If you have ever hiked or climbed to high altitudes in the mountains, you surely

Question

If you have ever hiked or climbed to high altitudes in the mountains, you surely have noticed how short of breath you get. This occurs because the air is thinner, so each breath contains fewer O2 molecules than at sea level. At the top of Mt. Everest, the pressure is only 13atm. Air contains 21.0 % O2 and 78.0 % N2, and an average human breath is 0.450 L of air. Part A. At the top of Mt. Everest, how many O2 molecules does each breath contain when the temperature is -16.0 F ? Part B. What percent is this of the number of O2 molecules you would get from a breath at sea level at -16.0 F ?

Explanation / Answer

A) we know that

PV = nRT

given

P = 13 atm

now

air contains 21 % 02

so

volume of oxygen per breath = 0.45 x 0.21 = 0.0945

T = -16 F = 246.483 K

now

PV = nRT

13 x 0.0945 = n x 0.0821 x 246.483

n = 0.0607

now

number of molecules = moles x avagadro number

so

number of molecules = 0.0607 x 6.023 x 10^23

number of molecules = 3.656 x 10^22

so

3.656 x 10^22   02 molecules are in each breath

B)

PV = nRT

now

P = 1 atm

so

1 x 0.0945 = n x 0.0821 x 246.483

n = 4.67 x 10-3

number of molecules = 4.67 x 10-3 x 6.023 x 10^23

number of molecules = 2.81 x 10^21

now

% = 2.81 x 10^21 x 100 / 3.656 x 10^22

% = 7.7

so

the percent is 7.7

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