# 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).

Aug 3, 2016

$\textsf{2.5 \textcolor{w h i t e}{x} g}$

#### Explanation:

The ideal gas equation gives us:

$\textsf{P V = n R T}$

$\textsf{P}$ is the pressure

$\textsf{V}$ is the volume

$\textsf{R}$ is the gas constant $\textsf{8.31 \textcolor{w h i t e}{x} \text{J/K/mol}}$

$\textsf{T}$ is the absolute temperature

$\textsf{n}$ is the number of moles

Rearranging:

$\textsf{n = \frac{P V}{R T}}$

Converting $\textsf{L}$ to $\textsf{{m}^{3}}$ and deg C to K gives:

$\textsf{n = \frac{102 \times \cancel{{10}^{3}} \times 2.20 \times \cancel{{10}^{- 3}}}{8.31 \times 310} = 0.087 \textcolor{w h i t e}{x} m o l}$

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

$\textsf{m = 0.0871 \times 29 = 2.5 \textcolor{w h i t e}{l} g}$ 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).