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When a person breaths, his lungs can hol...

When a person breaths, his lungs can hold up to 5.5 Litre of air at body temperature `37^(@)C` and atmospheric pressure `("1 atm = 101 kPa")`. This Air contains `21%` oxygen. Calculate the number of oxygen molecules in the lungs.

Text Solution

Verified by Experts

We can treat the air inside the lungs as an ideal gas. To find the number of molecules, we can use the ideal gas law.
PV = NkT
Here volume is given in the Litre. 1 Litre is volume occupied by a cube of side 10 cm
1 Litre = 10 cm `xx` 10 cm `xx` 10 cm = `10^(-3)m^(3)`
N = `(PV)/(kT) = (1.01 xx 10^(5) xx 5.5 xx 10^(-3))/(1.38 xx 10^(-23) xx 310)`
= 1.29 `xx 10^(23)` Molecules
Only `21%` of N are oxygen. The total number of oxygen molecules
`= 1.29 xx 10^(23) xx (21)/(100)`
Number of oxygen molecules = `2.7 xx 10^(22)` molecules
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