sample of neon effuses in 77 seconds</em>, you must use Graham's Law of effusion.
Graham's law of effusion states the rate of effusion of a gas is inversely proportional to the square root of the masses of its particles. Mathematically, that is:

Since, the other conditions (amount of gas and container) are the same for both gases, the rates and the times are inversely proportional; this is:

- By using the previous equations, you can <u>relate the times and the molar masses of the gases</u>:

- <u>Clear the unknown molar mass</u>:

- <u>Substitute the data</u>:
MolarMass₂ = (157 s / 77 s) × MolarMass₁
- <u>From a periodic table</u>, obtain the molar mass of neon gas:
Molar Mass₁ = 20.180 g/mol
∴ MolarMass₂ = (157 s / 77 s) × 20.180 g/mol = 41 g/mol
- Again from the periodic table, <u>find the noble gas with the molar mass closest to 41 g/mol</u>.
It is argon. The molar mass of argon is 30.948 g/mol. So, argon (Ar) is the answer.