A child's lungs can hold 2.20 L. How many grams of air do her lungs hold at a pressure of 102 kPa and a body temperature of 37°C?

Use a molar mass of 29 g for air, which is about 20% #O# (32 g/mol) and 80% #N_2# (28 g/mol).

1 Answer
Aug 3, 2016

Answer:

#sf(2.5color(white)(x)g)#

Explanation:

The ideal gas equation gives us:

#sf(PV=nRT)#

#sf(P)# is the pressure

#sf(V)# is the volume

#sf(R)# is the gas constant #sf(8.31color(white)(x)"J/K/mol")#

#sf(T)# is the absolute temperature

#sf(n)# is the number of moles

Rearranging:

#sf(n=(PV)/(RT))#

Converting #sf(L)# to #sf(m^3)# and deg C to K gives:

#sf(n=(102xxcancel(10^3)xx2.20xxcancel(10^(-3)))/(8.31xx310)=0.087color(white)(x)mol)#

Since we are told that 1 mole weighs 29g then the mass of air is given by:

#sf(m=0.0871xx29=2.5color(white)(l)g)# to 2 sig fig.

Sub note:

The Ideal Gas Equation applies to a closed system and the lungs are not a closed system. Lets assume that at 2.20 L the child hold its breath (though not for too long).