During your first day on the job as an anesthesiologist at V

During your first day on the job as an anesthesiologist at Vail summit medical center (altitude=3,350 m, pressure=70,000 Pa), you think back to CHEM 452 and realize that the usual 75% N2O / 25% O2 mixture in an anesthetic is not going to work at the high altitude since that recipe is formulated for sea level. Find the proportions of the two gases to use at Vail such that the partial pressure of oxygen at Vail is equal to the partial pressure of O2 that is attained at sea level with a 75/25 mixture. Note that the patient always breathes gas at approximately ambient pressure.

Solution

At sea level ambient pressure is 760mmHg = 760*133.322Pa = 101324.72Pa

Since , at sea level 25% is oxygen and 75% N₂O, therefore partial pressure of O₂ and N₂O are

P_O2 = 0.25*101324.72 =25331.18 Pa

and

P_N2O = 0.75*101324.72 =75992.4Pa

By the condition , the partial pressure of O₂ at vail (altitude=3,350 m, pressure=70,000 Pa) is equal to partial pressure of O₂ that is attained at sea level.

Let at vail x% N₂O is required in the mixture in an anesthetic and (100-x)% O₂ is required so that the patient always breathes gas at approximately ambient pressure.

At altitude=3,350 m, the pressure P_A=70,000 Pa

Therefore we can constitute the equation as

25331.18 +x% P_A = P_A

Or 25331.18 +x% 70,000 = 70,000

Or   70,000(1-0.01*x) =25331.18

Or 1-0.01*x =.362

Or x= 63.81%

and 1-x=36.2% (approx)

So the proportions of O₂ and N₂O gas to use at Vail in the mixture in an anesthetic is 36.2% to 63.81%

or else the proportions of O₂ and N₂O is 36.2 : 63.8