Question

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).

Answer 1

`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).