Final answer:
The unknown noble gas is identified by utilizing Graham's law and the given effusion times. By calculating the ratio of the effusion rates and comparing the derived molar mass, it is found that krypton (Kr) is the most likely candidate to match the unknown gas based on its effusion time and molar mass.
Step-by-step explanation:
To identify the unknown noble gas based on the effusion times provided, we can use Graham's law of effusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. To find the molar mass of the unknown gas, we can compare it to neon (Ne), whose effusion time is known. The formula derived from Graham's law is ∑ (r1 / r2) ^2 = M2 / M1 where r1 and r2 are the rates of effusion and M1 and M2 are the molar masses of the gases.
With 76 seconds for neon and 155 seconds for the unknown gas, we first find the ratio of the rates of effusion (rNe / run known) which is the inverse of the ratio of times (Tun known / tNe). Therefore, we have (155 s / 76 s) which gives us approximately 2.04. Squaring this ratio gives us approximately 4.16, which is also the ratio of the molar masses (MUnknown / MNe).
Since the molar mass of neon is approximately 20.18 g/mol, we multiply this by 4.16 to get the molar mass of the unknown gas, which is roughly 83.95 g/mol. When we compare this value to the molar masses of the potential noble gases, argon (AR), krypton (Kr), xenon (Xe), and helium (He), we find that the molar mass of krypton (Kr, approximately 83.8 g/mol) is the closest to our calculated value. Therefore, the unknown noble gas is most likely krypton (Kr).