The density of air under standard laboratory conditions is$\mathbf{1}\mathbf{.}\mathbf{29}\mathbf{kg}\mathbf{/}{\mathbf{m}}^{\mathbf{3}}$ , and about 20% of that air consists of oxygen. Typically, people breathe about 1/2 L of air per breath. (a) How many grams of oxygen does a person breathe in a day? (b) If this air is stored uncompressed in a cubical tank, how long is each side of the tank?

The given data can be listed below,

• The density of the air in standard lab conditions is,.${\mathrm{p}}_{\mathrm{A}}=1.29\mathrm{kg}/{\mathrm{m}}^3.$
• The amount of oxygen in the air is, $20\%$
• Oxygen intake of people per breath is,$\frac{1}{2}\mathrm{L}.$

Physically, the dimensions of any given object of arbitrary shape are provided clearly by the mass and density of the object. Density and mass have a directly proportional relation.

The density is more when the mass is packed more densely.

By unit conversion, the breathing intake of a person in one day is given by,

$\left(12\text{breathe/min}\right)\left(\frac{60\text{min}}{1\text{hr}}\right)\left(\frac{24\text{hr}}{1\text{day}}\right)=17,280\text{breathe/day}$

The volume of air breathed in one day is given by,

The mass of air breathed in one day is the density of air times the volume of air breathed.

So the mass of air is given by,

$m_A={\rho }_A\times V_A$

Here, ${\rho }_A$is the density of the air and $V_A$is the volume of the air.

Substitute values in the above,

$$\begin{gathered} m_A=1.29{\text{kg/m}}^3\times 8.64{\text{m}}^3 \\ =11.1\text{kg} \end{gathered}$$

The mass of oxygen in the air can be expressed as,

$m_o=20\%\left(m_A\right)$

Substitute value in the above equation.

Thus, the mass of the oxygenin grams a person breathes in a day is $2200\text{g}.$

The volume of a cube is given by,

Here, l is the length of the faces of the cubical tank.

Substitute values in the above,

Thus, the length of each side of the tank is $2.1\text{m}.$