During a persons typical breathing cycle, the CO_{2} concentration in the expired air rises to a peak of 4.6% by volume.

Calculate the partial pressure of the CO_{2} in the expired air at its peak, assuming 1 atm pressure and a body temperature of 37^{o}C .

We are asked to find the **partial pressure of CO _{2}** in the expired air assuming 1 atm pressure and a body temperature of 37

The Partial Pressure of a gas is equal to the pressure multiplied by the mole fraction of gas.

$\overline{){{\mathbf{P}}}_{{\mathbf{CO}}_{\mathbf{2}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathbf{\chi}}}_{{\mathbf{CO}}_{\mathbf{2}}\mathbf{}}{\mathbf{\times}}{{\mathbf{P}}}_{{\mathbf{atm}}}}$

**We will calculate the partial pressure of CO _{2} using the following steps:**

* Step 1**: Calculate the volume of CO _{2} and air in the solution.*

* Step 4:** Calculate the partial pressure of CO _{2}.*

*Step 1**: Calculate the volume of CO _{2} and air in the solution.*

Assume that we have 100 L of solution. The solute will be CO_{2}.

$\overline{){\mathbf{\%}}{{\mathbf{CO}}}_{{\mathbf{2}}}{\mathbf{(}}{\mathbf{v}}{\mathbf{/}}{\mathbf{v}}{\mathbf{)}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}\frac{\mathbf{vol}\mathbf{}\mathbf{of}\mathbf{}\mathbf{solute}}{\mathbf{vol}\mathbf{}\mathbf{of}\mathbf{}\mathbf{solution}}{\mathbf{x}}{\mathbf{}}{\mathbf{100}}}\phantom{\rule{0ex}{0ex}}\mathbf{4}\mathbf{.}\mathbf{6}\mathbf{\%}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{vol}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{CO}}_{\mathbf{2}}}{\mathbf{100}\mathbf{}\mathbf{L}\mathbf{}\mathbf{solution}}\mathbf{\times}\mathbf{100}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}{\mathbf{V}}_{{\mathbf{CO}}_{\mathbf{2}}\mathbf{}}\mathbf{=}\mathbf{}\mathbf{}\frac{\mathbf{4}\mathbf{.}\mathbf{6}\mathbf{}\mathbf{\%}\mathbf{}{\mathbf{CO}}_{\mathbf{2}}}{\mathbf{100}}\mathbf{\times}\mathbf{100}\mathbf{}\mathbf{L}\mathbf{}\mathbf{solution}\mathbf{}$

**V _{CO2 }= 4.6 L CO_{2}**

${\mathbf{V}}_{\mathbf{air}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{100}\mathbf{}\mathbf{L}\mathbf{}\mathbf{-}\mathbf{}\mathbf{4}\mathbf{.}\mathbf{6}\mathbf{}\mathbf{L}\phantom{\rule{0ex}{0ex}}$

**V _{air }= 95.4 L air**

*Step 2**: Calculate for the number of moles by using the Ideal Gas equation.*

Since mass, temperature, and pressure are given, we will use the **ideal gas equation **to calculate for the moles.

$\overline{){\mathbf{PV}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{nRT}}}$

P = pressure, atm

V = volume, L

n = moles, mol

R = gas constant = 0.08206 (L·atm)/(mol·K)

T = temperature, K

Partial Pressure