Question

Calculate the number of molecules in a deep breath of air whose volume is 2.15 L at body temperature, 37 ∘C, and a pressure of 740 torr .

Answer 1

`PV=nRT`

`n= (PV)/(RT)`

`n= (740 torr*2.15 L)/(62.4 (torr*L)/(mol*K) *(37celsius+273))`
n = 0.0822 mol

`0.0822 mol*6.022*10 ^(23) = 4.95*10 ^(22) molecules`

Answer 2

PV = nRT
R = 0.0821 L * atm / mol * K
(ideal gas constant)

First, convert 735 torr to atm. Divide by 760.
(1 atm = 760 torr)

735 torr * 1 atm / 760 torr = 0.967 atm
Then, convert 37 C to Kelvin. Just add 273.
37 C = 310K

n = PV / RT
= (0.967)(2.07) / (0.0821)(310)
= 0.0786 mol

0.0786 mol * 6.02 * 10^23 molecules / 1 mol = 4.73 * 10^22 molecules