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One mole of nitrogen gas at 0.8 atm takes 38 seconds to diffuse through a pinhole. One mole of a xenon-fluorine compound at 1.6 atm takes 57 seconds to diffuse through the same hole. Calculate the molar mass (g/mol) of the xenon-fluorine compound.

1. 128
2. 196
3. 254
4. 320

Correct answer: 254

Solution

Graham's law under different pressures: the effusion rate is proportional to P/sqrt(M). Since both release 1 mole, rate = 1/t. So (1/t1)/(1/t2) = (P1/P2) * sqrt(M2/M1). Substituting: (57/38) = (0.8/1.6) * sqrt(M2/28). Solving gives M2 = 254 g/mol, which matches XeF4 (Xe=131, F=19*4=76, total=207 — actually XeF4 is 207). Wait — let us recheck: 3/2 = 0.5 * sqrt(M2/28) => sqrt(M2/28) = 3 => M2 = 252 ~ 254. The closest known XeF compound with M~254 is XeF4 (Xe=131.3, 4F=76) = 207.3, or XeF2=169.3. Actually solving: sqrt(M2/28) = (57/38)*(1.6/0.8) = 1.5*2 = 3, so M2 = 9*28 = 252 ~ 254 (rounding). Answer 254 is correct.

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