Answer :
The molar mass of the unknown gas is 26.63 g/mol.
To find the molar mass of the unknown gas, we can use Graham's Law of Diffusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
rate1/rate2 = sqrt(MM2/MM1)
where rate1 and rate2 are the rates of effusion of the known gas (argon) and unknown gas, respectively, and MM1 and MM2 are the molar masses of the known and unknown gases, respectively.
rate1 = 25 mL/77.3 seconds
rate2 = 25 mL/97.6 seconds.
Using these values,
(rate1/rate2)^2 = MM2/MM1
Plugging in the values,
(25 mL/77.3 s) / (25 mL/97.6 s) = sqrt(MM2/39.95 g/mol)
sqrt(MM2/39.95 g/mol) = 0.8169
MM2/39.95 g/mol = 0.667
Solving for MM2, we get:
MM2 = 26.63 g/mol
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