The label on the 1.0 L tank in the ER has been smudged and you can make out that

Question

The label on the 1.0 L tank in the ER has been smudged and you can make out that the mixture is 23% O2 70% N2 and 7% Drug X. Relative effussion rates of the mixture are O2(1.18) N2(1.26) Drug X(1.00)

Drug MW (g/mol) Dosing (drug mg/patient kg*hr)

Desflurane 168.32 7.22

Sevoflurane 200.05 10.89

Xenon 131.29 11.89

Nitrous Oxide 44.45 13.32

What is the identity of the drug X

Quickly reading the pressure gauge you see that the tank contains 13.5 atm of pressure. Assuming room temp is 25 C how many moles of drug do you have at your disposal?

Explanation / Answer

as we know effusion rate is inverssly proportional to molecular wt.

so dX/dN2 = sqrt(Molecular wt of N2/ Molecular wt of X)

1/1.26 = sqrt(28/M)

M = 44.45 = molecular wt of X

so X is nitrous oxide

P of X = 13.5*7/100 = 0.945 atm

PV = nRT

0.945*1 = n*0.0821*298

n = 0.038 = 0.04 mole

so moles of drug X = 0.04 mole

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